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+Project Gutenberg's Discourse on Floating Bodies, by Galileo Galilei
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Discourse on Floating Bodies
+
+Author: Galileo Galilei
+
+Translator: Thomas Salusbury
+
+Release Date: October 12, 2011 [EBook #37729]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK DISCOURSE ON FLOATING BODIES ***
+
+
+
+
+Produced by Tim Madden and the Online Distributed
+Proofreading Team at https://www.pgdp.net (This file was
+produced from images generously made available by The
+Internet Archive)
+
+
+
+
+
+
+  [Transcriber's Notes
+
+  All apparent printer's errors retained. Variation in punctuation are
+  as in the original, but missing full stops at end of paragraphs have
+  been supplied. There are inconsistencies in the use of italics,
+  spacing of words and use of full stop after 'AXIOME', abbreviations
+  etc. All are retained to match text. There is a great variation in
+  spelling including multiple spellings of the same word, all spelling
+  has been retained to match text. There are several instances of
+  obviously missing letters or inverted n & u. These have been changed
+  or obvious letters replaced, with the changes surrounded by {}.
+
+  All instances are detailed at the end of the text. It should also be
+  noted that in the original text there is a missing line at the end of
+  page 24 in original text.
+
+  There are a number of instances in the original text where 'that' is
+  immediately followed by a second 'that' in the sentence. These could
+  be potential printer's errors or, since several of them make sense,
+  part of the author's style. They have been left in the text as they
+  appear in the original text.
+
+  The original text has many sidenotes, some are true sidenotes,
+  introductions to paragraphs etc, some acting as footnotes with some
+  marked in original text with *. These have been dealt with in three
+  ways with the footnotes placed after their relevant paragraph and
+  sidenotes place before their relevant paragraph.
+
+  1) Footnotes marked with capital letter. These were sidenotes in
+  original text marked with * in the original text and thus acting
+  like footnotes.
+
+  2) Footnotes marked with number. These were sidenotes in original
+  text that were unmarked but acting like normal footnotes. The anchor
+  in the text was placed at the most suitable relevant place in
+  comparison with the placement of the sidenote text in the margin,
+  but still should be considered only an approximate placement.
+
+  3) Sidenotes placed at start of the relevant paragraph. Some
+  sidenotes were considered not to be relevant as footnotes,
+  introductions to paragraphs etc, and were left as sidenotes before
+  their relevant paragraph.]
+
+       *       *       *       *       *
+
+
+
+
+                          A
+                      DISCOURSE
+                     _PRESENTED_
+                 TO THE MOST SERENE
+                   Don Cosimo II.
+                     GREAT DUKE
+                        _OF_
+                      TUSCANY,
+
+                     CONCERNING
+
+           The _NATATION_ of BODIES Vpon,
+                And _SUBMERSION_ In,
+                        THE
+                       WATER.
+
+        By GALILEUS GALILEI: Philosopher and
+   Mathematician unto His most Serene Highnesse.
+
+  Englished from the Second Edition of the ITALIAN,
+  compared with the Manuscript Copies, and reduced
+                 into PROPOSITIONS:
+
+             By _THOMAS SALUSBURY_, Esq;
+
+                      _LONDON_:
+
+            Printed by WILLIAM LEYBOURN:
+
+                    _M DC LXIII._
+
+       *       *       *       *       *
+
+                  [Decoration]
+
+
+
+
+                  A DISCOVRSE
+
+  Presented to the Most Serene DON COSIMO II.
+
+            GREAT DUKE of _TUSCANY_:
+
+                   CONCERNING
+
+  _The Natation of BODIES Upon, or Submersion_
+               _In, the WATER._
+
+
+
+
+Considering (Most Serene Prince) that the publishing this present
+Treatise, of so different an Argument from that which many expect, and
+which according to the intentions I proposed in my [A] Astronomicall
+_Adviso_, I should before this time have put forth, might peradventure
+make some thinke, either that I had wholly relinquished my farther
+imployment about the new Celestiall Observations, or that, at least, I
+handled them very remissely; I have judged fit to render an account,
+aswell of my deferring that, as of my writing, and publishing this
+treatise.
+
+    [A] His Nuncio Siderio.
+
+As to the first, the last discoveries of _Saturn_ to be
+tricorporeall, and of the mutations of Figure in _Venus_, like to
+those that are seen in the Moon, together with the Consequents
+depending thereupon, have not so much occasioned the demur, as the
+investigation of the times of the Conversions of each of the Four
+Medicean Planets about _Jupiter_, which I lighted upon in _April_ the
+year past, 1611, at my being in _Rome_; where, in the end, I
+assertained my selfe, that the first and neerest to _Jupiter_, moved
+about 8 _gr._ & 29 _m._ of its Sphere in an houre, makeing its whole
+revolution in one naturall day, and 18 hours, and almost an halfe. The
+second moves in its Orbe 14 _gr._ 13 _min._ or very neer, in an hour,
+and its compleat conversion is consummate in 3 dayes, 13 hours, and
+one third, or thereabouts. The third passeth in an hour, 2 _gr._ 6
+_min._ little more or less of its Circle, and measures it all in 7
+dayes, 4 hours, or very neer. The fourth, and more remote than the
+rest, goes in one houre, 0 _gr_ 54 _min._ and almost an halfe of its
+Sphere, and finisheth it all in 16 dayes, and very neer 18 hours. But
+because the excessive velocity of their returns or restitutions,
+requires a most scrupulous precisenesse to calculate their places, in
+times past and future, especially if the time be for many Moneths or
+Years; I am therefore forced, with other Observations, and more exact
+than the former, and in times more remote from one another, to correct
+the Tables of such Motions, and limit them even to the shortest
+moment: for such exactnesse my first Observations suffice not; not
+only in regard of the short intervals of Time, but because I had not
+as then found out a way to measure the distances between the said
+Planets by any Instrument: I Observed such Intervals with simple
+relation to the Diameter of the Body of _Jupiter_; taken, as we have
+said, by the eye, the which, though they admit not errors of above a
+Minute, yet they suffice not for the determination of the exact
+greatness of the Spheres of those Stars. But now that I have hit upon
+a way of taking such measures without failing, scarce in a very few
+Seconds, I will continue the observation to the very occultation of
+_JUPITER_, which shall serve to bring us to the perfect knowledge of
+the Motions, and Magnitudes of the Orbes of the said Planets, together
+also with some other consequences thence arising. I adde to these
+things the observation of some obscure Spots[1], which are discovered in
+the Solar Body, which changing, position in that, propounds to our
+consideration a great argument either that the Sun revolves in it
+selfe, or that perhaps other Starrs, in like manner as _Venus_ and
+_Mercury_, revolve about it, invisible in other times, by reason of
+their small digressions, lesse than that of _Mercury_, and only
+visible when they interpose between the Sun and our eye, or else hint
+the truth of both this and that; the certainty of which things ought
+not to be contemned, nor omitted.
+
+     [1] The Authors Observations of the Solar Spots
+
+  _Continuall observation hath at last assured me that these Spots
+  are matters contiguous to the Body of the Sun, there continually
+  produced in great number, and afterwards dissolved, some in a
+  shorter, some in a longer time, and to be by the Conversion or
+  Revolution of the Sun in it selfe, which in a Lunar Moneth, or
+  thereabouts, finisheth its Period, caried about in a Circle, an
+  accident great of it selfe, and greater for its Consequences._
+
+As to the other particular in the next place [B] Many causes have
+moved me to write the present Tract, the subject whereof, is the
+Dispute which I held some dayes since, with some learned men of this
+City, about which, as your Highnesse knows, have followed many
+Discourses: The principall of which Causes hath been the Intimation of
+your Highnesse, having commended to me Writing, as a singular means to
+make true known from false, reall from apparent Reasons, farr better
+than by Disputing vocally, where the one or the other, or very often
+both the Disputants, through too greate heate, or exalting of the
+voyce, either are not understood, or else being transported by
+ostentation of not yeilding to one another, farr from the first
+Proposition, with the novelty, of the various Proposals, confound both
+themselves and their Auditors.
+
+    [B] The occasion inducing the Author to write this Treatise.
+
+Moreover, it seemed to me convenient to informe your Highnesse of all
+the sequell, concerning the Controversie of which I treat, as it hath
+been advertised often already by others: and because the Doctrine
+which I follow, in the discussion of the point in hand, is different
+from that of _Aristotle_; and interferes with his Principles, I have
+considered that against the Authority of that most famous Man, which
+amongst many makes all suspected that comes not from the Schooles of
+the Peripateticks, its farr better to give ones Reasons by the Pen
+than by word of mouth, and therfore I resolved to write the present
+discourse: in which yet I hope to demonstrate that it was not out of
+capritiousnesse, or for that I had not read or understood _Aristotle_,
+that I sometimes swerve from his opinion, but because severall Reasons
+perswade me to it, and the same _Aristotle_ hath tought me to fix my
+judgment on that which is grounded upon Reason, and not on the bare
+Authority of the Master[2]; and it is most certaine according to the
+sentence of _Alcinoos_, that philosophating should be free. Nor is the
+resolution of our Question in my judgment without some benefit to the
+Universall[3], forasmuch as treating whether the figure of Solids
+operates, or not, in their going, or not going to the bottome in
+Water, in occurrences of building Bridges or other Fabricks on the
+Water, which happen commonly in affairs of grand import, it may be of
+great availe to know the truth.
+
+    [2] _Aristotle_ prefers Reason to the Authority ofan Author.
+
+    [3] The benefit of this Argument.
+
+I say therfore, that being the last Summer in company with certain
+Learned men, it was said in the argumentation; That Condensation was
+the propriety of Cold[4], and there was alledged for instance, the
+example of Ice: now I at that time said, that, in my judgment, the Ice
+should be rather Water rarified than condensed[5], and my reason was,
+because Condensation begets diminution of Mass, and augmentation of
+gravity, and Rarifaction causeth greater Lightness, and augmentarion
+of Masse: and Water in freezing, encreaseth in Masse, and the Ice made
+thereby is lighter than the Water on which it swimmeth.
+
+    [4] Condensation the Propriety of Cold, according to the
+    Peripateticks.
+
+    [5] Ice rather water rarified, than condensed, and why:
+
+  _What I say, is manifest, because, the medium subtracting from the
+  whole Gravity of Sollids the weight of such another Masse of the
+  said Medium; as_ Archimedes _proves in his_ [C] First Booke De
+  Insidentibus Humido; _when ever the Masse of the said Solid
+  encreaseth by Distraction, the more shall the_ Medium _detract from
+  its entire Gravity; and lesse, when by Compression it shall be
+  condensed and reduced to a lesse Masse._
+
+    [C] In lib: 1. of Natation of Bodies Prop. 7.
+
+    [Sidenote: Figure operates not in the Natation of Sollids.]
+
+It was answered me, tha{t} that proceeded not from the greater Levity,
+but from the Figure, large and flat, which not being able to penetrate
+the Resistance of the Water, is the cause that it submergeth not. I
+replied, that any piece of Ice, of whatsoever Figure, swims upon the
+Water, a manifest signe, that its being never so flat and broad, hath
+not any part in its floating: and added, that it was a manifest proofe
+hereof to see a piece of Ice of very broad Figure being thrust to the
+botome of the Water, suddenly return to flote atoppe, which had it
+been more grave, and had its swimming proceeded from its Forme, unable
+to penetrate the Resistance of the _Medium_, that would be altogether
+impossible; I concluded therefore, that the Figure was in sort a Cause
+of the Natation or Submersion of Bodies, but the greater or lesse
+Gravity in respect of the Water: and therefore all Bodyes heavier than
+it of what Figure soever they be, indifferently go to the bottome, and
+the lighter, though of any figure, float indifferently on the top: and
+I suppose that those which hold otherwise, were induced to that
+beliefe, by seeing how that diversity of Formes or Figures, greatly
+altereth the Velosity, and Tardity of Motion; so that Bodies of Figure
+broad and thin, descend far more leasurely into the Water, than those
+of a more compacted Figure, though both made of the same Matter: by
+which some might be induced to believe that the Dilatation of the
+Figure might reduce it to such amplenesse that it should not only
+retard but wholly impede and take away the Motion, which I hold to be
+false. Upon this Conclusion, in many dayes discourse, was spoken much,
+and many things, and divers Experiments produced, of which your
+Highnesse heard, and saw some, and in this discourse shall have all
+that which hath been produced against my Assertion, and what hath been
+suggested to my thoughts on this matter, and for confirmation of my
+Conclusion: which if it shall suffice to remove that (as I esteem
+hitherto false) Opinion, I shall thinke I have not unprofitably spent
+my paynes and time. and although that come not to passe, yet ought I
+to promise another benefit to my selfe, namely, of attaining the
+knowledge of the truth, by hearing my Fallacyes confuted, and true
+demonstrations produced by those of the contrary opinion.
+
+And to proceed with the greatest plainness and perspicuity that I can
+possible, it is, I conceive, necessary, first of all to declare what
+is the true, intrinsecall, and totall Cause, of the ascending of some
+Sollid Bodyes in the Water, and therein floating; or on the contrary,
+of their sinking and so much the rather in asmuch as I cannot satisfie
+myselfe in that which _Aristotle_ hath left written on this Subject.
+
+    [Sidenote: The cause of the Natation & submersion of Solids in
+    the Water.]
+
+I say then the Cause why some Sollid Bodyes descend to the Bottom of
+Water, is the excesse of their Gravity, above the Gravity of the
+Water; and on the contrary, the excess of the Waters Gravity above the
+Gravity of those, is the Cause that others do not descend, rather that
+they rise from the Bottom, and ascend to the Surface. This was
+subtilly demonstrated by _Archimedes_ in his Book Of the NATATION of
+BODIES: Conferred afterwards by a very grave Author, but, if I erre
+not invisibly, as below for defence of him, I shall endeavour to
+prove.
+
+I, with a different Method, and by other meanes, will endeavour to
+demonstrate the same, reducing the Causes of such Effects to more
+intrinsecall and immediate Principles, in which also are discovered
+the Causes of some admirable and almost incredible Accidents, as that
+would be, that a very little quantity of Water, should be able, with
+its small weight, to raise and sustain a Solid Body, an hundred or a
+thousand times heavier than it.
+
+And because demonstrative Order so requires, I shall define certain
+Termes, and afterwards explain some Propositions, of which, as of
+things true and obvious, I may make use of to my present purpose.
+
+
+
+
+DEFINITION I.
+
+  _I then call equally Grave_ in specie, _those Matters of which equall
+    Masses weigh equally._
+
+
+As if for example, two Balls, one of Wax, and the other of some Wood
+of equall Masse, were also equall in Weight, we say, that such Wood,
+and the Wax are _in specie_ equally grave.
+
+
+
+
+DEFINITION II.
+
+  _But equally grave in Absolute Gravity, we call two Sollids,
+    weighing equally, though of Mass they be unequall._
+
+
+As for example, a Mass of Lead, and another of Wood, that weigh each
+ten pounds, I call equall in Absolute Gravity, though the Mass of the
+Wood be much greater then that of the Lead.
+
+_And, consequently, less Grave_ in specie.
+
+
+
+
+DEFINITION III.
+
+  _I call a Matter more Grave_ in specie _than another, of which a
+    Mass, equall to a Mass of the other, shall weigh more._
+
+
+And so I say, that Lead is more grave _in specie_ than Tinn, because
+if you take of them two equall Masses, that of the Lead weigheth more.
+
+
+
+
+DEFINITION IV.
+
+  _But I call that Body more grave absolutely than this, if that
+    weigh more than this, without any respect had to the Masses._
+
+
+And thus a great piece of Wood is said to weigh more than a little
+lump of Lead, though the Lead be _in specie_ more heavy than the Wood.
+And the same is to be understood of the less grave _in specie_, and
+the less grave absolutely.
+
+These Termes defined, I take from the Mechanicks two Principles: the
+first is, that
+
+
+
+
+AXIOME. I.
+
+  _Weights absolutely equall, moved with equall Velocity, are of
+    equall Force and Moment in their operations._
+
+
+
+
+_DEFINITION V._
+
+  Moment, amongst Mechanicians, signifieth that Vertue, that Force,
+    or that Efficacy, with which the Mover moves, and the Moveable
+    resists.
+
+
+  _Which Vertue dependes not only on the simple Gravity, but on the
+  Velocity of the Motion, and on the diverse Inclinations of the
+  Spaces along which the Motion is made: For a descending Weight
+  makes a greater Impetus in a Space much declining, than in one less
+  declining; and in summe, what ever is the occasion of such Vertue,
+  it ever retaines the name of Moment; nor in my Judgement, is this
+  sence new in our Idiome, for, if I mistake not, I think we often
+  say; This is a weighty businesse, but the other is of small moment:
+  and we consider lighter matters and let pass those of Moment; a
+  Metaphor, I suppose, taken from the Mechanicks._
+
+As for example, two weights equall in absolute Gravity, being put
+into a Ballance of equall Arms, they stand in _Equilibrium_, neither
+one going down, nor the other up: because the equality of the
+Distances of both, from the Centre on which the Ballance is supported,
+and about which it moves, causeth that those weights, the said
+Ballance moving, shall in the same Time move equall Spaces, that is,
+shall move with equall Velocity, so that there is no reason for which
+this Weight should descend more than that, or that more than this; and
+therefore they make an _Equilibrium_, and their Moments continue of
+semblable and equall Vertue.
+
+The second Principle is; That
+
+
+
+
+AXIOME II.
+
+  _The Moment and Force of the Gravity, is encreased by the Velocity
+    of the Motion._
+
+
+So that Weights absolutely equall, but conjoyned with Velocity
+unequall, are of Force, Moment and Vertue unequall: and the more
+potent, the more swift, according to the proportion of the Velocity of
+the one, to the Velocity of the other. Of this we have a very
+pertinent example in the Balance or Stiliard of unequall Arms, at
+which Weights absolutely equall being suspended, they do not weigh
+down, and gravitate equally, but that which is at a greater distance
+from the Centre, about which the Beam moves, descends, raising the
+other, and the Motion of this which ascends is slow, and the other
+swift: and such is the Force and Vertue, which from the Velocity of
+the Mover, is conferred on the Moveable, which receives it, that it
+can exquisitely compensate, as much more Weight added to the other
+slower Moveable: so that if of the Arms of the Balance, one were ten
+times as long as the other, whereupon in the Beames moving about the
+Centre, the end of that would go ten times as far as the end of this,
+a Weight suspended at the greater distance, may sustain and poyse
+another ten times more grave absolutely than it: and that because the
+Stiliard moving, the lesser Weight shall move ten times faster than
+the bigger. It ought alwayes therefore to be understood, that Motions
+are according to the same Inclinations, namely, that if one of the
+Moveables move perpendicularly to the Horizon, then the other makes
+its Motion by the like Perpendicular; and if the Motion of one were to
+be made Horizontally; that then the other is made along the same
+Horizontall plain: and in summe, alwayes both in like Inclinations.
+This proportion between the Gravity and Velocity is found in all
+Mechanicall Instruments: and is considered by _Aristotle_, as a
+Principle in his _Mechanicall Questions_; whereupon we also may take
+it for a true Assumption, That
+
+
+
+
+AXIOME III.
+
+  _Weights absolutely unequall, do alternately counterpoyse and
+    become of equall Moments, as oft as their Gravities, with
+    contrary proportion, answer to the Velocity of their Motions._
+
+
+That is to say, that by how much the one is less grave than the other,
+by so much is it in a constitution of moving more swiftly than that.
+
+Having prefatically explicated these things, we may begin to enquire,
+what Bodyes those are which totally submerge in Water, and go to the
+Bottom, and which those that by constraint float on the top, so that
+being thrust by violence under Water, they return to swim, with one
+part of their Mass visible above the Surface of the Water: and this we
+will do by considering the respective operation of the said Solids,
+and of Water: Which operation followes the Submersion and sinking; and
+this it is[6], That in the Submersion that the Solid maketh, being
+depressed downwards by its proper Gravity, it comes to drive away the
+water from the place where it successively subenters, and the water
+repulsed riseth and ascends above its first levell, to which Ascent on
+the other side it, as being a grave Body of its own nature, resists:
+And because the descending Solid more and more immerging, greater and
+greater quantity of Water ascends, till the whole Sollid be submerged;
+its necessary to compare the Moments of the Resistance of the water to
+Ascension, with the Moments of the pressive Gravity of the Solid: And
+if the Moments of the Resistance of the water, shall equalize the
+Moments of the Solid, before its totall Immersion[7]; in this case
+doubtless there shall be made an _Equilibrium_, nor shall the Body
+sink any farther. But if the Moment of the Solid, shall alwayes exceed
+the Moments wherewith the repulsed water successively makes
+Resistance[8], that Solid shall not only wholly submerge under water, but
+shall descend to the Bottom. But if, lastly, in the instant of totall
+Submersion, the equality shall be made between the Moments of the
+prement Solid, and the resisting Water[9]; then shall rest, ensue, and
+the said Solid shall be able to rest indifferently, in whatsoever part
+of the water. By this time is manifest the necessity of comparing the
+Gravity of the water, and of the Solid[10]; and this comparison might at
+first sight seem sufficient to conclude and determine which are the
+Solids that float a-top, and which those that sink to the Bottom in
+the water, asserting that those shall float which are lesse grave _in
+specie_ than the water, and those submerge, which are _in specie_ more
+grave. For it seems in appearance, that the Sollid in sinking
+continually, raiseth so much Water in Mass, as answers to the parts of
+its own Bulk submerged: whereupon it is impossible, that a Solid less
+grave _in specie_, than water, should wholly sink, as being unable to
+raise a weight greater than its own, and such would a Mass of water
+equall to its own Mass be. And likewise it seems necessary, that the
+graver Solids do go to the Bottom, as being of a Force more than
+sufficient for the raising a Masse of water, equall to its own, though
+inferiour in weight. Nevertheless the business succeeds otherwise: and
+though the Conclusions are true, yet are the Causes thus assigned
+deficient, nor is it true, that the Solid in submerging, raiseth and
+repulseth Masses of Water, equall to the parts of it self submerged;
+but the Water repulsed, is alwayes less than the parts of the Solid
+submerged[11]: and so much the more by how much the Vessell in which the
+Water is contained is narrower: in such manner that it hinders not,
+but that a Solid may submerge all under Water, without raising so much
+Water in Mass, as would equall the tenth or twentieth part of its own
+Bulk: like as on the contrary, a very small quantity of Water, may
+raise a very great Solid Mass[12], though such Solid should weigh
+absolutely a hundred times as much, or more, than the said Water, if
+so be that the Matter of that same Solid be _in specie_ less grave
+than the Water. And thus a great Beam, as suppose of a 1000 weight,
+may be raised and born afloat by Water, which weighs not 50: and this
+happens when the Moment of the Water is compensated by the Velocity of
+its Motion.
+
+    [6] How the submersion of Solids in the Water, is effected.
+
+    [7] What Solids shall float on the Water.
+
+    [8] What Solids shall sinke to the botome.
+
+    [9] What Solids shall rest in all places of the Water.
+
+    [10] The Gravitie of the Water and Solid must be compared in all
+    Problems, of Natation of Bodies.
+
+    [11] The water repelled is ever less than the parts of the Sollid
+    submerged.
+
+    [12] _A_ small quantity of water, may float a very great Solid
+    Mass.
+
+But because such things, propounded thus in abstract, are somewhat
+difficult to be comprehended, it would be good to demonstrate them by
+particular examples; and for facility of demonstration, we will
+suppose the Vessels in which we are to put the Water, and place the
+Solids, to be inviron'd and included with sides erected perpendicular
+to the Plane of the Horizon, and the Solid that is to be put into such
+vessell to be either a streight Cylinder, or else an upright Prisme.
+
+_The which proposed and declared, I proceed to demonstrate the truth
+of what hath been hinted, forming the ensuing Theoreme._
+
+
+
+
+_THEOREME I._
+
+    [Sidenote: The Proportion of the water raised to the Solid
+    submerged.]
+
+  The Mass of the Water which ascends in the submerging of a Solid,
+    Prisme or Cylinder, or that abaseth in taking it out, is less
+    than the Mass of the said Solid, so depressed or advanced: and
+    hath to it the same proportion, that the Surface of the Water
+    circumfusing the Solid, hath to the same circumfused Surface,
+    together with the Base of the Solid.
+
+
+_Let the Vessell be A B C D, and in it the Water raised up to the
+Levell E F G, before the Solid Prisme H I K be therein immerged; but
+after that it is depressed under Water, let the Water be raised as
+high as the Levell L M, the Solid H I K shall then be all under Water,
+and the Mass of the elevated Water shall be L G, which is less than
+the Masse of the Solid depressed, namely of H I K, being equall to the
+only part E I K, which is contained under the first Levell E F G.
+Which is manifest, because if the Solid H I K be taken out, the Water
+I G shall return into the place occupied by the Mass E I K, where it
+was continuate before the submersion of the Prisme. And the Mass L G
+being equall to the Mass E K: adde thereto the Mass E N, and it shall
+be the whole Mass E M, composed of the parts of the Prisme E N, and of
+the Water N F, equall to the whole Solid H I K: And, therefore, the
+Mass L G shall have the same proportion to E M, as to the Mass H I K:
+But the Mass L G hath the same proportion to the Mass E M, as the
+Surface L M hath to the Surface M H: Therefore it is manifest, that
+the Mass of Water repulsed L G, is in proportion to the Mass of the
+Solid submerged H I K; as the Surface L M, namely, that of the Water
+ambient about the Sollid, to the whole Surface H M, compounded of the
+said ambient water, and the Base of the Prisme H N. But if we suppose
+the first Levell of the Water the according to the Surface H M, and
+the Prisme allready submerged H I K; and after to be taken out and
+raised to E A O, and the Water to be faln from the first Levell H L M
+as low as E F G; It is manifest, that the Prisme E A O being the same
+with H I K, its superiour part H O, shall be equall to the inferiour E
+I K: and remove the common part E N, and, consequently, the Mass of
+the Water L G is equall to the Mass H O; and, therefore, less than the
+Solid, which is without the Water, namely, the whole Prisme E A O, to
+which likewise, the said Mass of Water abated L G, hath the same
+proportion, that the Surface of the Waters circumfused L M hath to the
+same circumfused Surface, together with the Base of the Prisme A O:
+which hath the same demonstration with the former case above._
+
+[Illustration]
+
+_And from hence is inferred, that the Mass of the Water, that riseth
+in the immersion of the Solid, or that ebbeth in elevating it, is not
+equall to all the Mass of the Solid, which is submerged or elevated,
+but to that part only, which in the immersion is under the first
+Levell of the Water, and in the elevation remaines above the first
+Levell: Which is that which was to be demonstrated. We will now pursue
+the things that remain._
+
+And first we will demonstrate that,
+
+
+
+
+THEOREME II.
+
+    [Sidenote: The proportion of the water abated, to the Solid
+    raised.]
+
+  _When in one of the above said Vessels, of what ever breadth,
+    whether wide or narrow, there is placed such a Prisme or
+    Cylinder, inviron'd with Water, if we elevate that Solid
+    perpendicularly, the Water circumfused shall abate, and the
+    Abatement of the Water, shall have the same proportion to the
+    Elevation of the Prisme, as one of the Bases of the Prisme, hath
+    to the Surface of the Water Circumfused._
+
+
+[Illustration]
+
+Imagine in the Vessell, as is aforesaid, the Prisme A C D B to be
+placed, and in the rest of the Space the Water to be diffused as far
+as the Levell E A: and raising the Solid, let it be transferred to G
+M, and let the Water be abased from E A to N O: I say, that the
+descent of the Water, measured by the Line A O, hath the same
+proportion to the rise of the Prisme, measured by the Line G A, as the
+Base of the Solid G H hath to the Surface of the Water N O. The which
+is manifest: because the Mass of the Solid G A B H, raised above the
+first Levell E A B, is equall to the Mass of Water that is abased E N
+O A. Therefore, E N O A and G A B H are two equall Prismes; for of
+equall Prismes, the Bases answer contrarily to their heights:
+Therefore, as the Altitude A O is to the Altitude A G, so is the
+Superficies or Base G H to the Surface of the Water N O. If therefore,
+for example, a Pillar were erected in a waste Pond full of Water, or
+else in a Well, capable of little more then the Mass of the said
+Pillar, in elevating the said Pillar, and taking it out of the Water,
+according as it riseth, the Water that invirons it will gradually
+abate, and the abasement of the Water at the instant of lifting out
+the Pillar, shall have the same proportion, that the thickness of the
+Pillar hath to the excess of the breadth of the said Pond or Well,
+above the thickness of the said Pillar: so that if the breadth of the
+Well were an eighth part larger than the thickness of the Pillar, and
+the breadth of the Pond twenty five times as great as the said
+thickness, in the Pillars ascending one foot, the water in the Well
+shall descend seven foot, and that in the Pond only 1/25 of a foot.
+
+    [Sidenote: Why a Solid less grave _in specie_ than water, stayeth
+    not under water, in very small depths:]
+
+This Demonstrated, it will not be difficult to show the true cause,
+how it comes to pass, that,
+
+
+
+
+THEOREME III.
+
+  _A Prisme or regular Cylinder, of a substance specifically less
+    grave than Water, if it should be totally submerged in Water,
+    stayes not underneath, but riseth, though the Water circumfused
+    be very little, and in absolute Gravity, never so much inferiour
+    to the Gravity of the said Prisme._
+
+
+Let then the Prisme A E F B, be put into the Vessell C D F B, the same
+being less grave _in specie_ than the Water: and let the Water infused
+rise to the height of the Prisme: I say, that the Prisme left at
+liberty, it shall rise, being born up by the Water circumfused C D E
+A. For the Water C E being specifically more grave than the Solid A F,
+the absolute weight of the water C E, shall have greater proportion to
+the absolute weight of the Prisme A F, than the Mass C E hath to the
+Mass A F (in regard the Mass hath the same proportion to the Mass,
+that the weight absolute hath to the weight absolute, in case the
+Masses are of the same Gravity _in specie_.) But the Mass C E is to
+the Mass A F, as the Surface of the water A C, is to the Superficies,
+or Base of the Prisme A B; which is the same proportion as the ascent
+of the Prisme when it riseth, hath to the descent of the Water
+circumfused C E.
+
+[Illustration]
+
+Therefore, the absolute Gravity of the water C E, hath greater
+proportion to the absolute Gravity of the Prisme A F; than the Ascent
+of the Prisme A F, hath to the descent of the said water C E. The
+Moment, therefore, compounded of the absolute Gravity of the water C
+E, and of the Velocity of its descent, whilst it forceably repulseth
+and raiseth the Solid A F, is greater than the Moment compounded of
+the absolute Gravity of the Prisme A F, and of the Tardity of its
+ascent, with which Moment it contrasts and resists the repulse and
+violence done it by the Moment of the water: Therefore, the Prisme
+shall be raised.
+
+    [Sidenote: The Proportion according to which the Submersion &
+    Natation of Solids is made.]
+
+It followes, now, that we proceed forward to demonstrate more
+particularly, how much such Solids shall be inferiour in Gravity to
+the water elevated; namely, what part of them shall rest submerged,
+and what shall be visible above the Surface of the water: but first it
+is necessary to demonstrate the subsequent Lemma.
+
+
+
+
+LEMMA I.
+
+    [Sidenote: The absolute Gravity of Solids, are in a proportion
+    compounded of their Specifick Gravities, and of their Masses.]
+
+  _The absolute Gravities of Solids, have a proportion compounded of
+    the proportions of their specificall Gravities, and of their
+    Masses._
+
+
+[Illustration]
+
+Let A and B be two Solids. I say, that the Absolute Gravity of A,
+hath to the Absolute Gravity of B, a proportion compounded of the
+proportions of the specificall Gravity of A, to the Specificall
+Gravity of B, and of the Mass A to the Mass B. Let the Line D have the
+same proportion to E, that the specifick Gravity of A, hath to the
+specifick Gravity of B; and let E be to F, as the Mass A to the Mass
+B: It is manifest, that the proportion of D to F, is compounded of the
+proportions D and E; and E and F. It is requisite, therefore, to
+demonstrate, that as D is to F, so the absolute Gravity of A, is to
+the absolute Gravity of B. Take the Solid C, equall in Mass to the
+Solid A, and of the same Gravity _in specie_ with the Solid B.
+Because, therefore, A and C are equall in Mass, the absolute Gravity
+of A, shall have to the absolute Gravity of C, the same proportion, as
+the specificall Gravity of A, hath to the specificall Gravity of C, or
+of B, which is the same _in specie_; that is, as D is to E. And,
+because, C and B are of the same Gravity _in specie_, it shall be,
+that as the absolute weight of C, is to the absolute weight of B, so
+the Mass C, or the Mass A, is to the Mass B; that is, as the Line E to
+the Line F. As therefore, the absolute Gravity of A, is to the
+absolute Gravity of C, so is the Line D to the Line E: and, as the
+absolute Gravity of C, is to the absolute Gravity of B, so is the Line
+E to the Line F: Therefore, by Equality of proportion, the absolute
+Gravity of A, is to the absolute Gravity of B, as the Line D to the
+Line F: which was to be demonstrated. I proceed now to demonstrate,
+how that,
+
+
+
+
+THEOREME IV.
+
+    [Sidenote: The proportion of water requisite to make a Solid
+    swim:]
+
+  _If a Solid, Cylinder, or Prisme, lesse grave specifically than the
+    Water, being put into a Vessel, as above, of whatsoever
+    greatnesse, and the Water, be afterwards infused, the Solid shall
+    rest in the bottom, unraised, till the Water arrive to that part
+    of the Altitude, of the said Prisme, to which its whole Altitude
+    hath the same proportion, that the Specificall Gravity of the
+    Water, hath to the Specificall Gravity of the said Solid: but
+    infusing more Water, the Solid shall ascend._
+
+
+[Illustration]
+
+Let the Vessell be M L G N of any bigness, and let there be placed in
+it the Solid Prisme D F G E, less grave _in specie_ than the water;
+and look what proportion the Specificall Gravity of the water, hath to
+that of the Prisme, such let the Altitude D F, have to the Altitude F
+B. I say, that infusing water to the Altitude F B, the Solid D G shall
+not float, but shall stand in _Equilibrium_, so, that that every
+little quantity of water, that is infused, shall raise it. Let the
+water, therefore, be infused to the Levell A B C; and; because the
+Specifick Gravity of the Solid D G, is to the Specifick Gravity of the
+water, as the altitude B F is to the altitude F D; that is, as the
+Mass B G to the Mass G D; as the proportion of the Mass B G is to the
+Mass G D, as the proportion of the Mass G D is to the Mass A F, they
+compose the Proportion of the Mass B G to the Mass A F. Therefore, the
+Mass B G is to the Mass A F, in a proportion compounded of the
+proportions of the Specifick Gravity of the Solid G D, to the
+Specifick Gravity of the water, and of the Mass G D to the Mass A F:
+But the same proportions of the Specifick Gravity of G D, to the
+Specifick Gravity of the water, and of the Mass G D to the Mass A F,
+do also by the precedent _Lemma_, compound the proportion of the
+absolute Gravity of the Solid D G, to the absolute Gravity of the Mass
+of the water A F: Therefore, as the Mass B G is to the Mass A F, so is
+the Absolute Gravity of the Solid D G, to the Absolute Gravity of the
+Mass of the water A F. But as the Mass B G is to the Mass A F; so is
+the Base of the Prisme D E, to the Surface of the water A B; and so is
+the descent of the water A B, to the Elevation of the Prisme D G;
+Therefore, the descent of the water is to the elevation of the Prisme,
+as the absolute Gravity of the Prisme, is to the absolute Gravity of
+the water: Therefore, the Moment resulting from the absolute Gravity
+of the water A F, and the Velocity of the Motion of declination, with
+which Moment it forceth the Prisme D G, to rise and ascend, is equall
+to the Moment that results from the absolute Gravity of the Prisme D
+G, and from the Velocity of the Motion, wherewith being raised, it
+would ascend: with which Moment it resists its being raised: because,
+therefore, such Moments are equall, there shall be an _Equilibrium_
+between the water and the Solid. And, it is manifest, that putting a
+little more water unto the other A F, it will increase the Gravity and
+Moment, whereupon the Prisme D G, shall be overcome, and elevated till
+that the only part B F remaines submerged. Which is that that was to
+be demonstrated.
+
+
+COROLLARY I.
+
+    [Sidenote: _H_ow far Solids less grave _in specie_ than water, do
+    submerge.]
+
+  _By what hath been demonstrated, it is manifest, that Solids less
+    grave_ in specie _than the water, submerge only so far, that as
+    much water in Mass, as is the part of the Solid submerged, doth
+    weigh absolutely as much as the whole Solid._
+
+For, it being supposed, that the Specificall Gravity of the water, is
+to the Specificall Gravity of the Prisme D G, as the Altitude D F, is
+to the Altitude F B; that is, as the Solid D G is to the Solid B G; we
+might easily demonstrate, that as much water in Mass as is equall to
+the Solid B G, doth weigh absolutely as much as the whole Solid D G;
+For, by the _Lemma_ foregoing, the Absolute Gravity of a Mass of
+water, equall to the Mass B G, hath to the Absolute Gravity of the
+Prisme D G, a proportion compounded of the proportions, of the Mass B
+G to the Mass G D, and of the Specifick Gravit{y} of the water, to the
+Specifick Gravity of the Prisme: But the Gravity _in specie_ of the
+water, to the Gravity _in specie_ of the Prisme, is supposed to be as
+the Mass G D to the Mass G B. Therefore, the Absolute Gravity of a
+Mass of water, equall to the Mass B G, is to the Absolute Gravity of
+the Solid D G, in a proportion compounded of the proportions, of the
+Mass B G to the Mass G D, and of the Mass D G to the Mass G B; which
+is a proportion of equalitie. The Absolute Gravity, therefore, of a
+Mass of Water equall to the part of the Mass of the Prisme B G, is
+equall to the Absolute Gravity of the whole Solid D G.
+
+
+COROLLARY II.
+
+    [Sidenote: _A_ Rule to equilibrate Solids in the water.]
+
+  _It followes, moreover, that a Solid less grave than the water,
+    being put into a Vessell of any imaginable greatness, and water
+    being circumfused about it to such a height, that as much water
+    in Mass, as is the part of the Solid submerged, do weigh
+    absolutely as much as the whole Solid; it shall by that water be
+    justly sustained, be the circumfused Water in quantity greater or
+    lesser._
+
+[Illustration]
+
+For, if the Cylinder or Prisme M, less grave than the water, _v. gra._
+in Subsequiteriall proportion, shall be put into the capacious Vessell
+A B C D, and the water raised about it, to three quarters of its
+height, namely, to its Levell A D: it shall be sustained and exactly
+poysed in _Equilibrium_. The same will happen; if the Vessell E N S F
+were very small, so, that between the Vessell and the Solid M, there
+were but a very narrow space, and only capable of so much water, as
+the hundredth part of the Mass M, by which it should be likewise
+raised and erected, as before it had been elevated to three fourths of
+the height of the Solid: which to many at the first sight, may seem a
+notable Paradox, and beget a conceit, that the Demonstration of these
+effects, were sophisticall and fallacious: but, for those who so
+repute it, the Experiment is a means that may fully satisfie them. But
+he that shall but comprehend of what Importance Velocity of Motion is,
+and how it exactly compensates the defect and want of Gravity, will
+cease to wonder, in considering that at the elevation of the Solid M,
+the great Mass of water A B C D abateth very little, but the little
+Mass of water E N S F decreaseth very much, and in an instant, as the
+Solid M before did rise, howbeit for a very short space: Whereupon the
+Moment, compounded of the small Absolute Gravity of the water E N S F,
+and of its great Velocity in ebbing, equalizeth the Force and and
+Moment, that results from the composition of the immense Gravity of
+the water A B C D, with its great slownesse of ebbing; since that in
+the Elevation of the Sollid M, the abasement of the lesser water E S,
+is performed just so much more swiftly than the great Mass of water A
+C, as this is more in Mass than that which we thus demonstrate.
+
+    [Sidenote: _T_he proportion according to which water riseth and
+    falls in different Vessels at the Immersion and Elevation of
+    Solids.]
+
+In the rising of the Solid M, its elevation hath the same proportion
+to the circumfused water E N S F, that the Surface of the said water,
+hath to the Superficies or Base of the said Solid M; which Base hath
+the same proportion to the Surface of the water A D, that the
+abasement or ebbing of the water A C, hath to the rise or elevation of
+the said Solid M. Therefore, by Perturbation of proportion, in the
+ascent of the said Solid M, the abasement of the water A B C D, to the
+abasement of the water E N S F, hath the same proportion, that the
+Surface of the water E F, hath to the Surface of the water A D; that
+is, that the whole Mass of the water E N S F, hath to the whole Mass A
+B C D, being equally high: It is manifest, therefore, that in the
+expulsion and elevation of the Solid M, the water E N S F shall exceed
+in Velocity of _M_otion the water A B C D, asmuch as it on the other
+side is exceeded by that in quantity: whereupon their Moments in such
+operations, are mutually equall.
+
+[Illustration]
+
+  _And, for ampler confirmation, and clearer explication of this, let
+  us consider the present Figure, (which if I be not deceived, may
+  serve to detect the errors of some Practick Mechanitians who upon a
+  false foundation some times attempt impossible enterprizes,) in
+  which, unto the large Vessell E I D F, the narrow Funnell or Pipe I
+  C A B is continued, and suppose water infused into them, unto the
+  Levell L G H, which water shall rest in this position, not without
+  admiration in some, who cannot conceive how it can be, that the
+  heavie charge of the great Mass of water G D, pressing downwards,
+  should not elevate and repulse the little quantity of the other,
+  contained in the Funnell or Pipe C L, by which the descent of it is
+  resisted and hindered: But such wonder shall cease, if we begin to
+  suppose the water G D to be abased only to Q D, and shall
+  afterwards consider, what the water C L hath done, which to give
+  place to the other, which is descended from the Levell G H, to the
+  Levell Q O, shall of necessity have ascended in the same time, from
+  the Levell L unto A B. And the ascent L B, shall be so much greater
+  than the descent G Q, by how much the breadth of the Vessell G D,
+  is greater than that of the Funnell I C; which, in summe, is as
+  much as the water G D, is more than the water L C: but in regard
+  that the Moment of the Velocity of the Motion, in one Moveable,
+  compensates that of the Gravity of another what wonder is it, if
+  the swift ascent of the lesser Water C L, shall resist the slow
+  descent of the greater G D?_
+
+The same, therefore, happens in this operation, as in rhe Stilliard,
+in which a weight of two pounds counterpoyseth an other of 200,
+asoften as that shall move in the same time, a space 100 times greater
+than this: which falleth out when one Arme of the Beam is an hundred
+times as long as the other. Let the erroneous opinion of those
+therefore cease, who hold that a Ship is better, and easier born up in
+a great abundance of water, then in a lesser quantity[13], (_this was
+believed by_ Aristotle _in his Problems, Sect. 23, Probl. 2._) it being
+on the contrary true, that its possible, that a Ship may as well float
+in ten Tun of water, as in an Ocean.
+
+    [13] A ship flotes as well in ten Tun of Water as in an Ocean.
+
+    [Sidenote: A Solid specifiaclly graver than the water, cannot be
+    born up by any quantity of it.]
+
+But following our matter, I say, that by what hath been hitherto
+demonstrated, we may understand how, that
+
+
+COROLLARY III.
+
+  _One of the above named Solids, when more grave_ in specie _than the
+    water, can never be sustained, by any whatever quantity of it._
+
+For having seen how that the Moment wherewith such a Solid, as grave
+_in specie_ as the water, contrasts with the Moment of any Mass of
+water whatsoever, is able to retain it, even to its totall Submersion,
+without its ever ascending; it remaineth, manifest, that the water is
+far less able to raise it up, when it exceeds the same _in specie_:
+so, that though you infuse water till its totall Submersion, it shall
+still stay at the Bottome, and with such Gravity, and Resistance to
+Elevation, as is the excess of its Absolute Gravity, above the
+Absolute Gravity of a Mass equall to it, made of water, or of a Matter
+_in specie_ equally grave with the water: and, though you should
+moreover adde never so much water above the Levell of that which
+equalizeth the Altitude of the Solid, it shall not, for all that,
+encrease the Pression, or Gravitation, of the parts circumfused about
+the said Solid, by which greater pression, it might come to be
+repulsed; because, the Resistance is not made, but only by those parts
+of the water, which at the Motion of the said Solid do also move, and
+these are those only, which are comprehended by the two Superficies
+equidistant to the Horizon, and their parallels, that comprehend the
+Altitude of the Solid immerged in the water.
+
+I conceive, I have by this time sufficiently declared and opened the
+way to the contemplation of the true, intrinsecall and proper Causes
+of diverse Motions, and of the Rest of many Solid Bodies in diverse
+_Mediums_, and particularly in the water, shewing how all in effect,
+depend on the mutuall excesses of the Gravity of the Moveables and of
+the _Mediums_: and, that which did highly import, removing the
+Objection, which peradventure would have begotten much doubting, and
+scruple in some, about the verity of my Conclusion, namely, how that
+notwithstanding, that the excess of the Gravity of the water, above
+the Gravity of the Solid, demitted into it, be the cause of its
+floating and rising from the Bottom to the Surface, yet a quantity of
+water, that weighs not ten pounds, can raise a Solid that weighs above
+100 pounds: in that we have demonstrated, That it sufficeth, that such
+difference be found between the Specificall Gravities of the _Mediums_
+and Moveables, let the particular and absolute Gravities be what they
+will: insomuch, that a Solid, provided that it be Specifically less
+grave than the water, although its absolute weight were 1000 pounds,
+yet may it be born up and elevated by ten pounds of water, and less:
+and on the contrary, another Solid, so that it be Specifically more
+grave than the water, though in absolute Gravity it were not above a
+pound, yet all the water in the Sea, cannot raise it from the Bottom,
+or float it. This sufficeth me, for my present occasion, to have, by
+the above declared Examples, discovered and demonstrated, without
+extending such matters farther, and, as I might have done, into a long
+Treatise: yea, but that there was a necessity of resolving the above
+proposed doubt, I should have contented my self with that only, which
+is demonstrated by _Archimedes_, in his first _Book De Insidentibus
+humido_[14]: where in generall termes he infers and confirms the same
+Conclusions, namely, that Solids (_a_) less grave than water, swim or
+float upon it, the (_b_) more grave go to the Bottom, and the (_c_)
+equally grave rest indifferently in all places, yea, though they
+should be wholly under water.
+
+    [14] _Of Natation_ (a) _Lib. 1, Prop. 4._ (b) _Id. Lib. 1. Prop.
+    3._ (c) _Id. Lib. 1. Prop. 3._
+
+    [Sidenote: The Authors defence of _Archimedes_ his Doctrine,
+    against the oppositions of _Buonamico_.]
+
+But, because that this Doctrine of Archimedes, perused, transcribed
+and examined by _Signor Francesco Buonamico_, in his _fifth Book of
+Motion, Chap. 29_, and afterwards by him confuted, might by the
+Authority of so renowned, and famous a Philosopher, be rendered
+dubious, and suspected of falsity; I have judged it necessary to
+defend it, if I am able so to do, and to clear _Archimedes_, from
+those censures, with which he appeareth to be charged. _Buonamico_
+rejecteth the Doctrine of _Archimedes_, first[15], as not consentaneous
+with the Opinion of _Aristotle_, adding, that it was a strange thing
+to him, that the Water should exceed the Earth in Gravity[16], seeing on
+the contrary, that the Gravity of water, increaseth, by means of the
+participation of Earth. And he subjoyns presently after[17], that he was
+not satisfied with the Reasons of _Archimedes_, as not being able with
+that Doctrine, to assign the cause whence it comes, that a Boat and a
+Vessell, which otherwise, floats above the water, doth sink to the
+Bottom, if once it be filled with water; that by reason of the
+equality of Gravity, between the water within it, and the other water
+without, it should stay a top; but yet, nevertheless, we see it to go
+to the Bottom.
+
+    [15] His first Objection against the Doctrine of _Archimedes_.
+
+    [16] His Second Objection.
+
+    [17] His third Objection.
+
+He farther addes[18], that _Aristotle_ had clearly confuted the Ancients,
+who said, that light Bodies moved upwards[19], driven by the impulse of
+the more grave Ambient: which if it were so, it should seem of
+necessity to follow, that all naturall Bodies are by nature heavy, and
+none light: For that the same would befall the Fire and Air, if put in
+the Bottom of the water. And, howbeit, _Aristotle_ grants a Pulsion in
+the Elements, by which the Earth is reduced into a Sphericall Figure,
+yet nevertheless, in his judgement; it is not such that it can remove
+grave Bodies from their naturall places, but rather, that it send them
+toward the Centre, to which (as he somewhat obscurely continues to
+say,) the water principally moves, if it in the interim meet not with
+something that resists it, and, by its Gravity, thrusts it out of its
+place: in which case, if it cannot directly, yet at least as well as
+it can, it tends to the Centre: but it happens, that light Bodies by
+such Impulsion, do all ascend upward: but this properly they have by
+nature, as also, that other of swimming. He concludes, lastly[20], that he
+concurs with _Archimedes_ in his Conclusions; but not in the Causes,
+which he would referre to the facile and difficult Separation of the
+_Medium_, and to the predominance of the Elements, so that when the
+Moveable superates the power of the _Medium_; as for example, Lead
+doth the Continuity of water, it shall move thorow it, else not.
+
+    [18] His fourth Objection.
+
+    [19] The _A_ncients denyed _A_bsolute Levity.
+
+    [20] The causes of Natation & Submersion, according to the
+    Peripateticks.
+
+This is all that I have been able to collect, as produced against
+_Archimedes_ by _Signor Buonamico_: who hath not well observed the
+Principles and Suppositions of _Archimedes_; which yet must be false,
+if the Doctrine be false, which depends upon them; but is contented to
+alledge therein some Inconveniences, and some Repugnances to the
+Doctrine and Opinion of _Aristotle_. In answer to which Objections, I
+say, first[21], That the being of _Archimedes_ Doctrine, simply different
+from the Doctrine of _Aristotle_, ought not to move any to suspect it,
+there being no cause, why the Authority of this should be preferred to
+the Authority of the other: but, because, where the decrees of Nature
+are indifferently exposed to the intellectuall eyes of each, the
+Authority of the one and the other, loseth all a{u}thenticalness of
+Perswasion, the absolute power residing in Reason; therefore I pass to
+that which he alledgeth in the second place[22], as an absurd consequent
+of the Doctrine of _Archimedes_, namely, That water should be more
+grave than Earth. But I really find not, that ever _Archimedes_ said
+such a thing, or that it can be rationally deduced from his
+Conclusions: and if that were manifest unto me, I verily believe, I
+should renounce his Doctrine, as most erroneous. Perhaps this
+Deduction of _Buonamico_, is founded upon that which he citeth of the
+Vessel, which swims as long as its voyd of water, but once full it
+sinks to the Bottom, and understanding it of a Vessel of Earth, he
+infers against _Archimedes_ thus: Thou sayst that the Solids which
+swim, are less grave than water: this Vessell swimmeth: therefore,
+this Vessell is lesse grave than water. If this be the Illation. I
+easily answer, granting that this Vessell is lesse grave than water,
+and denying the other consequence, namely, that Earth is less Grave
+than Water. The Vessel that swims occupieth in the water, not only a
+place equall to the Mass of the Earth, of which it is formed; but
+equall to the Earth and to the Air together, contained in its
+concavity. And, if such a Mass compounded of Earth and Air, shall be
+less grave than such another quantity of water, it shall swim, and
+shall accord with the Doctrine of _Archimedes_; but if, again,
+removing the Air, the Vessell shall be filled with water, so that the
+Solid put in the water, be nothing but Earth, nor occupieth other
+place, than that which is only possest by Earth, it shall then go to
+the Bottom, by reason that the Earth is heavier than the water: and
+this corresponds well with the meaning of _Archimedes_. See the same
+effect illustrated, with such another Experiment, In pressing a Viall
+Glass to the Bottom of the water, when it is full of Air, it will meet
+with great resistance, because it is not the Glass alone, that is
+pressed under water, but together with the Glass a great Mass of Air,
+and such, that if you should take as much water, as the Mass of the
+Glass, and of the Air contained in it, you would have a weight much
+greater than that of the Viall, and of its Air: and, therefore, it
+will not submerge without great violence: but if we demit only the
+Glass into the water, which shall be when you shall fill the Glass
+with water, then shall the Glass descend to the Bottom; as superiour
+in Gravity to the water.
+
+    [21] The Authors answer to the first Objection.
+
+    [22] The Authors answer to the second Objection.
+
+Returning, therefore, to our first purpose; I say, that Earth is more
+grave than water, and that therefore, a Solid of Earth goeth to the
+bottom of it; but one may possibly make a composition of Earth and
+Air, which shall be less grave than a like Mass of Water; and this
+shall swim: and yet both this and the other experiment shall very well
+accord with the Doctrine of _Archimedes_. But because that in my
+judgment it hath nothing of difficulty in it, I will not positively
+affirme that _Signor Buonamico_, would by such a discourse object unto
+_Archimedes_ the absurdity of inferring by his doctrine, that Earth
+was less grave than Water, though I know not how to conceive what
+other accident he could have induced thence.
+
+Perhaps such a Probleme (in my judgement false) was read by _Signor
+Buonamico_ in some other Author, by whom peradventure it was
+attributed as a singular propertie, of some particular Water, and so
+comes now to be used with a double errour in confutation of
+_Archimedes_, since he saith no such thing, nor by him that did say it
+was it meant of the common Element of Water.
+
+    [Sidenote: The Authors answer to the third Objection.]
+
+The third difficulty in the doctrine of _Archimedes_ was, that he
+could not render a reason whence it arose, that a piece of Wood, and a
+Vessell of Wood, which otherwise floats, goeth to the bottom, if
+filled with Water. _Signor Buonamico_ hath supposed that a Vessell of
+Wood, and of Wood that by nature swims, as before is said, goes to the
+bottom, if it be filled with water; of which he in the following
+Chapter, which is the 30 of the fifth Book copiously discourseth: but
+I (speaking alwayes without diminution of his singular Learning) dare
+in defence of _Archimedes_ deny this experiment, being certain that a
+piece of Wood which by its nature sinks not in Water, shall not sinke
+though it be turned and converted into the forme of any Vessell
+whatsoever, and then filled with Water: and he that would readily see
+the Experiment in some other tractable Matter, and that is easily
+reduced into several Figures, may take pure Wax, and making it first
+into a Ball or other solid Figure, let him adde to it so much Lead as
+shall just carry it to the bottome, so that being a graine less it
+could not be able to sinke it, and making it afterwards into the forme
+of a Dish, and filling it with Water, he shall finde that without the
+said Lead it shall not sinke, and that with the Lead it shall descend
+with much slowness: & in short he shall satisfie himself, that the
+Water included makes no alteration. I say not all this while, but that
+its possible of Wood to make Barkes, which being filled with water,
+sinke; but that proceeds not through its Gravity, encreased by the
+Water, but rather from the Nailes and other Iron Workes, so that it no
+longer hath a Body less grave than Water, but one mixt of Iron and
+Wood, more grave than a like Masse of Water. Therefore let _Signor
+Buonamico_ desist from desiring a reason of an effect, that is not in
+nature: yea if the sinking of the Woodden Vessell when its full of
+Water, may call in question the Doctrine of _Archimedes_, which he
+would not have you to follow, is on the contrary consonant and
+agreeable to the Doctrine of the Peripateticks, since it aptly
+assignes a reason why such a Vessell must, when its full of Water,
+descend to the bottom; converting the Argument the other way, we may
+with safety say that the Doctrine of _Archimedes_ is true, since it
+aptly agreeth with true experiments, and question the other, whose
+Deductions are fastened upon erroneouss Conclusions. As for the other
+point hinted in this same Instance, where it seemes that _Benonamico_
+understands the same not only of a piece of wood, shaped in the forme
+of a Vessell, but also of massie Wood, which filled, _scilicet_, as I
+believe, he would say, soaked and steeped in Water, goes finally to
+the bottom that happens in some porose Woods, which, while their
+Porosity is replenished with Air, or other Matter less grave than
+Water, are Masses specificially less grave than the said Water, like
+as is that Viall of Glass whilest it is full of Air: but when, such
+light Matter departing, there succeedeth Water into the same
+Porosities and Cavities, there results a compound of Water and Glass
+more grave than a like Mass of Water: but the excess of its Gravity
+consists in the Matter of the Glass, and not in the Water, which
+cannot be graver than it self: so that which remaines of the Wood, the
+Air of its Cavities departing, if it shall be more grave _in specie_
+than Water, fil but its Porosities with Water, and you shall have a
+Compost of Water and of Wood more grave than Water, but not by vertue
+of the Water received into and imbibed by the Porosities, but of that
+Matter of the Wood which remains when the Air is departed: and being
+such it shall, according to the Doctrine of _Archimedes_, goe to the
+bottom, like as before, according to the same Doctrine it did swim.
+
+    [Sidenote: The Authors answer to the fourth Objection.]
+
+As to that finally which presents itself in the fourth place,
+namely, that the _Ancients_ have been heretofore confuted by
+_Aristotle_, who denying Positive and Absolute Levity, and truely
+esteeming all Bodies to be grave, said, that that which moved upward
+was driven by the circumambient Air, and therefore that also the
+Doctrine of _Archimedes_, as an adherent to such an Opinion was
+convicted and confuted: I answer first, that _Signor Buonamico_ in my
+judgement hath imposed upon _Archimedes_, and deduced from his words
+more than ever he intended by them, or may from his Propositions be
+collected, in regard that _Archimedes_ neither denies, nor admitteth
+Positive Levity, nor doth he so much as mention it: so that much less
+ought _Buonamico_ to inferre, that he hath denyed that it might be the
+Cause and Principle of the Ascension of Fire, and other Light Bodies[23]:
+having but only demonstrated, that Solid Bodies more grave than Water
+descend in it, according to the excess of their Gravity above the
+Gravity of that, he demonstrates likewise, how the less grave ascend
+in the same Water[24], accordng to its excess of Gravity, above the
+Gravity of them. So that the most that can be gathered from the
+Demonstration of _Archimedes_ is, that like as the excess of the
+Gravity of the Moveable above the Gravity of the Water, is the Cause
+that it descends therein, so the excess of the Gravity of the water
+above that of the Moveable, is a sufficient Cause why it descends not,
+but rather betakes it self to swim: not enquiring whether of moving
+upwards there is, or is not any other Cause contrary to Gravity: nor
+doth _Archimedes_ discourse less properly than if one should say: If
+the South Winde shall assault the Barke with greater _Impetus_ than is
+the violence with which the Streame of the River carries it towards
+the South, the motion of it shall be towards the North: but if the
+_Impetus_ of the Water shall overcome that of the Winde, its motion
+shall be towards the South. The discourse is excellent and would be
+unworthily contradicted by such as should oppose it, saying: Thou
+mis-alledgest as Cause of the motion of the Bark towards the South,
+the _Impetus_ of the Stream of the Water above that of the South
+Winde; mis-alledgest I say, for it is the Force of the North Winde
+opposite to the South, that is able to drive the Bark towards the
+South. Such an Objection would be superfluous, because he which
+alledgeth for Cause of the Motion the Stream of the Water, denies not
+but that the Winde opposite to the South may do the same, but only
+affirmeth that the force of the Water prevailing over the South Wind,
+the Bark shall move towards the South: and saith no more than is true.
+And just thus when _Archimedes_ saith, that the Gravity of the Water
+prevailing over that by which the moveable descends to the Bottom,
+such moveable shall be raised from the Bottom to the Surface alledgeth
+a very true Cause of such an Accident, nor doth he affirm or deny that
+there is, or is not, a vertue contrary to Gravity, called by some
+Levity, that hath also a power of moving some Matters upwards. Let
+therefore the Weapons of _Signor Buonamico_ be directed against
+_Plato_[25], and other _Ancients_, who totally denying _Levity_, and
+taking all Bodies to be grave, say that the Motion upwards is made,
+not from an intrinsecal Principle of the Moveable, but only by the
+Impulse of the _Medium_; and let _Archimedes_ and his Doctrine escape
+him, since he hath given him no Cause of quarelling with him. But if
+this Apologie, produced in defence of _Archimedes_, should seem to
+some insufficient to free him from the Objections and Arguments,
+produced by _Aristotle_ against _Plato_, and the other _Ancients_, as if
+they did also fight against _Archimedes_, alledging the Impulse of the
+Water as the Cause of the swimming of some Bodies less grave than it[26],
+I would not question, but that I should be able to maintaine the
+Doctrine of _Plato_ and those others to be most true, who absolutely
+deny Levity, and affirm no other Intrinsecal Principle of Motion to be
+in Elementary Bodies save only that towards the Centre of the Earth[27],
+nor no other Cause of moving upwards, speaking of that which hath the
+resemblance of natural Motion, but only the repulse of the _Medium_,
+fluid, and exceeding the Gravity of the Moveable[28]: and as to the
+Reasons of _Aristotle_ on the contrary, I believe that I could be able
+fully to answer them, and I would assay to do it, if it were
+absolutely necessary to the present Matter, or were it not too long a
+Digression for this short Treatise. I will only say, that if there
+were in some of our Ellementary Bodies an Intrinsecall Principle and
+Naturall Inclination to shun the Centre of the Earth, and to move
+towards the Concave of the Moon, such Bodies, without doubt, would
+more swiftly ascend through those _Mediums_ that least oppose the
+Velocity of the Moveable, and these are the more tenuous and subtle;
+as is, for example, the Air in comparison of the Water, we daily
+proving that we can with farre more expeditious Velocity move a Hand
+or a Board to and again in one than in the other[29]: nevertheless, we
+never could finde any Body, that did not ascend much more swiftly in
+the water than in the Air. Yea of Bodies which we see continually to
+ascend in the Water, there is none that having arrived to the confines
+of the Air, do not wholly lose their Motion[30]; even the Air it self,
+which rising with great Celerity through the Water, being once come to
+its Region it loseth all
+
+    [23] Of Natation, Lib. 1. Prop. 7.
+
+    [24] Of Natation, Lib. 1. Prop. 4.
+
+    [25] _Plato_ denyeth Positive Levity.
+
+    [26] The Authors defence of the doctrine of _Plato_ and the
+    _Ancients_, who absolutely deny Levity:
+
+    [27] According to _Plato_ there is no Principle of the Motion, of
+    descent in Naturall Bodies, save that to the Centre.
+
+    [28] No cause of the motion of Ascent, save the Impulse of the
+    _Medium_, exceeding the Moveable in Gravitie.
+
+    [29] Bodies ascend much swifter in the Water, than in the Air.
+
+    [30] All Bodies ascending through Water, lose their Motion,
+    comming to the confines of the Air.
+
+    [Sidenote: The lighter Bodies ascend more swiftly through Water.]
+
+And, howbeit, Experience shewes, that the Bodies, successively less
+grave, do most expeditiously ascend in water, it cannot be doubted,
+but that the Ignean Exhalations do ascend more swiftly through the
+water, than doth the Air: which Air is seen by Experience to ascend
+more swiftly through the Water, than the Fiery Exhalations through the
+Air[31]: Therefore, we must of necessity conclude, that the said
+Exhalations do much more expeditiously ascend through the Water, than
+through the Air; and that, consequently, they are moved by the Impulse
+of the Ambient _Medium_, and not by an intrinsick Principle that is in
+them, of avoiding the Centre of the Earth; to which other grave Bodies
+tend.
+
+    [31] Fiery Exhalations ascend thorow the Water more swiftly than
+    doth the Air; & the Air ascends more swiftly thorow the Water,
+    than Fire thorow the Air.
+
+    [Sidenote: _T_he Authors confutation of the Peripateticks Causes
+    of Natation & Submersion.]
+
+To that which for a finall conclusion, _Signor Buonamico_ produceth
+of going about to reduce the descending or not descending, to the
+easie and uneasie Division of the _Medium_, and to the predominancy of
+the Elements: I answer, as to the first part, that that cannot in any
+manner be admitted as a Cause, being that in none of the Fluid
+_Mediums_, as the Air, the Water, and other Liquids, there is any
+Resistance against Division[32], but all by every the least Force, are
+divided and penetrated, as I will anon demonstrate: so, that of such
+Resistance of Division there can be no Act, since it self is not in
+being. As to the other part, I say, that the predominancy of the
+Elements in Moveables[33], is to be considered, as far as to the excesse
+or defect of Gravity, in relation to the _Medium_: for in that Action,
+the Elements operate not, but only, so far as they are grave or light:
+therefore, to say that the Wood of the Firre sinks not, because Air
+predominateth in it, is no more than to say, because it is less grave
+than the Water. Yea, even the immediate Cause, is its being less grave
+than the Water[34]: and it being under the predominancy of the Air, is the
+Cause of its less Gravity: Therefore, he that alledgeth the
+predominancy of the Element for a Cause, brings the Cause of the
+Cause, and not the neerest and immediate Cause. Now, who knows not
+that the true Cause is the immediate, and not the mediate[35]? Moreover,
+he that alledgeth Gravity, brings a Cause most perspicuous to Sence[36]:
+The cause we may very easily assertain our selves; whether Ebony, for
+example, and Firre, be more or less grave than water: but whether
+Earth or Air predominates in them, who shall make that manifest?
+Certainly, no Experiment can better do it than to observe whether they
+swim or sink. So, that he who knows, not whether such a Solid swims,
+unless when he knows that Air predominates in it, knows not whether it
+swim, unless he sees it swim, for then he knows that it swims, when he
+knows that it is Air that predominates, but knows not that Air hath
+the predominance, unless he sees it swim: therefore, he knows not if
+it swims, till such time as he hath seen it swim.
+
+    [32] Water & other fluids void of Resistance against Division.
+
+    [33] _T_he predominancy of Elements in Moveables to be considered
+    only in relation to their excess or defect of Gravity in reference
+    to the _Medium_.
+
+    [34] _T_he immediate Cause of Natation is that the Moveable is
+    less grave than the Water.
+
+    [35] _T_he Peripateticks alledge for the reason of Natation the
+    Cause of the Cause.
+
+    [36] Gravity a Cause most perspicuous to sence.
+
+Let us not then despise those Hints, though very dark, which Reason,
+after some contemplation, offereth to our Intelligence, and lets be
+content to be taught by _Archimedes_, that then any Body shall
+submerge in water[37], when it shall be specifically more grave than it,
+and that if it shall be less grave[38], it shall of necessity swim, and
+that it will rest indifferently in any place under water, if its
+Gravity be perfectly like to that of the water.
+
+    [37] Lib 1. of Natation Prop. 7
+
+    [38] Id. Lib. 1. Prop. 4.
+
+These things explained and proved[39], I come to consider that which
+offers it self, touching what the Diversity of figure given unto the
+said Moveable hath to do with these Motions and Rests; and proceed to
+affirme, that,
+
+    [39] Id. Lib 1. Prop. 3.
+
+
+
+
+THEOREME V.
+
+    [Sidenote: Diversity of Figure no Cause of its absolute Natation
+    or Submersion.]
+
+  _The diversity of Figures given to this or that Solid, cannot any
+    way be a Cause of its absolute Sinking or Swimming._
+
+
+So that if a Solid being formed, for example, into a Sphericall
+Figure, doth sink or swim in the water, I say, that being formed into
+any other Figure, the same figure in the same water, shall sink or
+swim: nor can such its Motion by the Expansion or by other mutation of
+Figure, be impeded or taken away.
+
+    [Sidenote: The Expansion of Figure, retards the Velocity of the
+    ascent or descent of the Moveable in the water; but doth not
+    deprive it of all Motion.]
+
+The Expansion of the Figure may indeed retard its Velocity, aswell of
+ascent as descent, and more and more according as the said Figure is
+reduced to a greater breadth and thinness: but that it may be reduced
+to such a form as that that same matter be wholly hindred from moving
+in the same water, that I hold to be impossible. In this I have met
+with great contradictors, who producing some Experiments, and in
+perticular a thin Board of Ebony, and a Ball of the same Wood, and
+shewing how the Ball in Water descended to the bottom, and the Board
+being put lightly upon the Water submerged not, but rested; have held,
+and with the Authority of _Aristotle_, confirmed themselves in their
+Opinions, that the Cause of that Rest was the breadth of the Figure,
+u{n}able by its small weight to pierce and penetrate the Resistance of
+the Waters Crassitude, which Resistance is readily overcome by the
+other Sphericall Figure.
+
+This is the Principal point in the present Question, in which I
+perswade my self to be on the right side.
+
+Therefore, beginning to investigate with the examination of exquisite
+Experiments that really the Figure doth not a jot alter the descent or
+Ascent of the same Solids, and having already demonstrated that the
+greater or less Gravity of the Solid in relation to the Gravity of the
+_Medium_ is the cause of Descent or Ascent: when ever we would make
+proof of that, which about this Effect the diversity of Figure
+worketh, its necessary to make the Experiment with Matter wherein
+variety of Gravities hath no place. For making use of Matters which
+may be different in their Specifical Gravities, and meeting with
+varieties of effects of Ascending and Descending, we shall alwayes be
+left unsatisfied whether that diversity derive it self really from the
+sole Figure, or else from the divers Gravity also. We may remedy this
+by takeing one only Matter, that is tractable and easily reduceable
+into every sort of Figure. Moreover, it will be an excellent expedient
+to take a kinde of Matter, exactly alike in Gravity unto the Water:
+for that Matter, as far as pertaines to the Gravity, is indifferent
+either to Ascend or Descend; so that we may presently observe any the
+least difference that derives it self from the diversity of Figure.
+
+    [Sidenote: An Experiment in Wax, that proveth Figure to have no
+    Operation in Natation & Submersion.]
+
+Now to do this, Wax is most apt, which, besides its incapacity of
+receiveing any sensible alteration from its imbibing of Water, is
+ductile or pliant, and the same piece is easily reduceable into all
+Figures: and being _in Specie_ a very inconsiderable matter inferiour
+in Gravity to the Water, by mixing therewith a little of the fileings
+of Lead it is reduced to a Gravity exactly equall to that of the
+Water.
+
+This Matter prepared, and, for example, a Ball being made thereof as
+bigge as an Orange or biger, and that made so grave as to sink to the
+bottom, but so lightly, that takeing thence one only Grain of Lead, it
+returns to the top, and being added, it submergeth to the bottom, let
+the same Wax afterwards be made into a very broad and thin Flake or
+Cake; and then, returning to make the same Experiment, you shall see
+that it being put to the bottom, it shall, with the Grain of Lead rest
+below, and that Grain deducted, it shall ascend to the very Surface,
+and added again it shall dive to the bottom. And this same effect
+shall happen alwaies in all sort of Figures, as wel regular as
+irregular: nor shall you ever finde any that will swim without the
+removall of the Grain of Lead, or sinke to the bottom unless it be
+added: and, in short, about the going or not going to the Bottom, you
+shall discover no diversity, although, indeed, you shall about the
+quick and slow descent: for the more expatiated and distended Figures
+move more slowly aswel in the diveing to the bottom as in the rising
+to the top; and the other more contracted and compact Figures, more
+speedily. Now I know not what may be expected from the diversity of
+Figures, if the most contrary to one another operate not so much as
+doth a very small Grain of Lead, added or removed.
+
+Me thinkes I hear some of the Adversaries to raise a doubt upon my
+produced Experiment[40]. And first that they offer to my consideration,
+that the Figure, as a Figure simply, and disjunct from the Matter
+workes not any effect, but requires to be conjoyned with the Matter;
+and, furthermore, not with every Matter, but with those only,
+wherewith it may be able to execute the desired operation. Like as we
+see it verified by Experience, that the Acute and sharp Angle is more
+apt to cut, than the Obtuse; yet alwaies provided, that both the one
+and the other, be joyned with a Matter apt to cut, as for example,
+with Steel. Therefore, a Knife with a fine and sharp edge, cuts Bread
+or Wood with much ease, which it will not do, if the edge be blunt and
+thick: but he that will instead of Steel, take Wax, and mould it into
+a Knife, undoubtedly shall never know the effects of sharp and blunt
+edges: because neither of them will cut, the Wax being unable by
+reason of its flexibility, to overcome the hardness of the Wood and
+Bread. And, therefore, applying the like discourse to our purpose,
+they say, that the difference of Figure will shew different effects,
+touching Natation and Submersion, but not conjoyned with any kind of
+Matter, but only with those Matters which, by their Gravity, are apt
+to resist the Velocity of the water, whence he that would elect for
+the Matter, Cork or other light wood, unable, through its Levity, to
+superate the Crassitude of the water, and of that Matter should forme
+Solids of divers Figures, would in vain seek to find out what
+operation Figure hath in Natation or Submersion; because all would
+swim, and that not through any property of this or that Figure, but
+through the debility of the Matter, wanting so much Gravity, as is
+requisite to superate and overcome the Density and Crassitude of the
+water.
+
+    [40] An objection against the Experiment in Water.
+
+Its needfull, therefore, if wee would see the effect wrought by the
+Diversity of Figure, first to make choice of a Matter of its nature
+apt to penetrate the Crassitude of the water. And, for this effect[41],
+they have made choice of such a Matter, as fit, that being readily
+reduced into Sphericall Figure, goes to the Bottom; and it is Ebony,
+of which they afterwards making a small Board or Splinter, as thin as
+a Lath, have illustrated how that this, put upon the Surface of the
+water, rests there without descending to the Bottom: and making, on
+the otherside, of the same wood a Ball, no less than a hazell Nut,
+they shew, that this swims not, but descendes. From which Experiment,
+they think they may frankly conclude, that the Breadth of the Figure
+in the flat Lath or Board, is the cause of its not descending to the
+Bottom, for as much as a Ball of the same Matter, not different from
+the Board in any thing but in Figure, submergeth in the same water to
+the Bottom. The discourse and the Experiment hath really so much of
+probability and likelyhood of truth in it, that it would be no wonder,
+if many perswaded by a certain cursory observation, should yield
+credit to it; nevertheless, I think I am able to discover, how that it
+is not free from falacy.
+
+    [41] An Experiment in Ebany, brought to disprove the Experiment
+    in Wax.
+
+Beginning, therefore, to examine one by one, all the particulars that
+have been produced, I say, that Figures, as simple Figures, not only
+operate not in naturall things, but neither are they ever seperated
+from the Corporeall substance[42]: nor have I ever alledged them stript of
+sensible Matter, like as also I freely admit, that in our endeavouring
+to examine the Diversity of Accidents, dependant upon the variety of
+Figures, it is necessary to apply them to Matters, which obstruct not
+the various operations of those various Figures: and I admit and
+grant, that I should do very ill; if I would experiment the influence
+of Acutenesse of edge with a Knife of Wax, applying it to cut an Oak,
+because there is no Acuteness in Wax able to cut that very hard wood.
+But yet such an Experiment of this Knife, would not be besides the
+purpose, to cut curded Milk, or other very yielding Matter: yea, in
+such like Matters, the Wax is more commodious than Steel; for finding
+the diversity depending upon Angles, more or less Acute, for that Milk
+is indifferently cut with a Raisor, and with a Knife, that hath a
+blunt edge. It needs, therefore, that regard be had, not only to the
+hardness, solidity or Gravity of Bodies, which under divers figures,
+are to divide and penetrate some Matters, but it forceth also, that
+regard be had, on the other side, to the Resistance of the Matters, to
+be divided and penetrated. But since I have in making the Experiment
+concerning our Contest; chosen a Matter which penetrates the
+Resistance of the water; and in all figures descendes to the Bottome,
+the Adversaries can charge me with no defect; yea, I have propounded
+so much a more excellent Method than they, in as much as I have
+removed all other Causes, of descending or not descending to the
+Bottom, and retained the only sole and pure variety of Figures,
+demonstrating that the same Figures all descende with the only
+alteration of a Grain in weight: which Grain being removed, they
+return to float and swim; it is not true, therefore, (resuming the
+Example by them introduced) that I have gon{e} about to experiment the
+efficacy of Acuteness, in cutting with Matters unable to cut, but with
+Matters proportioned to our occasion, since they are subjected to no
+other variety, then that alone which depends on the Figure more or
+less acute.
+
+    [42] Figure is unseperable from Corporeall Substance.
+
+    [Sidenote: The answer to the Objection against the Experiment of
+    the Wax.]
+
+But let us proceed a little farther, and observe, how that indeed the
+Consideration, which, they say, ought to be had about the Election of
+the Matter, to the end, that it may be proportionate for the making of
+our experiment, is needlessly introduced, declaring by the example of
+Cutting, that like as Acuteness is inefficient to cut, unless when it
+is in a Matter hard and apt to superate the Resistance of the wood or
+other Matter, which we intend to cut; so the aptitude of descending or
+not descending in water, ought and can only be known in those Matters,
+that are able to overcome the Renitence, and superate the Crassitude
+of the water. Unto which, I say, that to make distinction and
+election, more of this than of that Matter, on which to impress the
+Figures for cutting or penetrating this or that Body, as the solidity
+or obdurateness of the said Bodies shall be greater or less, is very
+necessary: but withall I subjoyn, that such distinction, election and
+caution would be superfluous and unprofitable, if the Body to be cut
+or penetrated, should have no Resistance, or should not at all
+withstand the Cutting or Penitration: and if the Knife were to be used
+in cutting a Mist or Smoak, one of Paper would be equally serviceable
+with one of _Damascus_ Steel: and so by reason the water hath not any
+Resistance against the Penitration of any Solid Body, all choice of
+Matter is superfluous and needless, and the Election which I said
+above to have been well made of a Matter reciprocall in Gravity to
+water, was not because it was necessary, for the overcoming of the
+crassitude of the water, but its Gravity, with which only it resists
+the sinking of Solid Bodies: and for what concerneth the Resistance of
+the crassitude, if we narrowly consider it, we shall find that all
+Solid Bodies, as well those that sink, as those that swim, are
+indifferently accomodated and apt to bring us to the knowledge of the
+truth in question. Nor will I be frighted out of the belief of these
+Conclusions, by the Experiments which may be produced against me, of
+many severall Woods, Corks, Galls, and, moreover, of subtle slates and
+plates of all sorts of Stone and Mettall, apt by means of their
+Naturall Gravity, to move towards the Centre of the Earth, the which,
+nevertheless, being impotent, either through the Figure (as the
+Adversaries thinke) or through Levity, to break and penetrate the
+Continuity of the parts of the water, and to distract its union, do
+continue to swimm without submerging in the least: nor on the other
+side, shall the Authority of _Aristotle_ move me, who in more than one
+place, affirmeth the contrary to this, which Experience shews me.
+
+    [Sidenote: No Solid of such Levity, nor of such Figure, but that
+    it doth penetrate the Crassitude of the Water.]
+
+    [Sidenote: Bodies of all Figures, laid upon the water, do
+    penetrate its Crassitude, and in what proportion.]
+
+I return, therefore, to assert, that there is not any Solid of such
+Levity, nor of such Figure, that being put upon the water, doth not
+divide and penetrate its Crassitude: yea if any with a more
+perspicatious eye, shall return to observe more exactly the thin
+Boards of Wood, he shall see them to be with part of their thickness
+under water, and not only with their inferiour Superficies, to kisse
+the Superiour of the water, as they of necessity must have believed,
+who have said, that such Boards submerge not, as not being able to
+divide the Tenacity of the parts of the water: and, moreover, he shall
+see, that subtle shivers of Ebony, Stone or Metall, when they float,
+have not only broak the Continuity of the water, but are with all
+their thickness, under the Surface of it; and more and more, according
+as the Matters are more grave: so that a thin Plate of Lead, shall be
+lower than the Surface of the circumfused water, by at least twelve
+times the thickness of the Plate, and Gold shall dive below the Levell
+of the water, almost twenty times the thickness of the Plate, as I
+shall anon declare.
+
+But let us proceed to evince, that the water yields and suffers it
+self to be penetrated by every the lightest Body; and therewithall
+demonstrate, how, even by Matters that submerge not, we may come to
+know that Figure operates nothing about the going or not going to the
+Bottom, seeing that the water suffers it self to be penetrated equally
+by every Figure.
+
+    [Sidenote: The Experiment of a Cone, demitted with its Base, and
+    after with its Point downwards.]
+
+Make a Cone, or a Piramis of Cypress, of Firre, or of other Wood of
+like Gravity, or of pure Wax, and let its height be somewhat great,
+namely a handfull, or more, and put it into the water with the Base
+downwards: first, you shall see that it will penetrate the water, nor
+shall it be at all impeded by the largeness of the Base, nor yet shall
+it sink all under water, but the part towards the point shall lye
+above it: by which shall be manifest, first, that that Solid forbeares
+not to sink out of an inability to divide the Continuity of the water,
+having already divided it with its broad part, that in the opinion of
+the Adversaries is the less apt to make the division. The Piramid
+being thus fixed, note what part of it shall be submerged, and revert
+it afterwards with the point downwards, and you shall see that it
+shall not dive into the water more than before, but if you observe how
+far it shall sink, every person expert in Geometry, may measure, that
+those parts that remain out of the water, both in the one and in the
+other Experiment are equall to an hair: whence he may manifestly
+conclude, that the acute Figure which seemed most apt to part and
+penetrate the water, doth not part or penetrate it more than the large
+and spacious.
+
+And he that would have a more easie Experiment, let him take two
+Cylinders of the same Matter, one long and small, and the other short,
+but very broad, and let him put them in the water, not distended, but
+erect and endways: he shall see, if he diligently measure the parts of
+the one and of the other, that in each of them the part submerged,
+retains exactly the same proportion to that out of the water, and that
+no greater part is submerged of that long and small one, than of the
+other more spacious and broad: howbeit, this rests upon a very large,
+and that upon a very little Superficies of water: therefore the
+diversity of Figure, occasioneth neither facility, nor difficulty, in
+parting and penetrating the Continuity of the water, and,
+consequently, cannot be the Cause of the Natation or Submersion. He
+may likewise discover the non operating of variety of Figures, in
+arising from the Bottom of the water, towards the Surface, by taking
+Wax, and tempering it with a competent quantity of the filings of
+Lead, so that it may become a considerable matter graver than the
+water: then let him make it into a Ball, and thrust it unto the Bottom
+of the water; and fasten to it as much Cork, or other light matter, as
+just serveth to raise it, and draw it towards the Surface: for
+afterwards changing the same Wax into a thin Cake, or into any other
+Figure, that same Cork shall raise it in the same manner to a hair.
+
+This silenceth not my Antagonists, but they say, that all the
+discourse hitherto made by me little importeth to them, and that it
+serves their turn, that they have demonstrated in one only particular,
+and in what matter, and under what Figure pleaseth them, namely, in a
+Board and in a Ball of Ebony, that this put in the water, descends to
+the Bottom, and that stays atop to swim: and the Matter being the
+same, and the two Bodies differing in nothing but in Figure, they
+affirm, that they have with all perspicuity demonstrated and sensibly
+manifested what they undertook; and lastly, that they have obtained
+their intent. Nevertheless, I believe, and thinke, I can demonstrate,
+that that same Experiment proveth nothing against my Conclusion.
+
+    [Sidenote: In Experiments of Natation, the Solid is to be put
+    into, not upon the water.]
+
+And first, it is false, that the Ball descends, and the Board not: for
+the Board shall also descend, if you do to both the Figures, as the
+words of our Question requireth; that is, if you put them both into
+the water.
+
+    [Sidenote: The Question of Natation stated.]
+
+  _The words were these. That the Antagonists having an opinion, that
+  the Figure would alter the Solid Bodies, in relation to the
+  descending or not descending, ascending or not ascending in the
+  same_ Medium, _as_ v. gr. _in the same water, in such sort, that, for
+  Example, a Solid that being of a Sphericall Figure, shall descend
+  to the Bottom, being reduced into some other Figure, shall not
+  descend: I holding the contrary, do affirm, that a Corporeall Solid
+  Body, which reduced into a Sphericall Figure, or any other, shall
+  go to the Bottom, shall do the like under whatsoever other Figure,
+  {&}c._
+
+    [Sidenote: Place defined according to Aristotle.]
+
+But to be in the water, implies to be placed in the water, and by
+_Aristotles_ own Definition of place, to be placed, importeth to be
+invironed by the Superficies of the Ambient Body, therefore, then
+shall the two Figures be in the water, when the Superficies of the
+water, shall imbrace and inviron them: but when the Adversaries shew
+the Board of Ebony not descending to the Bottom, they put it not into
+the water, but upon the water, where being by a certain impediment (as
+by and by we will shew) retained, it is invironed, part by water, and
+part by air, which thing is contrary to our agreement, that was, that
+the Bodies should be in the water, and not part in water, and part in
+air.
+
+  _The which is again made manifest, by the questions being put as
+  well about the things which go to the Bottom, as those which arise
+  from the Bottom to swimme, and who sees not that things placed in
+  the Bottom, must have water about them._
+
+    [Sidenote: The confutation of the Experiment in the Ebany.]
+
+It is now to be noted, that the Board of Ebany and the Ball, put into
+the water, both sink, but the Ball more swiftly, and the Board more
+slowly; and slower and slower, according as it shall be more broad and
+thin, and of this Tardity the breadth of the Figure is the true Cause:
+But these broad Boards that slowly descend, are the same, that being
+put lightly upon the water, do swimm: Therefore, if that were true
+which the Adversaries affirm, the same numerical Figure, would in the
+same numericall water, cause one while Rest, and another while Tardity
+of Motion, which is impossible: for every perticular Figure which
+descends to the Bottom[43], hath of necessity its own determinate Tardity
+and slowness, proper and naturall unto it, according to which it
+moveth, so that every other Tardity, greater or lesser is improper to
+its nature: if, therefore, a Board, as suppose of a foot square,
+descendeth naturally with six degrees of Tardity, it is impossible,
+that it should descend with ten or twenty, unless some new impediment
+do arrest it. Much less can it, by reason of the same Figure rest, and
+wholly cease to move; but it is necessary, that when ever it resteth,
+there do some greater impediment intervene than the breadth of the
+Figure. Therefore, it must be somewhat else, and not the Figure, that
+stayeth the Board of Ebany above water, of which Figure the only
+Effect is the retardment of the Motion, according to which it
+descendeth more slowly than the Ball. Let it be confessed, therefore,
+rationally discoursing, that the true and sole Cause of the Ebanys
+going to the Bottom, is the excess of its Gravity above the Gravity of
+the water: and the Cause of the greater or less Tardity, the breadth
+of this Figure, or the contractedness of that: but of its Rest, it can
+by no means be allowed, that the quallity of the Figure, is the Cause
+thereof: aswell, because, making the Tardity greater, according as the
+Figure more dilateth, there cannot be so immense a Dilatation, to
+which there may not be found a correspondent immence Tardity without
+redusing it to Nullity of Motion; as, because the Figures produced by
+the Antagonists for effecters of Rest, are the self same that do also
+go to the Bottom.
+
+    [43] Every perticular Figure hath its own peculiar Tardity.
+
+I will not omit another reason, founded also upon Experience, and if
+I deceive not my self, manifestly concluding, how that the
+Introduction of the breadth or amplitude of Figure, and the Resistance
+of the water against penetration, have nothing to do in the Effect of
+descending, or ascending, or resting in the water. [D]Take a piece of
+wood or other Matter, of which a Ball ascends from the Bottom of the
+water to the Surface, more slowly than a Ball of Ebony of the same
+bignesse, so that it is manifest, that the Ball of Ebony more readily
+divideth the water in descending, than the other in ascending; as for
+Example, let the Wood be Walnut-tree. Then take a Board of
+Walnut-tree, like and equall to that of Ebony of the Antagonists,
+which swims; and if it be true, that this floats above water, by
+reason of the Figure, unable through its breadth, to pierce the
+Crassitude of the same, the other of Wallnut-tree, without all
+question, being thrust unto the Bottom, will stay there, as less apt,
+through the same impediment of Figure, to divide the said Resistance
+of the water. But if we shall find, and by experience see, that not
+only the thin Board, but every other Figure of the same Wallnut-tree
+will return to float, as undoubtedly we shall, then I must desier my
+opposers to forbear to attribute the floating of the Ebony, unto the
+Figure of the Board, in regard that the Resistance of the water is the
+same, as well to the ascent, as to the descent, and the force of the
+Wallnut-trees ascension, is lesse than the Ebonys force in going to
+the Bottom.
+
+    [D] The Figure & Resistance of the Medium against Division, have
+    nothing to do with the Effect of Natation or Submersion, by an
+    Experiment in Wallnut tree.
+
+    [Sidenote: An Experiment in Gold, to prove the non-operating of
+    Figure in Natation and Submersion.]
+
+Nay, I will say more, that if we shall consider Gold in comparison of
+water, we shall find, that it exceeds it in Gravity almost twenty
+times, so that the Force and Impetus, wherewith a Ball of Gold goes to
+the Bottom, is very great. On the contrary, there want not matters, as
+Virgins Wax, and some Woods, which are not above a fiftieth part less
+grave than water, whereupon their Ascension therein is very slow, and
+a thousand times weaker than the _Impetus_ of the Golds descent: yet
+notwithstanding, a plate of Gold swims without descending to the
+Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin
+Board of Wood, which put in the Bottom of the Water, shall rest there
+without ascending. Now if the Figure can obstruct the Penetration, and
+impede the descent of Gold, that hath so great an _Impetus_, how can
+it choose but suffice to resist the same Penetration of the other
+matter in ascending, when as it hath scarce a thousandth part of the
+_Impetus_ that the Gold hath in descending? Its therefore, necessary,
+that that which suspends the thin Plate of Gold, or Board of Ebony,
+upon the water, be some thing that is wanting to the other Cakes and
+Boards of Matters less grave than the water; since that being put to
+the Bottom, and left at liberty, they rise up to the Surface, without
+any obstruction: But they want not for flatness and breadth of Figure:
+Therefore, the spaciousnesse of the Figure, is not that which makes
+the Gold and Ebony to swim.
+
+And, because, that the excess of their Gravity above the Gravity of
+the water, is questionless the Cause of the sinking of the flat piece
+of Ebony, and the thin Plate of Gold, when they go to the Bottom,
+therefore, of necessity, when they float, the Cause of their staying
+above water, proceeds from Levity, which in that case, by some
+Accident, peradventure not hitherto observed, cometh to meet with the
+said Board, rendering it no longer as it was before, whilst it did
+sink more ponderous than the water, but less.
+
+Now, let us return to take the thin Plate of Gold, or of Silver, or
+the thin Board of Ebony, and let us lay it lightly upon the water, so
+that it stay there without sinking, and diligently observe its effect.
+And first, see how false the assertion of _Aristotle_, and our
+oponents is, to wit, that it stayeth above water, through its
+unability to pierce and penetrate the Resistance of the waters
+Crassitude: for it will manifestly appear, not only that the said
+Plates have penetrated the water, but also that they are a
+considerable matter lower than the Surface of the same, the which
+continueth eminent, and maketh as it were a Rampert on all sides,
+round about the said Plates, the profundity of which they stay
+swimming: and, according as the said Plates shall be more grave than
+the water, two, four, ten or twenty times, it is necessary, that their
+Superficies do stay below the universall Surface of the water, so much
+more, than the thickness of those Plates, as we shal more distinctly
+shew anon. In the mean space, for the more easie understanding of what
+I say, observe with me a little the present Scheme: in which let us
+suppose the Surface of the water to be distended, according to the
+Lines F L D B, upon which if one shall put a board of matter
+specifically more grave than water, but so lightly that it submerge
+not, it shall not rest any thing above, but shall enter with its whole
+thickness into the water: and, moreover, shall sink also, as we see by
+the Board A I, O I, whose breadth is wholly sunk into the water, the
+little Ramperts of water L A and D O incompassing it, whose
+Superficies is notably higher than the Superficies of the Board. See
+now whether it be true, that the said Board goes not to the Bottom, as
+being of Figure unapt to penetrate the Crassitude of the water.
+
+[Illustration]
+
+    [Sidenote: Why solids having penitrated the Water, do not proceed
+    to a totall Submersion.]
+
+But, if it hath already penetrated, and overcome the Continuity of
+the water, & is of its own nature more grave than the said water, why
+doth it not proceed in its sinking, but stop and suspend its self
+within that little dimple or cavitie, which with its ponderosity it
+hath made in the water? I answer; because that in submerging it self,
+so far as till its Superficies come to the Levell with that of the
+water, it loseth a part of its Gravity, and loseth the rest of it as
+it submergeth & descends beneath the Surface of the water, which
+maketh Ramperts and Banks round about it, and it sustaines this loss
+by means of its drawing after it, and carrying along with it, the Air
+that is above it, and by Contact adherent to it, which Air succeeds to
+fill the Cavity that is invironed by the Ramperts of water; so that
+that which in this case descends and is placed in the water, is not
+only the Board of Ebony or Plate of Iron, but a composition of Ebony
+and Air, from which resulteth a Solid no longer superiour in Gravity
+to the water, as was the simple Ebony, or the simple Gold. And, if we
+exactly consider, what, and how great the Solid is, that in this
+Experiment enters into the water, and contrasts with the Gravity of
+the same, it will be found to be all that which we find to be beneath
+the Surface of the water, the which is an aggregate and Compound of a
+Board of Ebony, and of almost the like quantity of Air, or a Mass
+compounded of a Plate of Lead, and ten or twelve times as much Air.
+But, Gentlemen, you that are my Antagonists in our Question, we
+require the Identity of Matter, and the alteration only of the Figure;
+therefore, you must remove that Air, which being conjoyned with the
+Board, makes it become another Body less grave than the Water, and put
+only the Ebony into the Water, and you shall certainly see the Board
+descend to the Bottom; and, if that do not happen, you have got the
+day. And to seperate the Air from the Ebony[44], there needs no more but
+only to bath the Superficies of the said Board with the same Water:
+for the Water being thus interposed between the Board and the Air, the
+other circumfused Water shall run together without any impediment, and
+shall receive into it the sole and bare Ebony, as it was to do.
+
+    [44] How to seperate the Air from Solids in demitting them into
+    the water.
+
+But, me thinks I hear some of the Adversaries cunningly opposing this,
+and telling me, that they will not yield, by any means, that their
+Board be wetted, because the weight added thereto by the Water, by
+making it heavier than it was before, draws it to the Bottom, and that
+the addition of new weight is contrary to our agreement, which was,
+that the Matter be the same.
+
+To this, I answer, first; that treating of the operation of Figure
+in Bodies put into the Water, none can suppose them to be put into the
+Water without being wet; nor do I desire more to be done to the Board,
+then I will give you leave to do to the Ball. Moreover, it is untrue,
+that the Board sinks by vertue of the new Weight added to it by the
+Water, in the single and slight bathing of it: for I will put ten or
+twenty drops of Water upon the same Board, whilst it is sustained upon
+the water; which drops, because not conjoyned with the other Water
+circumfused, shall not so encrease the weight of it, as to make it
+sink: but if the Board being taken out, and all the water wiped off
+that was added thereto, I should bath all its Superficies with one
+only very small drop, and put it again upon the water, without doubt
+it shall sink, the other Water running to cover it, not being retained
+by the superiour Air; which Air by the interposition of the thin vail
+of water, that takes away its Contiguity unto the Ebony, shall without
+Renitence be seperated, nor doth it in the least oppose the succession
+of the other Water: but rather, to speak better, it shall descend
+freely; because it shall be all invironed and covered with water, as
+soon as its superiour Superficies, before vailed with water, doth
+arrive to the Levell of the universall Surface of the said water. To
+say, in the next place, that water can encrease the weight of things
+that are demitted into it, is most false; for water hath no Gravity in
+water[45], since it descends not: yea, if we would well consider what any
+immense Mass of water doth put upon a grave Body; that is placed in
+it, we shall find experimentally, that it, on the contrary, will
+rather in a great part deminish the weight of it[46], and that we may be
+able to lift an huge Stone from the Bottom of the water, which the
+water being removed, we are not able to stir. Nor let them tell me by
+way of reply, that although the superposed water augment not the
+Gravity of things that are in it, yet it increaseth the ponderosity of
+those that swim, and are part in the water and part in the Air, as is
+seen, for Example, in a Brass Ketle[47], which whilst it is empty of
+water, and replenished only with Air shall swim, but pouring of Water
+therein, it shall become so grave, that it shall sink to the Bottom,
+and that by reason of the new weight added thereto. To this I will
+return answer, as above, that the Gravity of the Water, contained in
+the Vessel is not that which sinks it to the Bottom, but the proper
+Gravity of the Brass, superiour to the Specificall Gravity of the
+Water: for if the Vessel were less grave than water, the Ocean would
+not suffice to submerge it[48]. And, give me leave to repeat it again, as
+the fundamentall and principall point in this Case, that the Air
+contained in this Vessel before the infusion of the Water, was that
+which kept it a-float[49], since that there was made of it, and of the
+Brass, a Composition less grave than an equall quantity of Water: and
+the place that the Vessel occupyeth in the Water whilst it floats, is
+not equall to the Brass alone, but to the Brass and to the Air
+together, which filleth that part of the Vessel that is below the
+Levell of the water: Moreover, when the Water is infused, the Air is
+removed, and there is a composition made of Brass and of water, more
+grave _in specie_ than the simple water, but not by vertue of the
+water infused, as having greater Specifick Gravity than the other
+water, but through the proper Gravity of the Brass, and through the
+alienation of the Air. Now, as he that should say that Brass, that by
+its nature goes to the Bottom, being formed into the Figure of a
+Ketle[50], acquireth from that Figure a vertue of lying in the Water
+without sinking, would say that which is false; because that Brass
+fashioned into any whatever Figure, goeth always to the Bottom,
+provided, that that which is put into the water be simple Brass; and
+it is not the Figure of the Vessel that makes the Brass to float, but
+it is because that that is not purely Brass which is put into the
+water, but an aggregate of Brass and of Air: so is it neither more nor
+less false, that a thin Plate of Brass or of Ebony, swims by vertue of
+its dilated & broad Figure: for the truth is, that it bares up without
+submerging, because that that which is put in the water, is not pure
+Brass or simple Ebony, but an aggregate of Brass and Air, or of Ebony
+and Air. And, this is not contrary unto my Conclusion, the which,
+(having many a time seen Vessels of Mettall, and thin pieces of
+diverse grave Matters float, by vertue of the Air conjoyned with them)
+did affirm, That Figure was not the Cause of the Natation or
+Submersion of such Solids as were placed in the water. Nay more, I
+cannot omit, but must tell my Antagonists, that this new conceit of
+denying that the Superficies of the Board should be bathed, may beget
+in a third person an opinion of a poverty of Arguments of defence on
+their part, since that such bathing was never insisted upon by them in
+the beginning of our Dispute, and was not questioned in the least,
+being that the Originall of the discourse arose upon the swiming of
+Flakes of Ice, wherein it would be simplicity to require that their
+Superficies might bedry: besides, that whether these pieces of Ice be
+wet or dry they alwayes swim, and as the Adversaries say, by reason of
+the Figure.
+
+    [45] Water hath no Gravity in Water.
+
+    [46] Water deminisheth the Gravity of Solids immerged therein.
+
+    [47] The Experiment of a brass Ketle swiming when empty, & sinking
+    when full, alledged to prove that water gravitates in water,
+    answered.
+
+    [48] An Ocean sufficeth not to sink a Vessel specifically less
+    grave than water.
+
+    [49] Air, the Cause of the Natation of empty Vessels of Matters
+    graver _in specie_ than the water.
+
+    [50] Neither Figure, nor the breadth of Figure, is the Cause of
+    Natation.
+
+Some peradventure, by way of defence, may say, that wetting the Board
+of Ebony, and that in the superiour Superficies, it would, though of
+it self unable to pierce and penetrate the water, be born downwards,
+if not by the weight of the additionall water, at least by that desire
+and propension that the superiour parts of the water have to re-unite
+and rejoyn themselves: by the Motion of which parts, the said Board
+cometh in a certain manner, to be depressed downwards.
+
+    [Sidenote: The Bathed Solid descends not out of any affectation
+    of union in the upper parts of the water.]
+
+This weak Refuge will be removed, if we do but consider, that the
+repugnancy of the inferiour parts of the water, is as great against
+Dis-union, as the Inclination of its superiour parts is to union: nor
+can the uper unite themselves without depressing the board, nor can it
+descend without disuniting the parts of the nether Water: so that it
+doth follow, by necessary consequence, that for those respects, it
+shall not descend. Moreover, the same that may be said of the upper
+parts of the water, may with equall reason be said of the nether,
+namely, that desiring to unite, they shall force the said Board
+upwards.
+
+Happily, some of these Gentlemen that dissent from me, will wonder,
+that I affirm, that the contiguous superiour Air is able to sustain
+that Plate of Brass or of Silver, that stayeth above water; as if I
+would in a certain sence allow the Air[51], a kind of Magnetick vertue of
+sustaining the grave Bodies, with which it is contiguous. To satisfie
+all I may, to all doubts, I have been considering how by some other
+sensible Experiment I might demonstrate, how truly that little
+contiguous and superiour Air sustaines those Solids, which being by
+nature apt to descend to the Bottom, being placed lightly on the water
+submerge not, unless they be first thorowly bathed; and have found,
+that one of these Bodies having descended to the Bottom, by
+conveighing to it (without touching it in the least) a little Air,
+which conjoyneth with the top of the same, it becometh sufficient, not
+only, as before to sustain it, but also to raise it, and to carry it
+back to the top, where it stays and abideth in the same manner, till
+such time, as the assistance of the conjoyned Air is taken away. And
+to this effect, I have taken a Ball of Wax, and made it with a little
+Lead, so grave, that it leasurely descends to the Bottom, making with
+all its Superficies very smooth and pollite: and this being put gently
+into the water, almost wholly submergeth, there remaining vissible
+only a little of the very top[52], the which so long as it is conjoyned
+with the Air, shall retain the Ball a-top, but the Contiguity of the
+Air taken away by wetting it, it shall descend to the Bottom and there
+remain. Now to make it by vertue of the Air, that before sustained it
+to return again to the top, and stay there, thrust into the water a
+Glass reversed with the mouth downwards, the which shall carry with it
+the Air it contains, and move this towards the Ball, abasing it till
+such time that you see, by the transparency of the Glass, that the
+contained Air do arrive to the summity of the _B_all[53]: then gently
+withdraw the Glass upwards, and you shall see the _B_all to rise, and
+afterwards stay on the top of the water[54], if you carefully part the
+Glass and the water without overmuch commoving and disturbing it.
+There is, therefore, a certain affinity between the Air and other
+Bodies, which holds them unied, so, that they seperate not without a
+kind of violence. The same likewise is seen in the water[55]; for if we
+shall wholly submerge some Body in it, so that it be thorowly bathed,
+in the drawing of it afterwards gently out again, we shall see the
+water follow it, and rise notably above its Surface, before it
+seperates from it. Solid Bodies, also[56], if they be equall and alike in
+Superficies, so, that they make an exact Contact without the
+interposition of the least Air, that may part them in the seperation
+and yield untill that the ambient _Medium_ succeeds to replenish the
+place, do hold very firmly conjoyned, and are not to be seperated
+without great force but, because, the Air, Water, and other Liquids,
+very expeditiously shape themselves to contact with any Solid
+_B_odies, so that their Superficies do exquisitely adopt themselves to
+that of the Solids, without any thing remaining between them,
+therefore, the effect of this Conjunction and Adherence is more
+manifestly and frequently observed in them, than in hard and
+inflexible Bodies, whose Superficies do very rarely conjoyn with
+exactness of Contact[57]. This is therefore that Magnetick vertue, which
+with firm Connection conjoyneth all Bodies, that do touch without the
+interposition of flexible fluids; and, who knows, but that that a
+Contact, when it is very exact, may be a sufficient Cause of the Union
+and Continuity of the parts of a naturall _B_ody?
+
+    [51] _A_ Magnetisme in the _A_ir, by which it bears up those
+    Solids in the water, that are contiguous with it.
+
+    [52] The Effect of the Airs Contiguity in the Natation of Solids.
+
+    [53] The force of Contact.
+
+    [54] _A_n Affectation of Conjunction betwixt Solids and the Air
+    contiguous to them.
+
+    [55] The like affectation of Conjunction betwixt Solids & the
+    water.
+
+    [56] Also the like affectation and Conjunction betwixt Solids
+    themselves.
+
+    [57] Contact may be the Cause of the Continuity of Naturall
+    Bodies.
+
+Now, pursuing my purpose, I say; that it needs not, that we have
+recourse to the Tenacity, that the parts of the water have amongst
+themselves, by which they resist and oppose Division, Distraction, and
+Seperation, because there is no such Coherence and Resistance of
+Division for if there were, it would be no less in the internall parts
+than in those nearer the superiour or externall Surface, so that the
+same Board, finding alwayes the same Resistance and Renitence, would
+no less stop in the middle of the water than about the Surface, which
+is false. Moreover, what Resistance can we place in the Continuity of
+the water, if we see that it is impossible to find any Body of
+whatsoever Matter, Figure or Magnitude, which being put into the
+water, shall be obstructed and impeded by the Tenacity of the parts of
+the water to one another, so, but that it is moved upwards or
+downwards, according as the Cause of their Motion transports it? And,
+what greater proof of it can we desier, than that which we daily see
+in Muddy waters, which being put into Vessels to be drunk, and being,
+after some hours setling[58], still, as we say, thick in the end, after
+four or six dayes they are wholly setled, and become pure and clear?
+Nor can their Resistance of Penetration stay those impalpable and
+insensible Atomes of Sand, which by reason of their exceeding small
+force, spend six dayes in descending the space of half a yard.
+
+    [58] The settlement of _M_uddy Water, proveth that that Element
+    hath no aversion to Division.
+
+  _Nor let them say, that the seeing of such small Bodies, consume
+  six dayes in descending so little a way, is a sufficient Argument
+  of the Waters Resistance of Division; because that is no resisting
+  of Division, but a retarding of Motion; and it would be simplicity
+  to say, that a thing opposeth Division[59], and that in the same
+  instant, it permits it self to be divided: nor doth the Retardation
+  of Motion at all favour the Adversaries cause, for that they are to
+  instance in a thing that wholly prohibiteth Motion, and procureth
+  Rest; it is necessary, therefore, to find out Bodies that stay in
+  the water, if one would shew its repugnancy to Division, and not
+  such as move in it, howbeit but slowly._
+
+    [59] Water cannot oppose division, and at the same time permit it
+    self to be divided.
+
+What then is this Crassitude of the water, with which it resisteth
+Division? What, I beseech you, should it be, if we (as we have said
+above) with all diligence attempting the reduction of a Matter into so
+like a Gravity with the water, that forming it into a dilated Plate it
+rests suspended as we have said, between the two waters, it be
+impossible to effect it, though we bring them to such an
+Equiponderance, that as much Lead as the fourth part of a Grain of
+Musterd-seed, added to the same expanded Plate, that in Air [_i. e.
+out of the water_] shall weigh four or six pounds, sinketh it to the
+Bottom, and being substracted, it ascends to the Surface of the water?
+I cannot see, (if what I say be true, as it is most certain) what
+minute vertue and force we can possibly find or imagine, to which the
+Resistance of the water against Division and Penetration is not
+inferiour; whereupon, we must of necessity conclude that it is
+nothing: because, if it were of any sensible power, some large Plate
+might be found or compounded of a Matter alike in Gravity to the
+water, which not only would stay between the two waters; but,
+moreover, should not be able to descend or ascend without notable
+force. We may likewise collect the same from an other Experiment[60],
+shewing that the Water gives way also in the same manner to
+transversall Division; for if in a setled and standing water we should
+place any great Mass that goeth not to the bottom, drawing it with a
+single Womans Hair, we might carry it from place to place without any
+opposition, and this whatever Figure it hath, though that it possess a
+great space of water, as for instance, a great Beam would do moved
+side-ways. Perhaps some might oppose me and say, that if the
+Resistance of water against Division, as I affirm, were nothing; Ships
+should not need such a force of Oars and Sayles for the moving of them
+from place to place in a tranquile Sea, or standing Lake. To him that
+should make such an objection, I would reply[61], that the water
+contrasteth not against, nor simply resisteth Division, but a sudden
+Division, and with so much greater Renitence, by how much greater the
+Velocity is: and the Cause of this Resistance depends not on
+Crassitude, or any other thing that absolutely opposeth Division, but
+because that the parts of the water divided, in giving way to that
+Solid that is moved in it, are themselves also necessitated locally to
+move, some to the one side, and some to the other, and some downwards:
+and this must no less be done by the waves before the Ship, or other
+Body swimming through the water, than by the posteriour and
+subsequent; because, the Ship proceeding forwards, to make it self a
+way to receive its Bulk, it is requisite, that with the Prow it
+repulse the adjacent parts of the water, as well on one hand as on the
+other, and that it move them as much transversly, as is the half of
+the breadth of the Hull: and the like removall must those waves make,
+that succeeding the Poump do run from the remoter parts of the Ship
+towards those of the middle, successively to replenish the places,
+which the Ship in advancing forwards, goeth, leaving vacant. Now,
+because, all Motitions are made in Time[62], and the longer in greater
+time: and it being moreover true, that those Bodies that in a certain
+time are moved by a certain power such a certain space, shall not be
+moved the same space, and in a shorter Time, unless by a greater
+Power: therefore, the broader Ships move slower than the narrower,
+being put on by an equall Force: and the same Vessel requires so much
+greater force of Wind, or Oars, the faster it is to move.
+
+    [60] An hair will draw a great Mass thorow the Water; which
+    proveth, that it hath no Resistance against transversall
+    Division.
+
+    [61] How ships are moved in the water.
+
+    [62] Bodies moved a certain space in a certain Time, by a
+    certain power, cannot be moved the same space and in a shorter
+    time, but by a greater power.
+
+  _But yet for all this, any great Mass swimming in a standing Lake,
+  may be moved by any petit force; only it is true, that a lesser
+  force more slowly moves it: but if the waters Resistance of
+  Division, were in any manner sensible, it would follow, that the
+  said Mass, should, notwithstanding the percussion of some sensible
+  force, continue immoveable, which is not so[63]. Yea, I will say
+  farther, that should we retire our selves into the more internall
+  contemplation of the Nature of water and other Fluids, perhaps we
+  should discover the Constitution of their parts to be such, that
+  they not only do not oppose Division, but that they have not any
+  thing in them to be divided: so that the Resistance that is
+  observed in moving through the water[64], is like to that which we meet
+  with in passing through a great Throng of People, wherein we find
+  impediment, and not by any difficulty in the Division, for that
+  none of those persons are divided whereof the Croud is composed,
+  but only in moving of those persons side-ways which were before
+  divided and disjoyned: and thus we find Resistance in thrusting a
+  Stick into an heap of Sand, not because any part of the Sand is to
+  be cut in pieces, but only to be moved and raised[65]. Two manners of
+  Penetration, therefore, offer themselves to us, one in Bodies,
+  whose parts were continuall, and here Division seemeth necessary,
+  the other in the aggregates of parts not continuall, but contiguous
+  only[66], and here there is no necessity of dividing but of moving
+  only. Now, I am not well resolved, whether water and other Fluids
+  may be esteemed to be of parts continuall or contiguous only[67]; yet I
+  find my self indeed inclined to think that they are rather
+  contiguous (if there be in Nature no other manner of aggregating,
+  than by the union, or by the touching of the extreams:) and I am
+  induced thereto by the great difference that I see between the
+  Conjunction of the parts of an hard or Solid Body[68], and the
+  Conjunction of the same parts when the same Body shall be made
+  Liquid and Fluid: for if, for example, I take a Mass of Silver or
+  other Solid and hard Mettall, I shall in dividing it into two
+  parts, find not only the resistance that is found in the moving of
+  it only[69], but an other incomparably greater, dependent on that
+  vertue, whatever it be, which holds the parts united: and so if we
+  would divide again those two parts into other two, and successively
+  into others and others, we should still find a like Resistance, but
+  ever less by how much smaller the parts to be divided shall be; but
+  if, lastly, employing most subtile and acute Instruments, such as
+  are the most tenuous parts of the Fire, we shall resolve it
+  (perhaps) into its last and least Particles, there shall not be
+  left in them any longer either Resistance of Division, or so much
+  as a capacity of being farther divided, especially by Instruments
+  more grosse than the acuities of Fire: and what Knife or Rasor put
+  into well melted Silver can we finde, that will divide a thing
+  which surpasseth the separating power of Fire? Certainly none:
+  because either the whole shall be reduced to the most minute and
+  ultimate Divisions, or if there remain parts capable still of other
+  Subdidivisions, they cannot receive them, but only from acuter
+  Divisors than Fire; but a Stick or Rod of Iron, moved in the melted
+  Metall, is not such a one. Of a like Constitution and Consistence,
+  I account the parts of Water[70], and other Liquids to be, namely,
+  incapable of Division by reason of their Ienuity; or if not
+  absolutely indivisible, yet at least not to be divided by a Board,
+  or other Solid Body, palpable unto the hand, the Sector being
+  alwayes required to be more sharp than the Solid to be cut. Solid
+  Bodies, therefore, do only move, and not divide the Water[71], when put
+  into it; whose parts being before divided to the extreamest
+  minuity, and therefore capable of being moved, either many of them
+  at once, or few, or very few, they soon give place to every small
+  Corpuscle, that descends in the same: for that, it being little and
+  light, descending in the Air, and arriving to the Surface of the
+  Water, it meets with Particles of Water more small, and of less
+  Resistance against Motion and Extrusion, than is its own prement
+  and extrusive force; whereupon it submergeth, and moveth such a
+  portion of them, as is proportionate to its Power. There is not,
+  therefore, any Resistance in Water against Division, nay, there is
+  not in it any divisible parts. I adde; moreover, that in case yet
+  there should be any small Resistance found (which is absolutely
+  false)[72] haply in attempting with an Hair to move a very great natant
+  Machine, or in essaying by the addition of one small Grain of Lead
+  to sink, or by removall of it to raise a very broad Plate of
+  Matter, equall in Gravity with Water, (which likewise will not
+  happen, in case we proceed with dexterity) we may observe that that
+  Resistance is a very different thing from that which the
+  Adversaries produce for the Cause of the Natation of the Plate of
+  Lead or Board of Ebony, for that one may make a Board of Ebony,
+  which being put upon the Water swimmeth, and cannot be submerged,
+  no not by the addition of an hundred Grains of Lead put upon the
+  same, and afterwards being bathed, not only sinks, though the said
+  Lead be taken away, but though moreover a quantity of Cork, or of
+  some other light Body fastened to it, sufficeth not to hinder it
+  from sinking unto the bottome: so that you see, that although it
+  were granted that there is a certain small Resistance of Division
+  found in the substance of the Water, yet this hath nothing to do
+  with that Cause which supports the Board above the Water, with a
+  Resistance an hundred times greater than that which men can find in
+  the parts of the Water: nor let them tell me, that only the Surface
+  of the Water hath such Resistance[73], and not the internall parts, or
+  that such Resistance is found greatest in the beginning of the
+  Submersion, as it also seems that in the beginning, Motion meets
+  with greater opposition, than in the continuance of it; because,
+  first, I will permit, that the Water be stirred, and that the
+  superiour parts be mingled with the middle[74], and inferiour parts, or
+  that those above be wholly removed, and those in the middle only
+  made use off, and yet you shall see the effect for all that, to be
+  still the same: Moreover, that Hair which draws a Beam through the
+  Water, is likewise to divide the upperparts, and is also to begin
+  the Motion, and yet it begins it, and yet it divides it: and
+  finally, let the Board of Ebony be put in the midway, betwixt the
+  bottome and the top of the Water, and let it there for awhile be
+  suspended and setled, and afterwards let it be left at liberty, and
+  it will instantly begin its Motion, and will continue it unto the
+  bottome. Nay, more, the Board so soon as it is dimitted upon the
+  Water, hath not only begun to move and divide it, but is for a good
+  space dimerged into it._
+
+    [63] The parts of Liquids, so farre from resisting Division, that
+    they contain not any thing that may be divided.
+
+    [64] The Resistance a Solid findeth in moving through the water,
+    like to that we meet with in passing through a throng of people:
+
+    [65] Or in thrusting a Stick into an heap of Sand.
+
+    [66] Two kinds of Penetration, one in Bodies continuall, the other
+    in Bodies only contiguous.
+
+    [67] Water consists not of continuall, but only of contiguous
+    parts.
+
+    [68] _Se{e} what satisfaction he hath given, as to this point, in
+    Lib. de Motu. Dial. 2._
+
+    [69] Great difference betwixt the Conjunction of the parts of a
+    Body when Solid, and when fluid.
+
+    [70] Water consists of parts that admit of no farther division.
+
+    [71] Solids dimitted into the water, do onely move, and not divide
+    it.
+
+    [72] If there were any Resistance of Division in water, it must
+    needs be small, in that it is overcome by an Hair, a Grain of
+    Lead, or a slight bathing of the Solid.
+
+    [73] The uper parts of the Water, do no more resist Division than
+    the middle or lower parts.
+
+    [74] Waters Resistance of division, not greater in the beginning
+    of the Submersion.
+
+Let us receive it, therefore, for a true and undoubted Conclusion,
+That the Water hath not any Renitence against simple Division, and
+that it is not possible to find any Solid Body, be it of what Figure
+it will, which being put into the Water, its Motion upwards or
+downwards, according as it exceedeth, or shall be exceeded by the
+Water in Gravity (although such excesse and difference be insensible)
+shall be prohibited, and taken away, by the Crassitude of the said
+Water. When, therefore, we see the Board of Ebony, or of other Matter,
+more grave than the Water, to stay in the Confines of the Water and
+Air, without submerging, we must have recourse to some other
+Originall, for the investing the Cause of that Effect, than to the
+breadth of the Figure, unable to overcome the Renitence with which the
+Water opposeth Division, since there is no Resistance; and from that
+which is not in being, we can expect no Action. It remains most true,
+therefore, as we have said before, that this so succeds, for that that
+which in such manner put upon the water, not the same Body with that
+which is put _into_ the Water: because this which is put _into_ the
+Water, is the pure Board of Ebony, which for that it is more grave
+than the Water, sinketh, and that which is put _upon_ the Water, is a
+Composition of Ebony, and of so much Air, that both together are
+specifically less grave than the Water, and therefore they do not
+descend.
+
+I will farther confirm this which I say. Gentlemen, my Antagonists, we
+are agreed, that the excess or defect of the Gravity of the Solid,
+unto the Gravity of the Water, is the true and proper Cause of
+Natation or Submersion.
+
+    [Sidenote: Great Caution to be had in experimenting the operation
+    of Figure in Natation.]
+
+Now, if you will shew that besides the former Cause, there is another
+which is so powerfull, that it can hinder and remove the Submersion of
+those very Solids, that by their Gravity sink, and if you will say,
+that this is the breadth or ampleness of Figure, you are oblieged,
+when ever you would shew such an Experiment, first to make the
+circumstances certain, that that Solid which you put into the Water,
+be not less grave _in specie_ than it, for if you should not do so,
+any one might with reason say, that not the Figure, but the Levity was
+the cause of that Natation. But I say, that when you shall dimit a
+Board of Ebony into the Water, you do not put therein a Solid more
+grave _in specie_ than the Water, but one lighter, for besides the
+Ebony, there is in the Water a Mass of Air, united with the Ebony, and
+such, and so light, that of both there results a Composition less
+grave than the Water: See, therefore, that you remove the Air, and put
+the Ebony alone into the Water, for so you shall immerge a Solid more
+grave then the Water, and if this shall not go to the Bottom, you have
+well Philosophized and I ill.
+
+Now, since we have found the true Cause of the Natation of those
+Bodies, which otherwise, as being graver than the Water, would descend
+to the bottom, I think, that for the perfect and distinct knowledge of
+this business, it would be good to proceed in a way of discovering
+demonstratively those particular Accidents that do attend these
+effects, and,
+
+
+
+
+PROBL. I.
+
+    [Sidenote: To finde the proportion Figures ought to have to the
+    waters Gravity, that by help of the contiguous Air, they may
+    swim.]
+
+  _To finde what proportion severall Figures of different Matters
+    ought to have, unto the Gravity of the Water, that so they may be
+    able by vertue of the Contiguous Air to stay afloat._
+
+
+[Illustration]
+
+Let, therefore, for better illustration, D F N E be a Vessell,
+wherein the water is contained, and suppose a Plate or Board, whose
+thickness is comprehended between the Lines I C and O S, and let it be
+of Matter exceeding the water in Gravity, so that being put upon the
+water, it dimergeth and abaseth below the Levell of the said water,
+leaving the little Banks A I and B C, which are at the greatest height
+they can be, so that if the Plate I S should but descend any little
+space farther, the little Banks or Ramparts would no longer consist,
+but expulsing the Air A I C B, they would diffuse themselves over the
+Superficies I C, and would submerge the Plate. The height A I B C is
+therefore the greatest profundity that the little Banks of water admit
+of. Now I say, that from this, and from the proportion in Gravity,
+that the Matter of the Plate hath to the water, we may easily finde of
+what thickness, at most, we may make the said Plates, to the end, they
+may be able to bear up above water: for if the Matter of the Plate or
+Board I S were, for Example, as heavy again as the water, a Board of
+that Matter shall be, at the most of a thickness equall to the
+greatest height of the Banks, that is, as thick as A I is high: which
+we will thus demonstrate. Let the Solid I S be double in Gravity to
+the water, and let it be a regular Prisme, or Cylinder, to wit, that
+hath its two flat Superficies, superiour and inferiour, alike and
+equall, and at Right Angles with the other laterall Superficies, and
+let its thickness I O be equall to the greatest Altitude of the Banks
+of water: I say, that if it be put upon the water, it will not
+submerge: for the Altitude A I being equall to the Altitude I O, the
+Mass of the Air A B C I shall be equall to the Mass of the Solid C I O
+S: and the whole Mass A O S B double to the Mass I S; And since the
+Mass of the Air A C, neither encreaseth nor diminisheth the Gravity of
+the Mass I S, and the Solid I S was supposed double in Gravity to the
+water; Therefore as much water as the Mass submerged A O S B,
+compounded of the Air A I C B, and of the Solid I O S C, weighs just
+as much as the same submerged Mass A O S B: but when such a Mass of
+water, as is the submerged part of the Solid, weighs as much as the
+said Solid, it descends not farther, but resteth, as by (_a_)
+_Archimedes_[75], and above by us, hath been demonstrated: Therefore, I S
+shall descend no farther, but shall rest. And if the Solid I S shall
+be Sesquialter in Gravity to the water, it shall float, as long as its
+thickness be not above twice as much as the greatest Altitude of the
+Ramparts of water, that is, of A I. For I S being Sesquialter in
+Gravity to the water, and the Altitude O I, being double to I A, the
+Solid submerged A O S B, shall be also Sesquialter in Mass to the
+Solid I S. And because the Air A C, neither increaseth nor diminisheth
+the ponderosity of the Solid I S: Therefore, as much water in quantity
+as the submerged Mass A O S B, weighs as much as the said Mass
+submerged: And, therefore, that Mass shall rest. And briefly in
+generall.
+
+    [75] Of Natation Lib. 1. Prop. 3.
+
+[Illustration]
+
+
+
+
+THEOREME. VI.
+
+    [Sidenote: The proportion of the greatest thickness of Solids,
+    beyond which encreased they sink.]
+
+  _When ever the excess of the Gravity of the Solid above the Gravity
+    of the Water, shall have the same proportion to the Gravity of
+    the Water, that the Altitude of the Rampart, hath to the
+    thickness of the Solid, that Solid shall not sink, but being
+    never so little thicker it shall._
+
+
+[Illustration]
+
+Let the Solid I S be superior in Gravity to the water, and of such
+thickness, that the Altitude of the Rampart A I, be in proportion to
+the thickness of the Solid I O, as the excess of the Gravity of the
+said Solid I S, above the Gravity of a Mass of water equall to the
+Mass I S, is to the Gravity of the Mass of water equall to the Mass I
+S. I say, that the Solid I S shall not sinke, but being never so
+little thicker it shall go to the bottom: For being that as A I is to
+I O, so is the Excess of the Gravity of the Solid I S, above the
+Gravity of a Mass of water equall to the Mass I S, to the Gravity of
+the said Mass of water: Therefore, compounding, as A O is to O I, so
+shall the Gravity of the Solid I S, be to the Gravity of a Mass of
+water equall to the Mass I S: And, converting, as I O is to O A, so
+shall the Gravity of a Mass of water equall to the Mass I S, be to the
+Gravity of the Solid I S: But as I O is to O A, so is a Mass of water
+I S, to a Mass of water equall to the Mass A B S O: and so is the
+Gravity of a Mass of water I S, to the Gravity of a Mass of water A S:
+Therefore as the Gravity of a Mass of water, equall to the Mass I S,
+is to the Gravity of the Solid I S, so is the same Gravity of a Mass
+of water I S, to the Gravity of a Mass of Water A S: Therefore the
+Gravity of the Solid I S, is equall to the Gravity of a Mass of water
+equall to the Mass A S: But the Gravity of the Solid I S, is the same
+with the Gravity of the Solid A S, compounded of the Solid I S, and of
+the Air A B C I. Therefore the whole compounded Solid A O S B, weighs
+as much as the water that would be comprised in the place of the said
+Compound A O S B: And, therefore, it shall make an _Equilibrium_ and
+rest, and that same Solid I O S C shall sinke no farther. But if its
+thickness I O should be increased, it would be necessary also to
+encrease the Altitude of the Rampart A I, to maintain the due
+proportion: But by what hath been supposed, the Altitude of the
+Rampart A I, is the greatest that the Nature of the Water and Air do
+admit, without the waters repulsing the Air adherent to the
+Superficies of the Solid I C, and possessing the space A I C B:
+Therefore, a Solid of greater thickness than I O, and of the same
+Matter with the Solid I S, shall not rest without submerging, but
+shall descend to the bottome: which was to be demonstrated. In
+consequence of this that hath been demonstrated, sundry and various
+Conclusions may be gathered, by which the truth of my principall
+Proposition comes to be more and more confirmed, and the imperfection
+of all former Argumentations touching the present Question cometh to
+be discovered.
+
+_And first we gather from the things demonstrated, that,_
+
+
+
+
+THEOREME VII.
+
+    [Sidenote: The heaviest Bodies may swimme.]
+
+  _All Matters, how heavy soever, even to Gold it self, the heaviest
+    of all Bodies, known by us, may float upon the Water._
+
+
+Because its Gravity being considered to be almost twenty times greater
+than that of the water, and, moreover, the greatest Altitude that the
+Rampart of water can be extended to, without breaking the Contiguity
+of the Air, adherent to the Surface of the Solid, that is put upon the
+water being predetermined, if we should make a Plate of Gold so thin,
+that it exceeds not the nineteenth part of the Altitude of the said
+Rampart, this put lightly upon the water shall rest, without going to
+the bottom: and if Ebony shall chance to be in sesquiseptimall
+proportion more grave than the water, the greatest thickness that can
+be allowed to a Board of Ebony, so that it may be able to stay above
+water without sinking, would be seaven times more than the height of
+the Rampart Tinn, _v. gr._ eight times more grave than water, shall
+swimm as oft as the thickness of its Plate, exceeds not the 7th part
+of the Altitude of the Rampart.
+
+    [Sidenote: _He elsewhere cites this as a Proposition, therefore I
+    make it of that number._]
+
+And here I will not omit to note, as a second Corrollary dependent
+upon the things demonstrated, that,
+
+
+
+
+THEOREME VIII.
+
+    [Sidenote: Natation and Submersion, collected from the thickness,
+    excluding the length and breadth of Plates.]
+
+  _The Expansion of Figure not only is not the Cause of the Natation
+    of those grave Bodies, which otherwise do submerge, but also the
+    determining what be those Boards of Ebony, or Plates of Iron or
+    Gold that will swimme, depends not on it, rather that same
+    determination is to be collected from the only thickness of those
+    Figures of Ebony or Gold, wholly excluding the consideration of
+    length and breadth, as having no wayes any share in this Effect._
+
+
+It hath already been manifested, that the only cause of the Natation
+of the said Plates, is the reduction of them to be less grave than the
+water, by means of the connexion of that Air, which descendeth
+together with them, and possesseth place in the water; which place so
+occupyed, if before the circumfused water diffuseth it self to fill
+it, it be capable of as much water, as shall weigh equall with the
+Plate, the Plate shall remain suspended, and sinke no farther.
+
+Now let us see on which of these three dimensions of the Solid
+depends the terminating, what and how much the Mass of that ought to
+be, that so the assistance of the Air contiguous unto it, may suffice
+to render it specifically less grave than the water, whereupon it may
+rest without Submersion. It shall undoubtedly be found, that the
+length and breadth have not any thing to do in the said determination,
+but only the height, or if you will the thickness: for, if we take a
+Plate or Board, as for Example, of Ebony, whose Altitude hath unto the
+greatest possible Altitude of the Rampart, the proportion above
+declared, for which cause it swims indeed, but yet not if we never so
+little increase its thickness; I say, that retaining its thickness,
+and encreasing its Superficies to twice, four times, or ten times its
+bigness, or dminishing it by dividing it into four, or six, or twenty,
+or a hundred parts, it shall still in the same manner continue to
+float: but encreasing its thickness only a Hairs breadth, it will
+alwaies submerge, although we should multiply the Superficies a
+hundred and a hundred times. Now forasmuch as that this is a Cause,
+which being added, we adde also the Effect, and being removed, it is
+removed; and by augmenting or lessening the length or breadth in any
+manner, the effect of going, or not going to the bottom, is not added
+or removed: I conclude, that the greatness and smalness of the
+Superficies hath no influence upon the Natation or Submersion. And
+that the proportion of the Altitude of the Ramparts of Water, to the
+Altitude of the Solid, being constituted in the manner aforesaid, the
+greatness or smalness of the Superficies, makes not any variation, is
+manifest from that which hath been above demonstrated, and from this,
+that, _The Prisms and Cylinders which have the same Base, are in
+proportion to one another as their heights._ Whence Cylinders or
+Prismes[76], namely, the Board, be they great or little, so that they be
+all of equall thickness, have the same proportion to their
+Conterminall Air, which hath for Base the said Superficies of the
+Board, and for height the Ramparts of water; so that alwayes of that
+Air, and of the Board, Solids, are compounded, that in Gravity equall
+a Mass of water equall to the Mass of the Solids, compounded of Air,
+and of the Board: whereupon all the said Solids do in the same manner
+continue afloat. We will conclude in the third place, that,
+
+    [76] Prismes and Cylinders having the same Base, are to one
+    another as their heights.
+
+
+
+
+THEOREME. IX.
+
+    [Sidenote: All Figures of all Matters, float by hep of the
+    Rampart replenished with Air, and some but only touch the water.]
+
+  _All sorts of Figures of whatsoever Matter, albeit more grave than
+    the Water, do by Benefit of the said Rampart, not only float, but
+    some Figures, though of the gravest Matter, do stay wholly above
+    Water, wetting only the inferiour Surface that toucheth the
+    Water._
+
+
+And these shall be all Figures, which from the inferiour Base upwards,
+grow lesser and lesser; the which we shall exemplifie for this time in
+Piramides or Cones, of which Figures the passions are common. We will
+demonstrate therefore, that,
+
+  _It is possible to form a Piramide, of any whatsoever Matter
+  preposed, which being put with its Base upon the Water, rests not
+  only without submerging, but without wetting it more then its
+  Base._
+
+For the explication of which it is requisite, that we first
+demonstrate the subsequent Lemma, namely, that,
+
+
+
+
+LEMMA II.
+
+    [Sidenote: Solids whose Masses are in contrary proportion to
+    their Specifick Gravities are equall in absolute Gravity.]
+
+  _Solids whose Masses answer in proportion contrarily to their
+    Specificall Gravities, are equall in Absolute Gravities._
+
+
+[Illustration]
+
+Let A C and B be two Solids, and let the Mass A C be to the Mass B,
+as the Specificall Gravity of the Solid B, is to the Specificall
+Gravity of the Solid A C: I say, the Solids A C and B are equall in
+absolute weight, that is, equally grave. For if the Mass A C be equall
+to the Mass B, then, by the Assumption, the Specificall Gravity of B,
+shall be equall to the Specificall Gravity of A C, and being equall in
+Mass, and of the same Specificall Gravity they shall absolutely weigh
+one as much as another. But if their Masses shall be unequall, let the
+Mass A C be greater, and in it take the part C, equall to the Mass B.
+And, because the Masses B and C are equall; the Absolute weight of B,
+shall have the same proportion to the Absolute weight of C, that the
+Specificall Gravity of B, hath to the Specificall Gravity of C; or of
+C A, which is the same _in specie_: But look what proportion the
+Specificall Gravity of B, hath to the Specificall Gravity of C A, the
+like proportion, by the Assumption, hath the Mass C A, to the Mass B,
+that is, to the Mass C: Therefore, the absolute weight of B, to the
+absolute weight of C, is as the Mass A C to the Mass C: But as the
+Mass A C, is to the Mass C, so is the absolute weight of A C, to the
+absolute weight of C: Therefore the absolute weight of B, hath the
+same proportion to the absolute weight of C, that the absolute weight
+of A C, hath to the absolute weight of C: Therefore, the two Solids A
+C and B are equall in absolute Gravity: which was to be demonstrated.
+Having demonstrated this, I say,
+
+
+
+
+THEOREME X.
+
+    [Sidenote: There may be Cones and Piramides of any Matter, which
+    demitted into the water, rest only their Bases.]
+
+  _That it is possible of any assigned Matter, to form a Piramide or
+    Cone upon any Base, which being put upon the Water shall not
+    submerge, nor wet any more than its Base._
+
+
+[Illustration]
+
+Let the greatest possible Altitude of the Rampart be the Line D B,
+and the Diameter of the Base of the Cone to be made of any Matter
+assigned B C, at right angles to D B: And as the Specificall Gravity
+of the Matter of the Piramide or Cone to be made, is to the
+Specificall Gravity of the water, so let the Altitude of the Rampart D
+B, be to the third part of the Piramide or Cone A B C, described upon
+the Base, whose Diameter is B C: I say, that the said Cone A B C, and
+any other Cone, lower then the same, shall rest upon the Surface of
+the water B C without sinking. Draw D F parallel to B C, and suppose
+the Prisme or Cylinder E C, which shall be tripple to the Cone A B C.
+And, because the Cylinder D C hath the same proportion to the Cylinder
+C E, that the Altitude D B, hath to the Altitude B E: But the Cylinder
+C E, is to the Cone A B C, as the Altitude E B is to the third part of
+the Altitude of the Cone: Therefore, by Equality of proportion, the
+Cylinder D C is to the Cone A B C, as D B is to the third part of the
+Altitude B E: But as D B is to the third part of B E, so is the
+Specificall Gravity of the Cone A B C, to the Specificall Gravity of
+the water: Therefore, as the Mass of the Solid D C, is to the Mass of
+the Cone A _B_ C, so is the Specificall Gravity of the said Cone, to
+the Specificall Gravity of the water: Therefore, by the precedent
+Lemma, the Cone A B C weighs in absolute Gravity, as much as a Mass of
+Water equall to the Mass D C: But the water which by the imposition of
+the Cone A B C, is driven out of its place, is as much as would
+precisely lie in the place D C, and is equall in weight to the Cone
+that displaceth it: Therefore, there shall be an _Equilibrium_, and
+the Cone shall rest without farther submerging. And its manifest,
+
+
+COROLARY I.
+
+    [Sidenote: Amongst Cones of the same Base, those of least
+    Altitude shall sink the least.]
+
+  _That making upon the same Basis, a Cone of a less Altitude, it
+    shall be also less grave, and shall so much the more rest without
+    Submersion._
+
+
+COROLARY II.
+
+    [Sidenote: There may be Cones and Piramides of any Matter, which
+    demitted with the Point downwards do float atop.]
+
+  _It is manifest, also, that one may make Cones and Piramids of any
+    Matter whatsoever, more grave than the water, which being put
+    into the water, with the Apix or Point downwards, rest without
+    Submersion._
+
+Because if we reassume what hath been above demonstrated, of Prisms
+and Cylinders, and that on Bases equall to those of the said
+Cylinders, we make Cones of the same Matter, and three times as high
+as the Cylinders, they shall rest afloat, for that in Mass and Gravity
+they shall be equall to those Cylinders, and by having their Bases
+equall to those of the Cylinders, they shall leave equall Masses of
+Air included within the Ramparts. This, which for Example sake hath
+been demonstrated, in Prisms, Cylinders, Cones and Piramids, might be
+proved in all other Solid Figures, but it would require a whole Volume
+(such is the multitude and variety of their Symptoms and Accidents) to
+comprehend the particuler demonstration of them all, and of their
+severall Segments: but I will to avoid prolixity in the present
+Discourse, content my self, that by what I have declared every one of
+ordinary Capacity may comprehend, that there is not any Matter so
+grave, no not Gold it self, of which one may not form all sorts of
+Figures, which by vertue of the superiour Air adherent to them, and
+not by the Waters Resistance of Penetration, do remain afloat, so that
+they sink not. Nay, farther, I will shew, for removing that Error,
+that,
+
+
+
+
+THEOREME XI.
+
+    [Sidenote: A Piramide or Cone, demitted with the Point downwards
+    shal swim, with its Base downward shall sink.]
+
+  _A Piramide or Cone put into the Water, with the Point downward
+    shall swimme, and the same put with the Base downwards shall
+    sinke, and it shall be impossible to make it float._
+
+
+Now the quite contrary would happen, if the difficulty of Penetrating
+the water, were that which had hindred the descent, for that the said
+Cone is far apter to pierce and penetrate with its sharp Point, than
+with its broad and spacious Base.
+
+And, to demonstrate this, let the Cone be _A B C_, twice as grave as
+the water, and let its height be tripple to the height of the Rampart
+_D A E C_: I say, first, that being put lightly into the water with
+the Point downwards, it shall not descend to the bottom: for the
+Aeriall Cylinder contained betwixt the Ramparts _D A C E_, is equall
+in Mass to the Cone _A B C_; so that the whole Mass of the Solid
+compounded of the Air _D A C E_, and of the Cone _A B C_, shall be
+double to the Cone _A C B_: And, because the Cone _A B C_ is supposed
+to be of Matter double in Gravity to the water, therefore as much
+water as the whole Masse _D A B C E_, placed beneath the Levell of the
+water, weighs as much as the Cone _A B C_: and, therefore, there shall
+be an _Equilibrium_, and the Cone _A B C_ shall descend no lower. Now,
+I say farther, that the same Cone placed with the Base downwards,
+shall sink to the bottom, without any possibility of returning again,
+by any means to swimme.
+
+[Illustration]
+
+Let, therefore, the Cone be _A B D_, double in Gravity to the water,
+and let its height be tripple the height of the Rampart of water L B:
+It is already manifest, that it shall not stay wholly out of the
+water, because the Cylinder being comprehended betwixt the Ramparts _L
+B D P_, equall to the Cone _A B D_, and the Matter of the Cone, beig
+double in Gravity to the water, it is evident that the weight of the
+said Cone shall be double to the weight of the Mass of water equall to
+the Cylinder _L B D P_: Therefore it shall not rest in this state, but
+shall descend.
+
+[Illustration]
+
+
+COROLARY I.
+
+    [Sidenote: Much less shall the said Cone swim, if one immerge a
+    part thereof.]
+
+  _I say farther; that much lesse shall the said Cone stay afloat, if
+    one immerge a part thereof._
+
+Which you may see, comparing with the water as well the part that
+shall immerge as the other above water. Let us therefore of the Cone A
+B D, submergeth part N T O S, and advance the Point N S F above water.
+The Altitude of the Cone F N S, shall either be more than half the
+whole Altitude of the Cone F T O, or it shall not be more: if it shall
+be more than half, the Cone F N S shall be more than half of the
+Cylinder E N S C: for the Altitude of the Cone F N S, shall be more
+than Sesquialter of the Altitude of the Cylinder E N S C: And, because
+the Matter of the Cone is supposed to be double in Specificall Gravity
+to the water, the water which would be contained within the Rampart E
+N S C, would be less grave absolutely than the Cone F N S; so that the
+whole Cone F N S cannot be sustained by the Rampart: But the part
+immerged N T O S, by being double in Specificall Gravity to the water,
+shall tend to the bottom: Therefore, the whole _C_one F T O, as well
+in respect of the part submerged, as the part above water shall
+descend to the bottom. But if the Altitude of the Point F N S, shall
+be half the Altitude of the whole Cone F T O, the same Altitude of the
+said Cone F N S shall be Sesquialter to the Altitude E N: and,
+therefore, E N S C shall be double to the Cone F N S; and as much
+water in Mass as the _C_ylinder E N S C, would weigh as much as the
+part of the _C_one F N S. But, because the other immerged part N T O
+S, is double in Gravity to the water, a Mass of water equall to that
+compounded of the _C_ylinder E N S C, and of the Solid N T O S, shall
+weigh less than the _C_one F T O, by as much as the weight of a Mass
+of water equall to the Solid N T O S: Therefore, the _C_one sha{l}l
+also descend. Again, because the Solid N T O S, is septuple to the
+Cone F N S, to which the _C_ylinder E S is double, the proportion of
+the Solid N T O S, shall be to the _C_ylinder E N S C, as seaven to
+two: Therefore, the whole Solid compounded of the _C_ylinder E N S C,
+and of the Solid N T O S, is much less than double the Solid N T O S:
+Therefore, the single Solid N T O S, is much graver than a Mass of
+water equall to the Mass, compounded of the _C_ylinder E N S C, and of
+N T O S.
+
+
+COROLARY II.
+
+    [Sidenote: Part of the Cones towards the Cuspis removed, it shall
+    still sink.]
+
+  _From whence it followeth, that though one should remove and take
+    away the part of the Cone F N S, the sole remainder N T O S would
+    go to the bottom._
+
+
+COROLARY III.
+
+    [Sidenote: The more the Cone is immerged, the more impossible is
+    its floating.]
+
+  _And if we should more depress the Cone F T O, it would be so much
+    the more impossible that it should sustain it self afloat, the
+    part submerged N T O S still encreasing, and the Mass of Air
+    contained in the Rampart diminishing, which ever grows less, the
+    more the Cone submergeth._
+
+That Cone, therefore, that with its Base upwards, and its _Cuspis_
+downwards doth swimme, being dimitted with its Base downward must of
+necessity sinke. They have argued farre from the truth, therefore, who
+have ascribed the cause of Natation to waters resistance of Division,
+as to a passive principle, and to the breadth of the Figure, with
+which the division is to be made, as the Efficient.
+
+I come in the fourth place, to collect and conclude the reason of
+that which I have proposed to the Adversaries, namely,
+
+
+
+
+THEOREME XII.
+
+    [Sidenote: Solids of any Figure & greatnesse, that naturally
+    sink, may by help of the Air in the Rampart swimme.]
+
+  _That it is possible to fo{r}m Solid Bodies, of what Figure and
+    greatness soever, that of their own Nature goe to the Bottome;
+    But by the help of the Air contained in the Rampart, rest without
+    submerging._
+
+
+[Illustration]
+
+The truth of this Proposition is sufficiently manifest in all those
+Solid Figures, that determine in their uppermost part in a plane
+Superficies: for making such Figures of some Matter specifically as
+grave as the water, putting them into the water, so that the whole
+Mass be covered, it is manifest, that they shall rest in all places,
+provided, that such a Matter equall in weight to the water, may be
+exactly adjusted: and they shall by consequence, rest or lie even with
+the Levell of the water, without making any Rampart. If, therefore, in
+respect of the Matter, such Figures are apt to rest without
+submerging, though deprived of the help of the Rampart, it is
+manifest, that they may admit so much encrease of Gravity, (without
+encreasing their Masses) as is the weight of as much water as would be
+contained within the Rampart, that is made about their upper plane
+Surface: by the help of which being sustained, they shall rest afloat,
+but being bathed, they shall descend, having been made graver than the
+water. In Figures, therefore, that determine above in a plane, we may
+cleerly comprehend, that the Rampart added or removed, may prohibit or
+permit the descent: but in those Figures that go lessening upwards
+towards the top, some Persons may, and that not without much seeming
+Reason, doubt whether the same may be done, and especially by those
+which terminate in a very acute Point, such as are your Cones and
+small Piramids. Touching these, therefore, as more dubious than the
+rest, I will endeavour to demonstrate, that they also lie under the
+same Accident of going, or not going to the Bottom, be they of any
+whatever bigness. Let therefore the Cone be A B D, made of a matter
+specifically as grave as the water; it is manifest that being put all
+under water, it shall rest in all places (alwayes provided, that it
+shall weigh exactly as much as the water, which is almost impossible
+to effect) and that any small weight being added to it, it shall sink
+to the bottom: but if it shall descend downwards gently, I say, that
+it shall make the Rampart E S T O, and that there shall stay out of
+the water the point A S T, tripple in height to the Rampart E S: which
+is manifest, for the Matter of the Cone weighing equally with the
+water, the part submerged _S B D T_, becomes indifferent to move
+downwards or upwards; and the Cone _A S T_, being equall in Mass to
+the water that would be contained in the concave of the Rampart _E S T
+O_, shall be also equall unto it in Gravity: and, therefore, there
+shall be a perfect _Equilibrium_, and, consequently, a Rest. Now here
+ariseth a doubt, whether the Cone _A B D_ may be made heavier, in such
+sort, that when it is put wholly under water, it goes to the bottom,
+but yet not in such sort, as to take from the Rampart the vertue of
+sustaining it that it sink not, and, the reason of the doubt is this:
+that although at such time as the Cone _A B D_ is specifically as
+grave as the water, the Rampart _E S T O_ sustaines it, not only when
+the point _A S T_ is tripple in height to the Altitude of the Rampart
+_E S_, but also when a lesser part is above water; [for although in
+the Descent of the Cone the Point _A S T_ by little and little
+diminisheth, and so likewise the Rampart _E S T O_, yet the Point
+diminisheth in greater proportion than the Rampart, in that it
+diminisheth according to all the three Dimensions, but the Rampart
+according to two only, the Altitude still remaining the same; or, if
+you will, because the Cone _S {A} T_ goes diminishing, according to
+the proportion of the cubes of the Lines that do successively become
+the Diameters of the Bases of emergent Cones, and the Ramparts
+diminish according to the proportion of the Squares of the same Lines;
+whereupon the proportions of the Points are alwayes Sesquialter of the
+proportions of the Cylinders, contained within the Rampart; so that
+if, for Example, the height of the emergent Point were double, or
+equall to the height of the Rampart, in these cases, the Cylinder
+contained within the Rampart, would be much greater than the said
+Point, because it would be either sesquialter or tripple, by reason of
+which it would perhaps serve over and above to sustain the whole Cone,
+since the part submerged would no longer weigh any thing;] yet,
+nevertheless, when any Gravity is added to the whole Mass of the Cone,
+so that also the part submerged is not without some excesse of Gravity
+above the Gravity of the water, it is not manifest, whether the
+Cylinder contained within the Rampart, in the descent that the Cone
+shall make, can be reduced to such a proportion unto the emergent
+Point, and to such an excesse of Mass above the Mass of it, as to
+compensate the excesse of the Cones Specificall Gravity above the
+Gravity of the water: and the Scruple ariseth, because that howbeit in
+the descent made by the Cone, the emergent Point _A S T_ diminisheth,
+whereby there is also a diminution of the excess of the Cones Gravity
+above the Gravity of the water, yet the case stands so, that the
+Rampart doth also contract it self, and the Cylinder contained in it
+doth deminish. Nevertheless it shall be demonstrated, how that the
+Cone _A B D_ being of any supposed bignesse, and made at the first of
+a Matter exactly equall in Gravity to the Water, if there may be
+affixed to it some Weight, by means of which i{t} may descend to the
+bottom, when submerged under water, it may also by vertue of the
+Rampart stay above without sinking.
+
+[Illustration]
+
+[Illustration]
+
+Let, therefore, the Cone _A B D_ be of any supposed greatnesse, and
+alike in specificall Gravity to the water. It is manifest, that being
+put lightly into the water, it shall rest without descending; and it
+shall advance above water, the Point _A S T_, tripple in height to the
+height of the Rampart _E S_: Now, suppose the Cone _A B D_ more
+depressed, so that it advance above water, only the Point _A I R_,
+higher by half than the Point _A S T_, with the Rampart about it _C I
+R N_. And, because, the Cone _A B D_ is to the Cone _A I R_, as the
+cube of the Line _S T_ is to the cube of the Line _I R_, but the
+Cylinder _E S T O_, is to the Cylinder _C I R N_, as the Square of _S
+T_ to the Square of _I R_, the Cone _A S T_ shall be Octuple to the
+Cone _A I R_, and the Cylinder _E S T O_, quadruple to the Cylinder _C
+I R N_: But the Cone _A S T_, is equall to the Cylinder _E S T O_:
+Therefore, the Cylinder _C I R N_, shall be double to the Cone _A I
+R_: and the water which might be contained in the Rampart _C I R N_,
+would be double in Mass and in Weight to the Cone _A I R_, and,
+therefore, would be able to sustain the double of the Weight of the
+Cone _A I R_: Therefore, if to the whole Cone _A B D_, there be added
+as much Weight as the Gravity of the Cone _A I R_, that is to say, the
+eighth part of the weight of the Cone _A S T_, it also shall be
+sustained by the Rampart _C I R N_, but without that it shall go to
+the bottome: the Cone _A B D_, being, by the addition of the eighth
+part of the weight of the Cone _A S T_, made specifically more grave
+than the water. But if the Altitude of the Cone _A I R_, were two
+thirds of the Altitude of the Cone _A S T_, the Cone _A S T_ would be
+to the Cone _A I R_, as twenty seven to eight; and the Cylinder _E S T
+O_, to the Cylinder _C I R N_, as nine to four, that is, as twenty
+seven to twelve; and, therefore, the Cylinder _C I R N_, to the Cone
+_A I R_, as twelve to eight; and the excess of the Cylinder _C I R N_,
+above the Cone _A I R_, to the Cone _A S T_, as four to twenty seven:
+therefore if to the Cone _A B D_ be added so much weight as is the
+four twenty sevenths of the weight of the Cone _A S T_, which is a
+little more then its seventh part, it also shall continue to swimme,
+and the height of the emergent Point shall be double to the height of
+the Rampart. This that hath been demonstrated in Cones, exactly holds
+in Piramides, although the one or the other should be very sharp in
+their Point or Cuspis[77]: From whence we conclude, that the same Accident
+shall so much the more easily happen in all other Figures, by how much
+the less sharp the Tops shall be, in which they determine, being
+assisted by more spacious Ramparts.
+
+    [77] Natatio{n} easiest effected in Figures broad toward the top.
+
+
+
+
+THEOREME XIII.
+
+    [Sidenote: All Figures sink or swim, upon bathing or not bathing
+    of their tops.]
+
+  _All Figures, therefore, of whatever greatnesse, may go, and not
+    go, to the Bottom, according as their Sumities or Tops shall be
+    bathed or not bathed._
+
+
+And this Accident being common to all sorts of Figures, without
+exception of so much as one. Figure hath, therefore, no part in the
+production of this Effect, of sometimes sinking, and sometimes again
+not sinking, but only the being sometimes conjoyned to, and sometimes
+seperated from, the supereminent Air: which cause, in fine, who so
+shall rightly, and, as we say, with both his Eyes, consider this
+business, will find that it is reduced to, yea, that it really is the
+same with, the true, Naturall and primary cause of Natation or
+Submersion; to wit, the excess or deficiency of the Gravity of the
+water, in relation to the Gravity of that Solid Magnitude, that is
+demitted into the water. For like as a Plate of Lead, as thick as the
+back of a Knife, which being put into the water by it self alone goes
+to the bottom, if upon it you fasten a piece of Cork four fingers
+thick, doth continue afloat, for that now the Solid that is demitted
+in the water, is not, as before, more grave than the water, but less,
+so the Board of Ebony, of its own nature more grave than water; and,
+therefore, descending to the bottom, when it is demitted by it self
+alone into the water, if it shall be put upon the water, conjoyned
+with an Expanded vail of Air, that together with the Ebony doth
+descend, and that it be such, as that it doth make with it a compound
+less grave than so much water in Mass, as equalleth the Mass already
+submerged and depressed beneath the Levell of the waters Surface, it
+shall not descend any farther, but shall rest, for no other than the
+universall and most common cause, which is that Solid Magnitudes, less
+grave _in specie_ than the water, go not to the bottom.
+
+So that if one should take a Plate of Lead, as for Example, a finger
+thick, and an handfull broad every way, and should attempt to make it
+swimme, with putting it lightly on the water, he would lose his
+Labour, because that if it should be depressed an Hairs breadth beyond
+the possible Altitude of the Ramparts of water, it would dive and
+sink; but if whilst it is going downwards, one should make certain
+Banks or Ramparts about it, that should hinder the defusion of the
+water upon the said Plate, the which Banks should rise so high, as
+that they might be able to contain as much water, as should weigh
+equally with the said Plate, it would, witho{u}t all Question, descend
+no lower, but would rest, as being sustained by vertue of the Air
+contained within the aforesaid Ramparts: and, in short, there would be
+a Vessell by this means formed with the bottom of Lead. But if the
+thinness of the Lead shall be such, that a very small height of
+Rampart would suffice to contain so much Air, as might keep it afloat,
+it shall also rest without the Artificiall Banks or Ramparts, but yet
+not without the Air, because the Air by it self makes Banks sufficient
+for a small height, to resist the Superfusion of the water: so that
+that which in this case swimmes, is as it were a Vessell filled with
+Air, by vertue of which it continueth afloat.
+
+I will, in the last place, with an other Experime{n}t, attempt to
+remove all difficulties, if so be there should yet be any doubt left
+in any one, touching the opperation of this [E]Continuity of the Air,
+with the thin Plate which swims, and afterwards put an end to this
+part of my discourse.
+
+    [E] Or rather Contiguity,
+
+I suppose my self to be questioning with some of my Oponents.
+
+Whether Figure have any influence upon the encrease or diminution of
+the Resistance in any Weight against its being raised in the Air[78]; and
+I suppose, that I am to maintain the Affirmative, asserting that a
+Mass of Lead, reduced to the Figure of a Ball, shall be raised with
+less force, then if the same had been made into a thinne and broad
+Plate, because that it in this spacious Figure, hath a great quantity
+of Air to penetrate, and in that other, more compacted and contracted
+very little: and to demonstrate the truth of such my Opinion, I will
+hang in a small thred first the Ball or Bullet, and put that into the
+water, tying the thred that upholds it to one end of the Ballance that
+I hold in the Air, and to the other end I by degrees adde so much
+Weight, till that at last it brings up the Ball of Lead out of the
+water: to do which, suppose a Gravity of thirty Ounces sufficeth; I
+afterwards reduce the said Lead into a flat and thinne Plate, the
+which I likewise put into the water, suspended by three threds, which
+hold it parallel to the Surface of the water, and putting in the same
+manner, Weights to the other end, till such time as the Plate comes to
+be raised and drawn out of the water: I finde that thirty six ounces
+will not suffice to seperate it from the water, and raise it thorow
+the Air: and arguing from this Experiment, I affirm, that I have fully
+demonstrated the truth of my Proposition. Here my Oponents desires me
+to look down, shewing me a thing which I had not before observed, to
+wit, that in the Ascent of the Plate out of the water, it draws after
+it another Plate (_if I may so call it_) of water, which before it
+divides and parts from the inferiour Surface of the Plate of Lead, is
+raised above the Levell of the other water, more than the thickness of
+the back of a Knife: Then he goeth to repeat the Experiment with the
+Ball, and makes me see, that it is but a very small quantity of water,
+which cleaves to its compacted and contracted Figure: and then he
+subjoynes, that its no wonder, if in seperating the thinne and broad
+Plate from the water, we meet with much greater Resistance, than in
+seperating the Ball, since together with the Plate, we are to raise a
+great quantity of water, which occurreth not in the Ball: He telleth
+me moreover, how that our Question is, whether the Resistance of
+Elevation be greater in a dilated Plate of Lead, than in a Ball, and
+not whether more resisteth a Plate of Lead with a great quantity of
+water, or a Ball with a very little water: He sheweth me in the close,
+that the putting the Plate and the Ball first into the water, to make
+proofe thereby of their Resistance in the Air, is besides our case,
+which treats of Elivating in the Air, and of things placed in the Air,
+and not of the Resistance that is made in the Confines of the Air and
+water, and by things which are part in Air and part in water: and
+lastly, they make me feel with my hand, that when the thinne Plate is
+in the Air, and free from the weight of the water, it is raised with
+the very same Force that raiseth the Ball. Seeing, and understanding
+these things, I know not what to do, unless to grant my self
+convinced, and to thank such a Friend, for having made me to see that
+which I never till then observed: and, being advertised by this same
+Accident, to tell my Adversaries, that our Question is, whether a
+Board and a Ball of Ebony, equally go to the bottom in water, and not
+a Ball of Ebony and a Board of Ebony, joyned with another flat Body of
+Air: and, farthermore, that we speak of sinking, and not sinking to
+the bottom, in water, and not of that which happeneth in the Confines
+of the water and Air to Bodies that be part in the Air, and part in
+the water; nor much less do we treat of the greater or lesser Force
+requisite in seperating this or that Body from the Air; not omitting
+to tell them, in the last place, that the Air doth resist, and
+gravitate downwards in the water, just so much as the water (if I may
+so speak) gravitates and resists upwards in the Air, and that the same
+Force is required to sinke a Bladder under water, that is full of Air,
+as to raise it in the Air, being full of water, removing the
+consideration of the weight of that Filme or Skinne, and considering
+the water and the Air only. And it is likewise true, that the same
+Force is required to sink a Cup or such like Vessell under water,
+whilst it is full of Air, as to raise it above the Superficies of the
+water, keeping it with the mouth downwards; whilst it is full of
+water, which is constrained in the same manner to follow the Cup which
+contains it, and to rise above the other water into the Region of the
+Air, as the Air is forced to follow the same Vessell under the Surface
+of the water, till that in this c{a}se the water, surmounting the
+brimme of the Cup, breaks in, driving thence the Air, and in that
+case, the said brimme coming out of the water, and arriving to the
+Confines of the Air, the water falls down, and the Air sub-enters to
+fill the cavity of the Cup: upon which ensues, that he no less
+transgresses the Articles of the _Convention_, who produceth a Plate
+conjoyned with much Air, to see if it descend to the bottom in water,
+then he that makes proof of the Resistance against Elevation in Air
+with a Plate of Lead, joyned with a like quantity of water.
+
+    [78] An Experiment of the operation of Figures, in encreasing or
+    lessening of the Airs Resistance of Division.
+
+    [Sidenote: _Aristotles_ opinion touching the Operation of Figure
+    examined.]
+
+I have said all that I could at present think of, to maintain the
+Assertion I have undertook. It remains, that I examine that which
+_Aristotle_ hath writ of this matter towards the end of his Book De
+Cælo[79]; wherein I shall note two things: the one that it being true as
+hath been demonstrated, that Figure hath nothing to do about the
+moving or not moving it self upwards or downwards, its seemes that
+_Aristotle_ at his first falling upon this Speculation, was of the
+same opinion, as in my opinion may be collected from the examination
+of his words. 'Tis true, indeed, that in essaying afterwards to render
+a reason of such effect, as not having in my conceit hit upon the
+right, (which in the second place I will examine) it seems that he is
+brought to admit the largenesse of Figure, to be interessed in this
+operation. As to the first particuler, hear the precise words of
+_Aristotle_.
+
+    [79] _Aristot. de Cælo_ Lib. 4. Cap 6.
+
+_Figures are not the Causes of moving simply upwards or downwards, but
+of moving more slowly or swiftly[80][81], and by what means this comes to
+pass, it is not difficult to see._
+
+    [80] _Aristotle_ makes not Figure the cause of Motion absolutely,
+    but of swift or slow motion,
+
+    [81] Lib. 4. Cap. 6: Text. 42.
+
+Here first I note, that the terms being four, which fall under the
+present consideration, namely, Motion, Rest, Slowly and Swiftly: And
+_Aristotle_ naming figures as Causes of Tardity and Velocity,
+excluding them from being the Cause of absolute and simple Motion, it
+seems necessary, that he exclude them on the other side, from being
+the Cause of Rest, so that his meaning is this. Figures are not the
+Causes of moving or not moving absolutely, but of moving quickly or
+slowly: and, here, if any should say the mind of _Aristotle_ is to
+exclude Figures from being Causes of Motion, but yet not from being
+Causes of Rest, so that the sence would be to remove from Figures,
+there being the Causes of moving simply, but yet not there being
+Causes of Rest, I would demand, whether we ought with _Aristotle_ to
+understand, that all Figures universally, are, in some manner, the
+causes of Rest in those Bodies, which otherwise would move, or else
+some particular Figures only, as for Example, broad and thinne
+Figures: If all indifferently, then every Body shall rest: because
+every Body hath some Figure, which is false; but if some particular
+Figures only may be in some manner a Cause of Rest, as, for Example,
+the broad, then the others would be in some manner the Causes of
+Motion: for if from seeing some Bodies of a contracted Figure move,
+which after dilated into Plates rest, may be inferred, that the
+Amplitude of Figure hath a part in the Cause of that Rest; so from
+seeing such like Figures rest, which afterwards contracted move, it
+may with the same reason be affirmed, that the united and contracted
+Figure, hath a part in causing Motion, as the remover of that which
+impeded it: The which again is directly opposite to what _Aristotle_
+saith, namely, that Figures are not the Causes of Motion. Besides, if
+_Aristotle_ had admitted and not excluded Figures from being Causes of
+not moving in some Bodies, which moulded into another Figure would
+move, he would have impertinently propounded in a dubitative manner,
+in the words immediately following, whence it is, that the large and
+thinne Plates of Lead or Iron, rest upon the water, since the Cause
+was apparent, namely, the Amplitude of Figure. Let us conclude,
+therefore, that the meaning of _Aristotle_ in this place is to affirm,
+that Figures are not the Causes of absolutely moving or not moving,
+but only of moving swiftly or slowly: which we ought the rather to
+believe, in regard it is indeed a most true conceipt and opinion. Now
+the mind of _Aristotle_ being such, and appearing by consequence,
+rather contrary at the first sight, then favourable to the assertion
+of the Oponents, it is necessary, that their Interpretation be not
+exactly the same with that, but such, as being in part understood by
+some of them, and in part by others, was set down: and it may easily
+be indeed so, being an Interpretation consonent to the sence of the
+more famous Interpretors, which is, that the Adverbe _Simply_ or
+_Absolutely_, put in the Text, ought not to be joyned to the Verbe to
+_Move_, but with the Noun _Causes_: so that the purport of
+_Aristotles_ words, is to affirm, That Figures are not the Causes
+absolutely of moving or not moving, but yet are Causes _Secundum
+quid_, _viz._ in some sort; by which means, they are called Auxiliary
+and Concomitant Causes: and this Proposition is received and asserted
+as true by _Signor Buonamico Lib. 5. Cap. 28._ where he thus writes.
+_There are other Causes concomitant, by which some things float, and
+others sink, among which the Figures of Bodies hath the first place_,
+&c.
+
+Concerning this Proposition, I meet with many doubts and difficulties,
+for which me thinks the words of _Aristotle_ are not capable of such a
+construction and sence, and the difficulties are these.
+
+First in the order and disposure of the words of _Aristotle_, the
+particle _Simpliciter_, or if you will _absoluté_, is conjoyned with
+the Verb _to move_, and seperated from the Noun _Causes_, the which is
+a great presumption in my favour, seeing that the writing and the Text
+saith, Figures are not the Cause of moving simply upwards or
+downwards, but of quicker or slower Motion: and, saith not, Figures
+are not simply the Causes of moving upwards or downwards, and when the
+words of a Text receive, transposed, a sence different from that which
+they sound, taken in the order wherein the Author disposeth them, it
+is not convenient to inverte them. And who will affirm that
+_Aristotle_ desiring to write a Proposition, would dispose the words
+in such sort, that they should import a different, nay, a contrary
+sence? contrary, I say, because understood as they are written; they
+say, that Figures are not the Causes of Motion, but inverted, they
+say, that Figures are the Causes of Motion, &c.
+
+Moreover, if the intent of _Aristotle_ had been to say, that Figures
+are not simply the Causes of moving upwards or downwards, but only
+Causes _Secundum quid_, he would not have adjoyned those words, _but
+they are Causes of the more swift or slow Motion_; yea, the subjoining
+this would have been not only superfluous but false, for that the
+whole tenour of the Proposition would import thus much. Figures are
+not the absolute Causes of moving upwards or downwards, but are the
+absolute Cause of the swift or slow Motion; which is not true: because
+the primary Causes of greater or lesser Velocity, are by _Aristotle_
+in the 4th of his _Physicks_, _Text. 71._ attributed to the greater or
+lesser Gravity of Moveables, compared among themselves, and to the
+greater or lesser Resistance of the _Medium's_, depending on their
+greater or less Crassitude: and these are inserted by _Aristotle_ as
+the primary Causes; and these two only are in that place nominated:
+and Figure comes afterwards to be considered, _Text. 74._ rather as an
+Instrumentall Cause of the force of the Gravity, the which divides
+either with the Figure, or with the _Impetus_; and, indeed, Figure by
+it self without the force of Gravity or Levity, would opperate
+nothing.
+
+I adde, that if _Aristotle_ had an opinion that Figure had been in
+some sort the Cause of moving or not moving, the inquisition which he
+makes immediately in a doubtfull manner, whence it comes, that a Plate
+of Lead flotes, would have been impertinent; for if but just before he
+had said, that Figure was in a certain sort the Cause of moving or not
+moving, he needed not to call in Question, by what Cause the Plate of
+Lead swims, and then ascribing the Cause to its Figure; and framing a
+discourse in this manner. Figure is a Cause _Secundum quid_ of not
+sinking: but, now, if it be doubted, for what Cause a thin Plate of
+Lead goes not to the bottom; it shall be answered, that that proceeds
+from its Figure: a discourse which would be indecent in a Child, much
+more in _Aristotle_; For where is the occasion of doubting? And who
+sees not, that if _Aristotle_ had held, that Figure was in some sort a
+Cause of Natation, he would without the least Hesitation have writ;
+That Figure is in a certain sort the Cause of Natation, and therefore
+the Plate of Lead in respect of its large and expatiated Figure swims;
+but if we take the proposition of _Aristotle_ as I say, and as it is
+written, and as indeed it is true, the ensuing words come in very
+oppositely, as well in the introduction of swift and slow, as in the
+question, which very pertinently offers it self, and would say thus
+much.
+
+Figures are not the Cause of moving or not moving simply upwards or
+downwards, but of moving more quickly or slowly: But if it be so, the
+Cause is doubtfull, whence it proceeds, that a Plate of Lead or of
+Iron broad and thin doth swim, &c. And the occasion of the doubt is
+obvious, because it seems at the first glance, that the Figure is the
+Cause of this Natation, since the same Lead, or a less quantity, but
+in another Figure, goes to the bottom, and we have already affirmed,
+that the Figure hath no share in this effect.
+
+Lastly, if the intent of _Aristotle_ in this place had been to say,
+that Figures, although not absolutely, are at least in some measure
+the Cause of moving or not moving: I would have it considered, that he
+names no less the Motion upwards, than the other downwards: and
+because in exemplifying it afterwards, he produceth no other
+Experiments than of a Plate of Lead, and Board of Ebony, Matters that
+of their own Nature go to the bottom, but by vertue (as our
+Adversaries say) of their Figure, rest afloat; it is fit that they
+should produce some other Experiment of those Matters, which by their
+Nature swims, but retained by their Figure rest at the bottom. But
+since this is impossible to be done, we conclude, that _Aristotle_ in
+this place, hath not attributed any action to the Figure of simply
+moving or not moving.
+
+But though he hath exquisitely Philosophiz'd, in investigating the
+solution of the doubts he proposeth, yet will I not undertake to
+maintain, rather various difficulties, that present themselves unto
+me, give me occasion of suspecting that he hath not entirely displaid
+unto us, the true Cause of the present Conclusion: which difficulties
+I will propound one by one, ready to change opinion, whenever I am
+shewed, that the Truth is different from what I say; to the confession
+whereof I am much more inclinable than to contradiction.
+
+    [Sidenote: _Aristotle_ erred in affirming a Needle dimitted long
+    wayes to sink.]
+
+_Aristotle_ having propounded the Question, whence it proceeds, that
+broad Plates of Iron or Lead, float or swim; he addeth (as it were
+strengthening the occasion of doubting) forasmuch as other things,
+less, and less grave, be they round or long, as for instance a Needle
+go to the bottom. Now I here doubt, or rather am certain that a Needle
+put lightly upon the water, rests afloat, no less than the thin Plates
+of Iron or Lead. I cannot believe, albeit it hath been told me, that
+some to defend _Aristotle_ should say, that he intends a Needle
+demitted not longwayes but endwayes, and with the Point downwards;
+nevertheless, not to leave them so much as this, though very weak
+refuge, and which in my judgement _Aristotle_ himself would refuse, I
+say it ought to be understood, that the Needle must be demitted,
+according to the Dimension named by _Aristotle_, which is the length:
+because, if any other Dimension than that which is named, might or
+ought to be taken, I would say, that even the Plates of Iron and Lead,
+sink to the bottom, if they be put into the water edgewayes and not
+flatwayes. But because _Aristotle_ saith, broad Figures go not to the
+bottom, it is to be understood, being demitted broadwayes: and,
+therefore, when he saith, long Figures as a Needle, albeit light, rest
+not afloat, it ought to be understood of them when demitted longwayes.
+
+  _Moreover, to say that_ Aristotle _is to be understood of the
+  Needle demitted with the Point downwards, is to father upon him a
+  great impertinency; for in this place he saith, that little
+  Particles of Lead or Iron, if they be round or long as a Needle, do
+  sink to the bottome; so that by his Opinion, a Particle or small
+  Grain of Iron cannot swim: and if he thus believed, what a great
+  folly would it be to subjoyn, that neither would a Needle demitted
+  endwayes swim? And what other is such a Needle, but many such like
+  Graines accumulated one upon another? It was too unworthy of such a
+  man to say, that one single Grain of Iron could not swim, and that
+  neither can it swim, though you put a hundred more upon it._
+
+Lastly, either _Aristotle_ believed, that a Needle demitted longwayes
+upon the water, would swim, or he believed that it would not swim: If
+he believed it would not swim, he might well speak as indeed he did;
+but if he believed and knew that it would float, why, together with
+the dubious Problem of the Natation of broad Figures, though of
+ponderous Matter, hath he not also introduced the Question; whence it
+proceeds, that even long and slender Figures, howbeit of Iron or Lead
+do swim? And the rather, for that the occasion of doubting seems
+greater in long and narrow Figures, than in broad and thin, as from
+_Aristotles_ not having doubted of it, is manifested.
+
+No lesser an inconvenience would they fasten upon _Aristotle_, who in
+his defence should say, that he means a Needle pretty thick, and not a
+small one; for take it for granted to be intended of a small one; and
+it shall suffice to reply, that he believed that it would swim; and I
+will again charge him with having avoided a more wonderfull and
+intricate Probleme, and introduced the more facile and less
+wonderfull.
+
+We say freely therefore, that _Aristotle_ did hold, that only the
+broad Figure did swim, but the long and slender, such as a Needle,
+not. The which nevertheless is false, as it is also false in round
+Bodies: because, as from what hath been predemonstrated, may be
+gathered, little Balls of Lead and Iron, do in like manner swim.
+
+    [Sidenote: _Aristotle_ affirmeth some Bodies volatile for their
+    Minuity, Text. 42.]
+
+He proposeth likewise another Conclusion, which likewise seems
+different from the truth, and it is, That some things, by reason of
+their littleness fly in the Air, as the small dust of the Earth, and
+the thin leaves of beaten Gold: but in my Opinion, Experience shews
+us, that that happens not only in the Air, but also in the water, in
+which do descend, even those Particles or Atomes of Earth, that
+disturbe it, whose minuity is such, that they are not deservable, save
+only when they are many hundreds together. Therefore, the dust of the
+Earth, and beaten Gold, do not any way sustain themselves in the Air,
+but descend downwards, and only fly to and again in the same, when
+strong Windes raise them, or other agitations of the Air commove them:
+and this also happens in the commotion of the water, which raiseth its
+Sand from the bottom, and makes it muddy. But _Aristotle_ cannot mean
+this impediment of the commotion, of which he makes no mention, nor
+names other than the lightness of such Minutiæ or Atomes, and the
+Resistance of the Crassitudes of the Water and Air, by which we see,
+that he speakes of a calme, and not disturbed and agitated Air: but in
+that case, neither Gold nor Earth, be they never so small, are
+sustained, but speedily descend.
+
+    [Sidenote: _Democritus_ placed the Cause of Natation in certain
+    fiery Atomes.]
+
+He passeth next to confute _Democritus_[82], which, by his Testimony would
+have it, that some Fiery Atomes, which continually ascend through the
+water, do spring upwards, and sustain those grave Bodies, which are
+very broad, and that the narrow descend to the bottom, for that but a
+small quantity of those Atomes, encounter and resist them.
+
+    [82] _Aristot. De Cælo_ lib. 4. cap. 6. text. 43.
+
+I say, _Aristotle_ confutes this position[83], saying, that that should
+much more occurre in the Air, as the same _Democritus_ instances
+against himself, but after he had moved the objection, he slightly
+resolves it, with saying, that those Corpuscles which ascend in the
+Air, make not their _Impetus_ conjunctly. Here I will not say, that
+the reason alledged by _Democritus_ is true[84], but I will only say, it
+seems in my judgement, that it is not wholly confuted by _Aristotle_,
+whilst he saith, that were it true, that the calid ascending Atomes,
+should sustain Bodies grave, but very broad, it would much more be
+done in the Air, than in Water, for that haply in the Opinion of
+_Aristotle_, the said calid Atomes ascend with much greater Force and
+Velocity through the Air, than through the water. And if this be so,
+as I verily believe it is, the Objection of _Aristotle_ in my
+judgement seems to give occasion of suspecting, that he may possibly
+be deceived in more than one particular: First, because those calid
+Atomes, (whether they be Fiery Corpuscles, or whether they be
+Exhalations, or in short, whatever other matter they be, that ascends
+upwards through the Air) cannot be believed to mount faster through
+Air, than through water: but rather on the contrary, they peradventure
+move more impetuously through the water, than through the Air, as hath
+been in part demonstrated above. And here I cannot finde the reason,
+why _Aristotle_ seeing, that the descending Motion of the same
+Moveable, is more swift in Air, than in water, hath not advertised us,
+that from the contrary Motion, the contrary should necessarily follow;
+to wit, that it is more swift in the water, than in the Air: for since
+that the Moveable which descendeth, moves swifter through the Air,
+than through the water, if we should suppose its Gravity gradually to
+diminish, it would first become such, that descending swiftly through
+the Air, it would descend but slowly through the water: and then
+again, it might be such, that descending in the Air, it should ascend
+in the water: and being made yet less grave, it shall ascend swiftly
+through the water, and yet descend likewise through the Air: and in
+short, before it can begin to ascend, though but slowly through the
+Air, it shall ascend swiftly through the water: how then is it true,
+that ascending Moveables move swifter through the Air, than through
+the water?
+
+    [83] _Democritus_ confuted by _Aristotle_, text 43.
+
+    [84] _Aristotles_ confutation of _Democritus_ refuted by the
+    Author.
+
+That which hath made _Aristotle_ believe, the Motion of Ascent to be
+swifter in Air, than in water, was first, the having referred the
+Causes of slow and quick, as well in the Motion of Ascent, as of
+Descent, only to the diversity of the Figures of the Moveable, and to
+the more or less Resistance of the greater or lesser Crassitude, or
+Rarity of the _Medium_; not regarding the comparison of the Excesses
+of the Gravities of the Moveables, and of the _Mediums_: the which
+notwithstanding, is the most principal point in this affair: for if
+the augmentation and diminution of the Tardity or Velocity, should
+have only respect to the Density or Rarity of the _Medium_, every Body
+that descends in Air, would descend in water: because whatever
+difference is found between the Crassitude of the water, and that of
+the Air, may well be found between the Velocity of the same Moveable
+in the Air, and some other Velocity: and this should be its proper
+Velocity in the water, which is absolutely false. The other occasion
+is, that he did believe, that like as there is a positive and
+intrinsecall Quality, whereby Elementary Bodies have a propension of
+moving towards the Centre of the Earth, so there is another likewise
+intrinsecall[85], whereby some of those Bodies have an _Impetus_ of flying
+the Centre, and moving upwards: by Vertue of which intrinsecall
+Principle, called by him Levity, the Moveables which have that same
+Motion more easily penetrate the more subtle _Medium_, than the more
+dense: but such a Proposition appears likewise uncertain, as I have
+above hinted in part, and as with Reasons and Experiments, I could
+demonstrate, did not the present Argument importune me, or could I
+dispatch it in few words.
+
+    [85] Lib. 4. Cap. 5.
+
+The Objection therefore of _Aristotle_ against _Democritus_, whilst he
+saith, that if the Fiery ascending Atomes should sustain Bodies grave,
+but of a distended Figure, it would be more observable in the Air than
+in the water, because such Corpuscles move swifter in that, than in
+this, is not good; yea the contrary would evene, for that they ascend
+more slowly through the Air: and, besides their moving slowly, they
+ascend, not united together, as in the water, but discontinue, and, as
+we say, scatter: And, therefore, as _Democritus_ well replyes,
+resolving the instance they make not their push or _Impetus_
+conjunctly.
+
+_Aristotle_, in the second place, deceives himself, whilst he will
+have the said grave Bodies to be more easily sustained by the said
+Fiery ascending Atomes in the Air than in the Water: not observing,
+that the said Bodies are much more grave in that, than in this, and
+that such a Body weighs ten pounds in the Air, which will not in the
+water weigh 1/2 an ounce; how can it then be more easily sustained in
+the Air, than in the Water?
+
+    [Sidenote: _Democritus_ confuted by the Authour.]
+
+Let us conclude, therefore, that _Democritus_ hath in this particular
+better Philosophated than _Aristotle_. But yet will not I affirm, that
+_Democritus_ hath reason'd rightly, but I rather say, that there is a
+manifest Experiment that overthrows his Reason, and this it is, That
+if it were true, that calid ascending Atomes should uphold a Body,
+that if they did not hinder, would go to the bottom, it would follow,
+that we may find a Matter very little superiour in Gravity to the
+water, the which being reduced into a Ball, or other contracted
+Figure, should go to the bottom, as encountring but few Fiery Atomes;
+and which being distended afterwards into a dilated and thin Plate,
+should come to be thrust upwards by the impulsion of a great Multitude
+of those Corpuscles, and at last carried to the very Surface of the
+water: which wee see not to happen; Experience shewing us, that a Body
+_v. gra._ of a Sphericall Figure, which very hardly, and with very
+great leasure goeth to the bottom, will rest there, and will also
+descend thither, being reduced into whatsoever other distended Figure.
+We must needs say then, either that in the water, there are no such
+ascending Fiery Atoms, or if that such there be, that they are not
+able to raise and lift up any Plate of a Matter, that without them
+would go to the bottom: Of which two Positions, I esteem the second to
+be true, understanding it of water, constituted in its naturall
+Coldness. But if we take a Vessel of Glass, or Brass, or any other
+hard matter, full of cold water, within which is put a Solid of a flat
+or concave Figure, but that in Gravity exceeds the water so little,
+that it goes slowly to the bottom; I say, that putting some burning
+Coals under the said Vessel, as soon as the new Fiery Atomes shall
+have penetrated the substance of the Vessel, they shall without doubt,
+ascend through that of the water, and thrusting against the foresaid
+Solid, they shall drive it to the Superficies, and there detain it, as
+long as the incursions of the said Corpuscles shall last, which
+ceasing after the removall of the Fire, the Solid being abandoned by
+its supporters, shall return to the bottom.
+
+But _Democritus_ notes, that this Cause only takes place when we
+treat of raising and sustaining of Plates of Matters, but very little
+heavier than the water, or extreamly thin: but in Matters very grave,
+and of some thickness, as Plates of Lead or other Mettal, that same
+Effect wholly ceaseth: In Testimony of which, let's observe that such
+Plates, being raised by the Fiery Atomes, ascend through all the depth
+of the water, and stop at the Confines of the Air, still staying under
+water: but the Plates of the Opponents stay not, but only when they
+have their upper Superficies dry, nor is there any means to be used,
+that when they are within the water, they may not sink to the bottom.
+The cause, therefore, of the Supernatation of the things of which
+_Democritus_ speaks is one, and that of the Supernatation of the
+things of which we speak is another. But, returning to _Aristotle_[86],
+methinks that he hath more weakly confuted _Democritus_, than
+_Democritus_ himself hath done: For _Aristotle_ having propounded the
+Objection which he maketh against him, and opposed him with saying,
+that if the calid ascendent Corpuscles were those that raised the thin
+Plate, much more then would such a Solid be raised and born upwards
+through the Air, it sheweth that the desire in _Aristotle_ to detect
+_Democritus_, was predominate over the exquisiteness of Solid
+Philosophizing: which desire of his he hath discovered in other
+occasions, and that we may not digress too far from this place, in the
+Text precedent to this Chapter which we have in hand[87]; where he
+attempts to confute the same _Democritus_ for that he, not contenting
+himself with names only, had essayed more particularly to declare what
+things Gravity and Levity were; that is, the Causes of descending and
+ascending, (and had introduced Repletion and Vacuity) ascribing this
+to Fire, by which it moves upwards, and that to the Earth, by which it
+descends; afterwards attributing to the Air more of Fire, and to the
+water more of Earth. But _Aristotle_ desiring a positive Cause, even
+of ascending Motion, and not as _Plato_, or these others, a simple
+negation, or privation, such as Vacuity would be in reference to
+Repletion[88], argueth against _Democritus_ and saith: If it be true, as
+you suppose, then there shall be a great Mass of water, which shall
+have more of Fire, than a small Mass of Air, and a great Mass of Air,
+which shall have more of Earth than a little Mass of water, whereby it
+would ensue, that a great Mass of Air, should come more swiftly
+downwards, than a little quantity of water: But that is never in any
+case soever: Therefore _Democritus_ discourseth erroneously.
+
+    [86] _Aristotle_ shews his desire of finding _Democritus_ in an
+    Error, to exceed that of discovering Truth.
+
+    [87] Cap. 5. Text 41.
+
+    [88] Id. ibid.
+
+But in my opinion, the Doctrine of _Democritus_ is not by this
+allegation overthrown, but if I erre not, the manner of _Aristotle_
+deduction either concludes not, or if it do conclude any thing, it may
+with equall force be restored against himself. _Democritus_ will grant
+to _Aristotle_, that there may be a great Mass of Air taken, which
+contains more Earth, than a small quantity of water, but yet will
+deny, that such a Mass of Air, shall go faster downwards than a little
+water, and that for many reasons. First, because if the greater
+quantity of Earth, contained in the great Mass of Air, ought to cause
+a greater Velocity than a less quantity of Earth, contained in a
+little quantity of water, it would be necessary, first, that it were
+true, that a greater Mass of pure Earth, should move more swiftly than
+a less: But this is false, though _Aristotle_ in many places affirms
+it to be true: because not the greater absolute, but the greater
+specificall Gravity, is the cause of greater Velocity[89]: nor doth a Ball
+of Wood, weighing ten pounds, descend more swiftly than one weighing
+ten Ounces, and that is of the same Matter: but indeed a Bullet of
+Lead of four Ounces, descendeth more swiftly than a Ball of Wood of
+twenty Pounds: because the Lead is more _grave in specie_ than the
+Wood. Therefore, its not necessary, that a great Mass of Air, by
+reason of the much Earth contained in it, do descend more swiftly than
+a little Mass of water[90], but on the contrary, any whatsoever Mass of
+water, shall move more swiftly than any other of Air, by reason the
+participation of the terrene parts _in specie_ is greater in the
+water, than in the Air. Let us note, in the second place, how that in
+multiplying the Mass of the Air, we not only multiply that which is
+therein of terrene, but its Fire also: whence the Cause of ascending,
+no less encreaseth, by vertue of the Fire, than that of descending on
+the account of its multiplied Earth. It was requisite in increasing
+the greatness of the Air, to multiply that which it hath of terrene
+only, leaving its Fire in its first state, for then the terrene parts
+of the augmented Air, overcoming the terrene parts of the small
+quantity of water, it might with more probability have been pretended,
+that the great quantity of Air, ought to descend with a greater
+_Impetus_, than the little quantity of water.
+
+    [89] The greater Specificall, not the greater absolute Gravity,
+    is the Cause of Velocity.
+
+    [90] Any Mass of water shal move more swiftly, than any of Air,
+    and why.
+
+Therefore, the Fallacy lyes more in the Discourse of _Aristotle_, than
+in that of _Democritus_, who with severall other Reasons might oppose
+_Aristotle_, and alledge; If it be true, that the extreame Elements be
+one simply grave, and the other simply light, and that the mean
+Elements participate of the one, and of the other Nature; but the Air
+more of Levity, and the water more of Gravity, then there shall be a
+great Mass of Air, whose Gravity shall exceed the Gravity of a little
+quantity of water, and therefore such a Mass of Air shall descend more
+swiftly than that little water: But that is never seen to occurr:
+Therefore its not true, that the mean Elements do participate of the
+one, and the other quality. This argument is fallacious, no less than
+the other against _Democritus_.
+
+Lastly, _Aristotle_ having said, that if the Position of _Democritus_
+were true, it would follow, that a great Mass of Air should move more
+swiftly than a small Mass of water, and afterwards subjoyned, that
+that is never seen in any Case: methinks others may become desirous to
+know of him in what place this should evene, which he deduceth against
+_Democritus_, and what Experiment teacheth us, that it never falls out
+so. To suppose to see it in the Element of water, or in that of the
+Air is vain, because neither doth water through water, nor Air through
+Air move, nor would they ever by any whatever participation others
+assign them, of Earth or of Fire: the Earth, in that it is not a Body
+fluid, and yielding to the mobility of other Bodies, is a most
+improper place and _Medium_ for such an Experiment: _Vacuum_,
+according to the same _Aristotle_ himself, there is none, and were
+there, nothing would move in it: there remains the Region of Fire, but
+being so far distant from us, what Experiment can assure us, or hath
+assertained _Aristotle_ in such sort, that he should as of a thing
+most obvious to sence, affirm what he produceth in confutation of
+_Democritus_, to wit, that a great Mass of Air, is moved no swifter
+than a little one of water? But I will dwell no longer upon this
+matter, whereon I have spoke sufficiently: but leaving _Democritus_, I
+return to the Text of _Aristotle_, wherein he goes about to render the
+true reason, how it comes to pass, that the thin Plates of Iron or
+Lead do swim on the water; and, moreover, that Gold it self being
+beaten into thin Leaves, not only swims in water, but flyeth too and
+again in the Air. He supposeth that of Continualls[91], some are easily
+divisible, others not: and that of the easily divisible, some are more
+so, and some less: and these he affirms we should esteem the Causes.
+He addes that that is easily divisible, which is well terminated, and
+the more the more divisible, and that the Air is more so, than the
+water, and the water than the Earth. And, lastly, supposeth that in
+each kind, the lesse quantity is easlyer divided and broken than the
+greater.
+
+    [91] _De Cælo_ l. 4. c. 6. t. 44.
+
+Here I note, that the Conclusions of _Aristotle_ in generall are all
+true, but methinks, that he applyeth them to particulars, in which
+they have no place, as indeed they have in others, as for Example, Wax
+is more easily divisible than Lead, and Lead than Silver, inasmuch as
+Wax receives all the terms more easlier than Lead, and Lead than
+Silver. Its true, moreover, that a little quantity of Silver is
+easlier divided than a great Mass: and all these Propositions are
+true, because true it is, that in Silver, Lead and Wax, there is
+simply a Resistance against Division, and where there is the absolute,
+there is also the respective. But if as well in water as in Air, there
+be no Renitence against simple Division, how can we say, that the
+water is easlier divided than the Air? We know not how to extricate
+our selves from the Equivocation: whereupon I return to answer, that
+Resistance of absolute Division is one thing, and Resistance of
+Division made with such and such Velocity is another. But to produce
+Rest, and to abate the Motion, the Resistance of absolute Division is
+necessary; and the Resistance of speedy Division, causeth not Rest,
+but slowness of Motion. But that as well in the Air, as in water,
+there is no Resistance of simple Division, is manifest, for that there
+is not found any Solid Body which divides not the Air, and also the
+water: and that beaten Gold, or small dust, are not able to superate
+the Resistance of the Air, is contrary to that which Experience shews
+us, for we see Gold and Dust to go waving to and again in the Air, and
+at last to descend downwards, and to do the same in the water, if it
+be put therein, and separated from the Air. And, because, as I say,
+neither the water, nor the Air do resist simple Division, it cannot be
+said, that the water resists more than the Air. Nor let any object
+unto me, the Example of most light Bodies, as a Feather, or a little
+of the pith of Elder, or water-reed that divides the Air and not the
+water, and from this infer, that the Air is easlier divisible than the
+water; for I say unto them, that if they do well observe, they shall
+see the same Body likewise divide the Continuity of the water[92], and
+submerge in part, and in such a part, as that so much water in Mass
+would weigh as much as the whole Solid. And if they shal yet persist
+in their doubt, that such a Solid sinks not through inability to
+divide the water, I will return them this reply, that if they put it
+under water, and then let it go, they shall see it divide the water,
+and presently ascend with no less celerity, than that with which it
+divided the Air in descending: so that to say that this Solid ascends
+in the Air, but that coming to the water, it ceaseth its Motion, and
+therefore the water is more difficult to be divided, concludes
+nothing: for I, on the contrary, will propose them a piece of Wood, or
+of Wax, which riseth from the bottom of the water, and easily divides
+its Resistance, which afterwards being arrived at the Air, stayeth
+there, and hardly toucheth it; whence I may aswell say, that the water
+is more easier divided than the Air.
+
+    [92] _Archimed. De Insident. humi_ lib. 2. prop. 1.
+
+I will not on this occasion forbear to give warning of another fallacy
+of these persons, who attribute the reason of sinking or swimming to
+the greater or lesse Resistance of the Crassitude of the water against
+Division, making use of the example of an Egg, which in sweet water
+goeth to the bottom, but in salt water swims; and alledging for the
+cause thereof, the faint Resistance of fresh water against Division,
+and the strong Resistance of salt water. But if I mistake not, from
+the same Experiment, we may aswell deduce the quite contrary; namely,
+that the fresh water is more dense, and the salt more tenuous and
+subtle, since an Egg from the bottom of salt water speedily ascends to
+the top, and divides its Resistance, which it cannot do in the fresh,
+in whose bottom it stays, being unable to rise upwards. Into such like
+perplexities, do false Principles Lead men: but he that rightly
+Philosophating, shall acknowledge the excesses of the Gravities of the
+Moveables and of the Mediums, to be the Causes of those effects, will
+say, that the Egg sinks to the bottom in fresh water, for that it is
+more grave than it, and swimeth in the salt, for that its less grave
+than it: and shall without any absurdity, very solidly establish his
+Conclusions.
+
+Therefore the reason totally ceaseth, that _Aristotle_ subjoyns in the
+Text saying[93]; The things, therefore, which have great breadth remain
+above, because they comprehend much, and that which is greater, is not
+easily divided. Such discoursing ceaseth, I say, because its not true,
+that there is in water or in Air any Resistance of Division; besides
+that the Plate of Lead when it stays, hath already divided and
+penetrated the Crassitude of the water, and profounded it self ten or
+twelve times more than its own thickness: besides that such Resistance
+of Division, were it supposed to be in the water, could not rationally
+be affirmed to be more in its superiour parts than in the middle, and
+lower: but if there were any difference, the inferiour should be the
+more dense, so that the Plate would be no less unable to penetrate the
+lower, than the superiour parts of the water; nevertheless we see that
+no sooner do we wet the superiour Superficies of the Board or thin
+Piece of Wood, but it precipitatly, and without any retension,
+descends to the bottom.
+
+    [93] Text 45.
+
+I believe not after all this, that any (thinking perhaps thereby to
+defend _Aristotle_) will say, that it being true, that the much water
+resists more than the little, the said Board being put lower
+descendeth, because there remaineth a less Mass of water to be divided
+by it: because if after the having seen the same Board swim in four
+Inches of water, and also after that in the same to sink, he shall try
+the same Experiment upon a profundity of ten or twenty fathom water,
+he shall see the very self same effect. And here I will take occasion
+to remember, for the removall of an Error that is too common; That
+that Ship or other whatsoever Body, that on the depth of an hundred or
+a thousand fathom, swims with submerging only six fathom of its own
+height, [_or in the Sea dialect, that draws six fathom water_] shall
+swim in the same manner in water, that hath but six fathom and half an
+Inch of depth[94]. Nor do I on the other side, think that it can be said,
+that the superiour parts of the water are the more dense, although a
+most grave Authour hath esteemed the superiour water in the Sea to be
+so, grounding his opinion upon its being more salt, than that at the
+bottom: but I doubt the Experiment, whether hitherto in taking the
+water from the bottom, the Observatour did not light upon some spring
+of fresh water there spouting up: but we plainly see on the contrary,
+the fresh Waters of Rivers to dilate themselves for some miles beyond
+their place of meeting with the salt water of the Sea, without
+descending in it, or mixing with it, unless by the intervention of
+some commotion or turbulency of the Windes.
+
+    [94] A Ship that in 100 Fathome water draweth 6 Fathome, shall
+    float in 6 Fathome and 1/2 an Inch of depth.
+
+But returning to _Aristotle_, I say, that the breadth of Figure hath
+nothing to do in this business more or less, because the said Plate of
+Lead, or other Matter, cut into long Slices, swim neither more nor
+less[95]; and the same shall the Slices do, being cut anew into little
+pieces, because its not the breadth but the thickness that operates in
+this business. I say farther, that in case it were really true, that
+the Renitence to Division were the proper Cause of swimming[96], the
+Figures more narrow and short, would much better swim than the more
+spacious and broad, so that augmenting the breadth of the Figure, the
+facility of supernatation will be deminished, and decreasing, that
+this will encrease.
+
+    [95] Thickness not breadth of Figure to be respected in Natation.
+
+    [96] Were Renitence the cause of Natation, breadth of Figure would
+    hinder the swiming of Bodies.
+
+And for declaration of what I say, consider that when a thin Plate of
+Lead descends, dividing the water, the Division and discontinuation is
+made between the parts of the water, invironing the perimeter or
+Circumference of the said Plate, and according to the bigness greater
+or lesser of that circuit, it hath to divide a greater or lesser
+quantity of water, so that if the circuit, suppose of a Board, be ten
+Feet in sinking it flatways, it is to make the seperation and
+division, and to so speak, an incission upon ten Feet of water; and
+likewise a lesser Board that is four Feet in Perimeter, must make an
+incession of four Feet. This granted, he that hath any knowledge in
+Geometry, will comprehend, not only that a Board sawed in many long
+thin pieces, will much better float than when it was entire, but that
+all Figures, the more short and narrow they be, shall so much the
+better swim. Let the Board A B C D be, for Example, eight Palmes long,
+and five broad, its circuit shall be twenty six Palmes; and so many
+must the incession be, which it shall make in the water to descend
+therein: but if we do saw ir, as suppose into eight little pieces,
+according to the Lines E F, G H, {&}c. making seven Segments, we must
+adde to the twenty six Palmes of the circuit of the whole Board,
+seventy others; whereupon the eight little pieces so cut and
+seperated, have to cut ninty six Palmes of water. And, if moreover, we
+cut each of the said pieces into five parts, reducing them into
+Squares, to the circuit of ninty six Palmes, with four cuts of eight
+Palmes apiece; we shall adde also sixty four Palmes, whereupon the
+said Squares to descend in the water, must divide one hundred and
+sixty Palmes of water, but the Resistance is much greater than that of
+twenty six; therefore to the lesser Superficies, we shall reduce them,
+so much the more easily will they float: and the same will happen in
+all other Figures, whose Superficies are simular amongst themselves,
+but different in bigness: because the said Superficies, being either
+deminished or encreased, always diminish or encrease their Perimeters
+in subduple proportion; to wit, the Resistance that they find in
+penetrating the water; therefore the little pieces gradually swim,
+with more and more facility as their breadth is lessened.
+
+[Illustration]
+
+  _This is manifest; for keeping still the same height of the Solid,
+  with the same proportion as the Base encreaseth or deminisheth,
+  doth the said Solid also encrease or diminish; whereupon the Solid
+  more diminishing than the Circuit, the Cause of Submersion more
+  diminisheth than the Cause of Natation: And on the contrary, the
+  Solid more encreasing than the Circuit, the Cause of Submersion
+  encreaseth more, that of Natation less._
+
+And this may all be deduced out of the Doctrine of _Aristotle_ against
+his own Doctrine.
+
+Lastly, to that which we read in the latter part of the Text[97], that is
+to say, that we must compare the Gravity of the Moveable with the
+Resistance of the Medium against Division, because if the force of the
+Gravity exceed the Resistance of the _Medium_, the Moveable will
+descend, if not it will float. I need not make any other answer, but
+that which hath been already delivered; namely, that its not the
+Resistance of absolute Division, (which neither is in Water nor Air)
+but the Gravity of the _Medium_ that must be compared with the Gravity
+of the Moveables; and if that of the _Medium_ be greater, the Moveable
+shall not descend, nor so much as make a totall Submersion, but a
+partiall only; because in the place which it would occupy in the
+water, there must not remain a Body that weighs less than a like
+quantity of water: but if the Moveable be more grave, it shall descend
+to the bottom, and possess a place where it is more conformable for it
+to remain, than another Body that is less grave. And this is the only
+true proper and absolute Cause of Natation and Submersion, so that
+nothing else hath part therein: and the Board of the Adversaries
+swimmeth, when it is conjoyned with as much Air, as, together with it,
+doth form a Body less grave than so much water as would fill the place
+that the said Compound occupyes in the water; but when they shall
+demit the simple Ebony into the water, according to the Tenour of our
+Question, it shall alwayes go to the bottom, though it were as thin as
+a Paper.
+
+    [97] Lib. 4. c. 6. Text 45.
+
+[Decoration]
+
+FINIS.
+
+[Decoration]
+
+       *       *       *       *       *
+
+  [Detailed Transcriber's Notes
+
+  The text has been made to match the original text as much as
+  possible including variation in spelling, punctuation, italics etc.
+  The following, details apparent printer's errors as well as changes
+  or additions to aid readability of text.
+
+  Page 1, missing full stop after abbreviation gr. '0 gr 54 min.'.
+
+  Page 3, sidenote, missing space between words 'the Authority ofan
+  Author.'.
+
+  Page 3, printer's error, augmentarion for augmentation 'and
+  augmentarion of Masse'.
+
+  Page 4, missing letter t 'tha{t} that proceeded not'.
+
+  Page 4, printer's error or inconsistent punctuation, 'my paynes and
+  time. and although'.
+
+  Page 6, inconsistent punctuation, full stop after axiome where as
+  there are none after those following 'AXIOME. I.'.
+
+  Page 9, missing full stop added to end of paragraph 'or else an
+  upright Prisme.'.
+
+  Page 11, printer's error, missing letter C in illustration, 'the
+  Prisme A C D B to be placed'.
+
+  Page 15, printer's error or archaic lettering, final y looking like
+  a 7 in original text'and of the Specifick Gravit{y}'.
+
+  Page 16, printer's error, letter N for T in text to refer to
+  illustration, 'if the Vessell E N S F'.
+
+  Page 16, printer's error, duplicate word in text 'equalizeth the
+  Force and and Moment,'.
+
+  Page 17, printer's error, rhe for the 'as in rhe Stilliard,'.
+
+  Page 17, missing space between words 'asoften as that'.
+
+  Page 18, sidenote, printer's error, specifiaclly for specifically
+  'A Solid specifiaclly graver'.
+
+  Page 20, potential printer's error, properly for property, 'but
+  this properly they have'.
+
+  Page 20, printer's error, n for u 'loseth all a{u}thenticalness'.
+
+  Page 22, printer's error or variation in spelling, Benonamico for
+  Buonamico 'it seemes that Benonamico'.
+
+  Page 23, printer's error, missing i 'accordng to its excess'.
+
+  Page 24, missing line at the end of page in original text 'its
+  Region it loseth all'.
+
+  Page 26, missing letter n 'u{n}able by its small weight'.
+
+  Page 29, missing letter e 'that I have gon{e} about'.
+
+  Page 32, unclear symbol in original text 'other Figure, {&}c.'.
+
+  Page 37, potential printer's error, comma in unusual position
+  'whatever Figure, goeth always'.
+
+  Page 38, missing space between words 'Superficies might bedry:'.
+
+  Page 39, missing letter t, unied for united 'which holds them unied'.
+
+  Page 41, printer's error, Motitions for Motions 'all Motitions are
+  made'.
+
+  Page 42, sidenote, possible missing letter e, 'Se{e} what satisfaction'.
+
+  Page 43, printer's error, Subdidivisions for Subdivisions, 'other
+  Subdidivisions,'.
+
+  Page 49, missing letter i, dminishing for diminishing 'or dminishing
+  it by dividing'.
+
+  Page 50, sidenote, printer's error, missing letter l, hep for help
+  'float by hep of'.
+
+  Page 53, printer's error, missing letter n, beig for being 'beig
+  double in Gravity'.
+
+  Page 54, printer's error, missing letter l, 'sha{l}l also descend.'.
+
+  Page 55, printer's error, missing letter r, 'to fo{r}m Solid Bodies'.
+
+  Page 56, printer's error, missing letter A, 'Cone S {A} T'.
+
+  Page 57, printer's error, missing letter t, 'of which i{t} may
+  descend'.
+
+  Page 58, sidenote, printer's error, inverted n, 'Natatio{n} easiest
+  effected'.
+
+  Page 59, missing letter u, 'witho{u}t all Question,'.
+
+  Page 59, printer's error, inverted n, 'with an other Experime{n}t'.
+
+  Page 59, potential printer's error, sidenote ends with comma, 'Or
+  rather Contiguity,'.
+
+  Page 61, missing letter a, 'that in this c{a}se the water,'.
+
+  Page 74, printer's error, ir for it, 'but if we do saw ir,'.
+
+  Page 75, unclear symbol in original text '{&}c. making seven
+  Segments'.
+  ]
+
+
+
+
+
+End of Project Gutenberg's Discourse on Floating Bodies, by Galileo Galilei
+
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+
+<pre>
+
+Project Gutenberg's Discourse on Floating Bodies, by Galileo Galilei
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Discourse on Floating Bodies
+
+Author: Galileo Galilei
+
+Translator: Thomas Salusbury
+
+Release Date: October 12, 2011 [EBook #37729]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK DISCOURSE ON FLOATING BODIES ***
+
+
+
+
+Produced by Tim Madden and the Online Distributed
+Proofreading Team at https://www.pgdp.net (This file was
+produced from images generously made available by The
+Internet Archive)
+
+
+
+
+
+
+</pre>
+
+
+
+<div class="bbox">
+  <p><b>Transcriber's Notes:</b></p>
+
+  <p>All apparent printer's errors retained. Variation in punctuation are
+  as in the original, but missing full stops at end of paragraphs have
+  been supplied. There are inconsistencies in the use of italics,
+  spacing of words and use of full stop after 'AXIOME', abbreviations
+  etc. All are retained to match text. There is a great variation in
+  spelling including multiple spellings of the same word, all spelling
+  has been retained to match text. There are several instances of
+  obviously missing letters or inverted n &amp; u. These have been changed
+  or obvious letters replaced, with the changes surrounded by {}.</p>
+
+  <p>All instances are detailed at the end of the text. It should also be
+  noted that in the original text there is a missing line at the end of
+  page 24 in original text.</p>
+
+  <p>There are a number of instances in the original text where 'that' is
+  immediately followed by a second 'that' in the sentence. These could
+  be potential printer's errors or, since several of them make sense,
+  part of the author's style. They have been left in the text as they
+  appear in the original text.</p>
+
+  <p>The images have been retouched to clean up the diagrams and to improve
+  readability of lettering where possible.</p>
+
+</div>
+
+<hr style="width: 65%;" />
+
+
+
+
+<p class="center bt_m">A</p>
+<p class="center bt_vvl">DISCOURSE</p>
+<p class="center bt_vsp"><i>PRESENTED</i></p>
+<p class="center bt_m bt_vsp">TO THE MOST SERENE</p>
+<p class="center bt_l">Don Cosimo II.</p>
+<p class="center bt_vl">GREAT DUKE</p>
+<p class="center bt_m bt_sp"><i>OF</i></p>
+<p class="center bt_vvl bt_sp">TUSCANY,</p>
+
+<p class="center bt_sp">CONCERNING</p>
+
+<p class="center bt_m">The <i class="bt_sp">NATATION</i> of <span class="bt_sp">BODIES</span> Vpon,</p>
+<p class="center bt_m">And<i class="bt_sp"> SUBMERSION </i>In,</p>
+<p class="center bt_vsp">THE</p>
+<p class="center bt_vvl bt_sp">WATER.</p>
+
+<p class="center">By <span class="smcap bt_sp">Galileus Galilei</span>: Philosopher and</p>
+<p class="center bt_s">Mathematician unto His most Serene Highnesse.</p>
+
+<hr style="width: 65%;" />
+
+<p class="center">Englished from the Second Edition of the <span class="smcap bt_sp">Italian</span>,</p>
+<p class="center bt_s">compared with the Manuscript Copies, and reduced</p>
+<p class="center bt_s">into <span class="bt_sp">PROPOSITIONS</span>:</p>
+
+<p class="center">By<i class="bt_sp"> THOMAS SALUSBURY</i>, Esq;</p>
+
+<hr style="width: 65%;" />
+
+<p class="center"><i class="bt_sp bt_ms">LONDON</i>:</p>
+
+<p class="center bt_ms">Printed by <span class="smcap bt_sp">William Leybourn</span>:</p>
+
+<p class="center bt_ms bt_sp"><i>M DC LXIII.</i></p>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
+<div class="figcenter" style="width: 605px;">
+<img src="images/i003a.png" width="605" height="43" alt="" title="" />
+</div>
+
+<p class="center bt_l bt_vsp">  A DISCOVRSE</p>
+
+<p class="center">Presented to the Most Serene <span class="smcap bt_sp">Don Cosimo</span> II.</p>
+
+<p class="center"><span class="smcap">Great Duke</span> of<i class="bt_sp"> TUSCANY</i>:</p>
+
+<p class="center bt_sp bt_ms">CONCERNING</p>
+
+<p class="center"><i>The Natation of<span class="bt_sp"> BODIES</span> Upon, or Submersion</i></p>
+<p class="center"><i>In, the<span class="bt_sp"> WATER</span>.</i></p>
+
+
+<div class="figleft_dc" style="width: 105px;">
+<img src="images/i003b.png" width="105" height="119" alt="C" title="" />
+</div>
+
+<p>Onsidering (Most Serene Prince) that the publishing this present
+Treatise, of so different an Argument from that which many expect, and
+which according to the intentions I proposed in my * Astronomicall <span class="sidenote">His Nuncio Siderio.</span>
+<i>Adviso</i>, I should before this time have put forth, might peradventure
+make some thinke, either that I had wholly relinquished my farther
+imployment about the new Celestiall Observations, or that, at least, I
+handled them very remissely; I have judged fit to render an account,
+aswell of my deferring that, as of my writing, and publishing this
+treatise.</p>
+
+<p>As to the first, the last discoveries of <i>Saturn</i> to be
+tricorporeall, and of the mutations of Figure in <i>Venus</i>, like to
+those that are seen in the Moon, together with the Consequents
+depending thereupon, have not so much occasioned the demur, as the
+investigation of the times of the Conversions of each of the Four
+Medicean Planets about <i>Jupiter</i>, which I lighted upon in <i>April</i> the
+year past, 1611, at my being in <i>Rome</i>; where, in the end, I
+assertained my selfe, that the first and neerest to <i>Jupiter</i>, moved
+about 8 <i>gr.</i> &amp; 29 <i>m.</i> of its Sphere in an houre, makeing its whole
+revolution in one naturall day, and 18 hours, and almost an halfe. The
+second moves in its Orbe 14 <i>gr.</i> 13 <i>min.</i> or very neer, in an hour,
+and its compleat conversion is consummate in 3 dayes, 13 hours, and
+one third, or thereabouts. The third passeth in an hour, 2 <i>gr.</i> 6
+<i>min.</i> little more or less of its Circle, and measures it all in 7
+dayes, 4 hours, or very neer. The fourth, and more remote than the
+rest, goes in one houre, <a name="tnd_1" id="tnd_1"></a><a href="#tn_1" class="tnlink" title="missing full stop after abbreviation gr.">0 <i>gr</i> 54 <i>min.</i></a> and almost an halfe of its
+Sphere, and finisheth it all in 16 dayes, and very neer 18 hours. But
+because the excessive velocity of their returns or restitutions,
+requires a most scrupulous precisenesse to calculate their places, in
+<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span>
+times past and future, especially if the time be for many Moneths or
+Years; I am therefore forced, with other Observations, and more exact
+than the former, and in times more remote from one another, to correct
+the Tables of such Motions, and limit them even to the shortest
+moment: for such exactnesse my first Observations suffice not; not
+only in regard of the short intervals of Time, but because I had not
+as then found out a way to measure the distances between the said
+Planets by any Instrument: I Observed such Intervals with simple
+relation to the Diameter of the Body of <i>Jupiter</i>; taken, as we have
+said, by the eye, the which, though they admit not errors of above a
+Minute, yet they suffice not for the determination of the exact
+greatness of the Spheres of those Stars. But now that I have hit upon
+a way of taking such measures without failing, scarce in a very few
+Seconds, I will continue the observation to the very occultation of
+<span class="bt_ssp"><i>JUPITER</i></span>, which shall serve to bring us to the perfect knowledge of
+the Motions, and Magnitudes of the Orbes of the said Planets, together <span class="sidenote">The Authors Observations of the Solar Spots</span>
+also with some other consequences thence arising. I adde to these
+things the observation of some obscure Spots, which are discovered in
+the Solar Body, which changing, position in that, propounds to our
+consideration a great argument either that the Sun revolves in it
+selfe, or that perhaps other Starrs, in like manner as <i>Venus</i> and
+<i>Mercury</i>, revolve about it, invisible in other times, by reason of
+their small digressions, lesse than that of <i>Mercury</i>, and only
+visible when they interpose between the Sun and our eye, or else hint
+the truth of both this and that; the certainty of which things ought
+not to be contemned, nor omitted.</p>
+
+<p><i>Continuall observation hath at last assured me that these Spots
+are matters contiguous to the Body of the Sun, there continually
+produced in great number, and afterwards dissolved, some in a
+shorter, some in a longer time, and to be by the Conversion or
+Revolution of the Sun in it selfe, which in a Lunar Moneth, or
+thereabouts, finisheth its Period, caried about in a Circle, an
+accident great of it selfe, and greater for its Consequences.</i></p>
+
+<div class="sidenote">The occasion inducing the Author to write this
+Treatise.</div>
+
+<p>As to the other particular in the next place * Many causes have
+moved me to write the present Tract, the subject whereof, is the
+Dispute which I held some dayes since, with some learned men of this
+City, about which, as your Highnesse knows, have followed many
+Discourses: The principall of which Causes hath been the Intimation of
+your Highnesse, having commended to me Writing, as a singular means to
+make true known from false, reall from apparent Reasons, farr better
+than by Disputing vocally, where the one or the other, or very often
+<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span>
+both the Disputants, through too greate heate, or exalting of the
+voyce, either are not understood, or else being transported by
+ostentation of not yeilding to one another, farr from the first
+Proposition, with the novelty, of the various Proposals, confound both
+themselves and their Auditors.</p>
+
+<p>Moreover, it seemed to me convenient to informe your Highnesse of all
+the sequell, concerning the Controversie of which I treat, as it hath
+been advertised often already by others: and because the Doctrine
+which I follow, in the discussion of the point in hand, is different
+from that of <i>Aristotle</i>; and interferes with his Principles, I have
+considered that against the Authority of that most famous Man, which
+amongst many makes all suspected that comes not from the Schooles of
+the Peripateticks, its farr better to give ones Reasons by the Pen
+than by word of mouth, and therfore I resolved to write the present
+discourse: in which yet I hope to demonstrate that it was not out of
+capritiousnesse, or for that I had not read or understood <i>Aristotle</i>,
+that I sometimes swerve from his opinion, but because severall Reasons
+perswade me to it, and the same <i>Aristotle</i> hath tought me to fix my
+judgment on that which is grounded upon Reason, and not on the bare
+<span class="sidenote"><i>Aristotle</i> prefers Reason to the <a name="tnd_3a" id="tnd_3a"></a><a href="#tn_3a" class="tnlink" title="missing space between words">Authority ofan
+Author.</a></span>
+Authority of the Master; and it is most certaine according to the
+sentence of <i>Alcinoos</i>, that philosophating should be free. Nor is the
+resolution of our Question in my judgment without some benefit to the
+<span class="sidenote">The benefit of this Argument.</span>
+Universall, forasmuch as treating whether the figure of Solids
+operates, or not, in their going, or not going to the bottome in
+Water, in occurrences of building Bridges or other Fabricks on the
+Water, which happen commonly in affairs of grand import, it may be of
+great availe to know the truth.</p>
+
+<p>I say therfore, that being the last Summer in company with certain
+Learned men, it was said in the argumentation; That Condensation was
+<span class="sidenote">Condensation the Propriety of Cold, according to the
+Peripateticks.</span>
+the propriety of Cold, and there was alledged for instance, the
+example of Ice: now I at that time said, that, in my judgment, the Ice
+<span class="sidenote">Ice rather water rarified, than condensed, and why:</span>
+should be rather Water rarified than condensed, and my reason was,
+because Condensation begets diminution of Mass, and augmentation of
+gravity, and Rarifaction causeth greater Lightness, <a name="tnd_3b" id="tnd_3b"></a><a href="#tn_3b" class="tnlink" title="printer's error, augmentarion for augmentation">and augmentarion
+of Masse:</a> and Water in freezing, encreaseth in Masse, and the Ice made
+thereby is lighter than the Water on which it swimmeth.</p>
+
+<p><i>What I say, is manifest, because, the medium subtracting from the
+whole Gravity of Sollids the weight of such another Masse of the
+<span class="sidenote">In lib: 1. of Natation of Bodies Prop. 7.</span>
+said Medium; as</i> Archimedes <i>proves in his</i> * First Booke De
+Insidentibus Humido; <i>when ever the Masse of the said Solid
+encreaseth by Distraction, the more shall the</i> Medium <i>detract from
+its entire Gravity; and lesse, when by Compression it shall be
+condensed and reduced to a lesse Masse.</i></p>
+<p><span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span></p>
+<div class="sidenote">Figure operates not in the Natation of Sollids.</div>
+
+<p>It was answered me, <a name="tnd_4a" id="tnd_4a"></a><a href="#tn_4a" class="tnlink" title="missing letter t">tha{t} that proceeded not</a> from the greater Levity,
+but from the Figure, large and flat, which not being able to penetrate
+the Resistance of the Water, is the cause that it submergeth not. I
+replied, that any piece of Ice, of whatsoever Figure, swims upon the
+Water, a manifest signe, that its being never so flat and broad, hath
+not any part in its floating: and added, that it was a manifest proofe
+hereof to see a piece of Ice of very broad Figure being thrust to the
+botome of the Water, suddenly return to flote atoppe, which had it
+been more grave, and had its swimming proceeded from its Forme, unable
+to penetrate the Resistance of the <i>Medium</i>, that would be altogether
+impossible; I concluded therefore, that the Figure was in sort a Cause
+of the Natation or Submersion of Bodies, but the greater or lesse
+Gravity in respect of the Water: and therefore all Bodyes heavier than
+it of what Figure soever they be, indifferently go to the bottome, and
+the lighter, though of any figure, float indifferently on the top: and
+I suppose that those which hold otherwise, were induced to that
+beliefe, by seeing how that diversity of Formes or Figures, greatly
+altereth the Velosity, and Tardity of Motion; so that Bodies of Figure
+broad and thin, descend far more leasurely into the Water, than those
+of a more compacted Figure, though both made of the same Matter: by
+which some might be induced to believe that the Dilatation of the
+Figure might reduce it to such amplenesse that it should not only
+retard but wholly impede and take away the Motion, which I hold to be
+false. Upon this Conclusion, in many dayes discourse, was spoken much,
+and many things, and divers Experiments produced, of which your
+Highnesse heard, and saw some, and in this discourse shall have all
+that which hath been produced against my Assertion, and what hath been
+suggested to my thoughts on this matter, and for confirmation of my
+Conclusion: which if it shall suffice to remove that (as I esteem
+hitherto false) Opinion, I shall thinke I have not unprofitably spent
+<a name="tnd_4b" id="tnd_4b"></a><a href="#tn_4b" class="tnlink" title="printer's error or inconsistent punctuation">my paynes and time. and although</a> that come not to passe, yet ought I
+to promise another benefit to my selfe, namely, of attaining the
+knowledge of the truth, by hearing my Fallacyes confuted, and true
+demonstrations produced by those of the contrary opinion.</p>
+
+<p>And to proceed with the greatest plainness and perspicuity that I can
+possible, it is, I conceive, necessary, first of all to declare what
+is the true, intrinsecall, and totall Cause, of the ascending of some
+Sollid Bodyes in the Water, and therein floating; or on the contrary,
+of their sinking and so much the rather in asmuch as I cannot satisfie
+myselfe in that which <i>Aristotle</i> hath left written on this Subject.</p>
+
+<div class="sidenote">The cause of the Natation &amp; submersion of Solids in
+the Water.</div>
+
+<p><span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span></p>
+<p>I say then the Cause why some Sollid Bodyes descend to the Bottom of
+Water, is the excesse of their Gravity, above the Gravity of the
+Water; and on the contrary, the excess of the Waters Gravity above the
+Gravity of those, is the Cause that others do not descend, rather that
+they rise from the Bottom, and ascend to the Surface. This was
+subtilly demonstrated by <i>Archimedes</i> in his Book Of the <span class="smcap bt_ssp">Natation</span> of
+<span class="smcap bt_ssp">Bodies</span>: Conferred afterwards by a very grave Author, but, if I erre
+not invisibly, as below for defence of him, I shall endeavour to
+prove.</p>
+
+<p>I, with a different Method, and by other meanes, will endeavour to
+demonstrate the same, reducing the Causes of such Effects to more
+intrinsecall and immediate Principles, in which also are discovered
+the Causes of some admirable and almost incredible Accidents, as that
+would be, that a very little quantity of Water, should be able, with
+its small weight, to raise and sustain a Solid Body, an hundred or a
+thousand times heavier than it.</p>
+
+<p>And because demonstrative Order so requires, I shall define certain
+Termes, and afterwards explain some Propositions, of which, as of
+things true and obvious, I may make use of to my present purpose.</p>
+
+
+
+
+<h2><a name="DEFINITION_I" id="DEFINITION_I"></a>DEFINITION I.</h2>
+
+<p class="def_head"><i>I then call equally Grave</i> in specie, <i>those Matters of which equall
+Masses weigh equally.</i></p>
+
+
+<p>As if for example, two Balls, one of Wax, and the other of some Wood
+of equall Masse, were also equall in Weight, we say, that such Wood,
+and the Wax are <i>in specie</i> equally grave.</p>
+
+
+
+
+<h2><a name="DEFINITION_II" id="DEFINITION_II"></a>DEFINITION II.</h2>
+
+<p class="def_head"><i>But equally grave in Absolute Gravity, we call two Sollids,
+weighing equally, though of Mass they be unequall.</i></p>
+
+
+<p>As for example, a Mass of Lead, and another of Wood, that weigh each
+ten pounds, I call equall in Absolute Gravity, though the Mass of the
+Wood be much greater then that of the Lead.</p>
+
+<p><i>And, consequently, less Grave</i> in specie.</p>
+
+
+
+
+<h2><a name="DEFINITION_III" id="DEFINITION_III"></a>DEFINITION III.</h2>
+
+<p class="def_head"><i>I call a Matter more Grave</i> in specie <i>than another, of which a
+Mass, equall to a Mass of the other, shall weigh more.</i></p>
+
+
+<p><span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span></p>
+<p>And so I say, that Lead is more grave <i>in specie</i> than Tinn, because
+if you take of them two equall Masses, that of the Lead weigheth more.</p>
+
+
+
+
+<h2><a name="DEFINITION_IV" id="DEFINITION_IV"></a>DEFINITION IV.</h2>
+
+<p class="def_head"><i>But I call that Body more grave absolutely than this, if that
+weigh more than this, without any respect had to the Masses.</i></p>
+
+
+<p>And thus a great piece of Wood is said to weigh more than a little
+lump of Lead, though the Lead be <i>in specie</i> more heavy than the Wood.
+And the same is to be understood of the less grave <i>in specie</i>, and
+the less grave absolutely.</p>
+
+<p>These Termes defined, I take from the Mechanicks two Principles: the
+first is, that</p>
+
+
+
+
+<h2><a name="AXIOME_I" id="AXIOME_I"></a><a name="tnd_6" id="tnd_6"></a><a href="#tn_6" class="tnlink" title="inconsistent punctuation, full stop after axiome">AXIOME. I.</a></h2>
+
+<p class="def_head"><i>Weights absolutely equall, moved with equall Velocity, are of
+equall Force and Moment in their operations.</i></p>
+
+
+
+<h2><a name="DEFINITION_V" id="DEFINITION_V"></a><i>DEFINITION V.</i></h2>
+
+<p class="def_head">Moment, amongst Mechanicians, signifieth that Vertue, that Force,
+or that Efficacy, with which the Mover moves, and the Moveable
+resists.</p>
+
+
+<p><i>Which Vertue dependes not only on the simple Gravity, but on the
+Velocity of the Motion, and on the diverse Inclinations of the
+Spaces along which the Motion is made: For a descending Weight
+makes a greater Impetus in a Space much declining, than in one less
+declining; and in summe, what ever is the occasion of such Vertue,
+it ever retaines the name of Moment; nor in my Judgement, is this
+sence new in our Idiome, for, if I mistake not, I think we often
+say; This is a weighty businesse, but the other is of small moment:
+and we consider lighter matters and let pass those of Moment; a
+Metaphor, I suppose, taken from the Mechanicks.</i></p>
+
+<p>As for example, two weights equall in absolute Gravity, being put
+into a Ballance of equall Arms, they stand in <i>Equilibrium</i>, neither
+one going down, nor the other up: because the equality of the
+Distances of both, from the Centre on which the Ballance is supported,
+and about which it moves, causeth that those weights, the said
+Ballance moving, shall in the same Time move equall Spaces, that is,
+shall move with equall Velocity, so that there is no reason for which
+<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>
+this Weight should descend more than that, or that more than this; and
+therefore they make an <i>Equilibrium</i>, and their Moments continue of
+semblable and equall Vertue.</p>
+
+<p>The second Principle is; That</p>
+
+
+
+
+<h2><a name="AXIOME_II" id="AXIOME_II"></a>AXIOME II.</h2>
+
+<p class="def_head"><i>The Moment and Force of the Gravity, is encreased by the Velocity
+of the Motion.</i></p>
+
+
+<p>So that Weights absolutely equall, but conjoyned with Velocity
+unequall, are of Force, Moment and Vertue unequall: and the more
+potent, the more swift, according to the proportion of the Velocity of
+the one, to the Velocity of the other. Of this we have a very
+pertinent example in the Balance or Stiliard of unequall Arms, at
+which Weights absolutely equall being suspended, they do not weigh
+down, and gravitate equally, but that which is at a greater distance
+from the Centre, about which the Beam moves, descends, raising the
+other, and the Motion of this which ascends is slow, and the other
+swift: and such is the Force and Vertue, which from the Velocity of
+the Mover, is conferred on the Moveable, which receives it, that it
+can exquisitely compensate, as much more Weight added to the other
+slower Moveable: so that if of the Arms of the Balance, one were ten
+times as long as the other, whereupon in the Beames moving about the
+Centre, the end of that would go ten times as far as the end of this,
+a Weight suspended at the greater distance, may sustain and poyse
+another ten times more grave absolutely than it: and that because the
+Stiliard moving, the lesser Weight shall move ten times faster than
+the bigger. It ought alwayes therefore to be understood, that Motions
+are according to the same Inclinations, namely, that if one of the
+Moveables move perpendicularly to the Horizon, then the other makes
+its Motion by the like Perpendicular; and if the Motion of one were to
+be made Horizontally; that then the other is made along the same
+Horizontall plain: and in summe, alwayes both in like Inclinations.
+This proportion between the Gravity and Velocity is found in all
+Mechanicall Instruments: and is considered by <i>Aristotle</i>, as a
+Principle in his <i>Mechanicall Questions</i>; whereupon we also may take
+it for a true Assumption, That</p>
+
+
+
+
+<h2><a name="AXIOME_III" id="AXIOME_III"></a>AXIOME III.</h2>
+
+<p class="def_head"><i>Weights absolutely unequall, do alternately counterpoyse and
+become of equall Moments, as oft as their Gravities, with
+contrary proportion, answer to the Velocity of their Motions.</i></p>
+
+
+<p><span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span></p>
+<p>That is to say, that by how much the one is less grave than the other,
+by so much is it in a constitution of moving more swiftly than that.</p>
+
+<p>Having prefatically explicated these things, we may begin to enquire,
+what Bodyes those are which totally submerge in Water, and go to the
+Bottom, and which those that by constraint float on the top, so that
+being thrust by violence under Water, they return to swim, with one
+part of their Mass visible above the Surface of the Water: and this we
+will do by considering the respective operation of the said Solids,
+and of Water: Which operation followes the Submersion and sinking; and
+<span class="sidenote">How the submersion of Solids in the Water, is
+effected.</span>
+this it is, That in the Submersion that the Solid maketh, being
+depressed downwards by its proper Gravity, it comes to drive away the
+water from the place where it successively subenters, and the water
+repulsed riseth and ascends above its first levell, to which Ascent on
+the other side it, as being a grave Body of its own nature, resists:
+And because the descending Solid more and more immerging, greater and
+greater quantity of Water ascends, till the whole Sollid be submerged;
+its necessary to compare the Moments of the Resistance of the water to
+Ascension, with the Moments of the pressive Gravity of the Solid: And
+if the Moments of the Resistance of the water, shall equalize the
+<span class="sidenote">What Solids shall float on the Water.</span>
+Moments of the Solid, before its totall Immersion; in this case
+doubtless there shall be made an <i>Equilibrium</i>, nor shall the Body
+sink any farther. But if the Moment of the Solid, shall alwayes exceed
+the Moments wherewith the repulsed water successively makes
+<span class="sidenote">What Solids shall sinke to the botome.</span>
+Resistance, that Solid shall not only wholly submerge under water, but
+shall descend to the Bottom. But if, lastly, in the instant of totall
+Submersion, the equality shall be made between the Moments of the
+<span class="sidenote">What Solids shall rest in all places of the Water.</span>
+prement Solid, and the resisting Water; then shall rest, ensue, and
+the said Solid shall be able to rest indifferently, in whatsoever part
+of the water. By this time is manifest the necessity of comparing the
+<span class="sidenote">The Gravitie of the Water and Solid must be compared in
+all Problems, of Natation of Bodies.</span>
+Gravity of the water, and of the Solid; and this comparison might at
+first sight seem sufficient to conclude and determine which are the
+Solids that float a-top, and which those that sink to the Bottom in
+the water, asserting that those shall float which are lesse grave <i>in
+specie</i> than the water, and those submerge, which are <i>in specie</i> more
+grave. For it seems in appearance, that the Sollid in sinking
+continually, raiseth so much Water in Mass, as answers to the parts of
+its own Bulk submerged: whereupon it is impossible, that a Solid less
+grave <i>in specie</i>, than water, should wholly sink, as being unable to
+raise a weight greater than its own, and such would a Mass of water
+equall to its own Mass be. And likewise it seems necessary, that the
+graver Solids do go to the Bottom, as being of a Force more than
+sufficient for the raising a Masse of water, equall to its own, though
+inferiour in weight. Nevertheless the business succeeds otherwise: and
+<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span>
+though the Conclusions are true, yet are the Causes thus assigned
+deficient, nor is it true, that the Solid in submerging, raiseth and
+repulseth Masses of Water, equall to the parts of it self submerged;
+but the Water repulsed, is alwayes less than the parts of the Solid
+<span class="sidenote">The water repelled is ever less than the parts of the
+Sollid submerged.</span>
+submerged: and so much the more by how much the Vessell in which the
+Water is contained is narrower: in such manner that it hinders not,
+but that a Solid may submerge all under Water, without raising so much
+Water in Mass, as would equall the tenth or twentieth part of its own
+Bulk: like as on the contrary, a very small quantity of Water, may
+<span class="sidenote"><i>A</i> small quantity of water, may float a very great
+Solid Mass.</span>
+raise a very great Solid Mass, though such Solid should weigh
+absolutely a hundred times as much, or more, than the said Water, if
+so be that the Matter of that same Solid be <i>in specie</i> less grave
+than the Water. And thus a great Beam, as suppose of a 1000 weight,
+may be raised and born afloat by Water, which weighs not 50: and this
+happens when the Moment of the Water is compensated by the Velocity of
+its Motion.</p>
+
+<p>But because such things, propounded thus in abstract, are somewhat
+difficult to be comprehended, it would be good to demonstrate them by
+particular examples; and for facility of demonstration, we will
+suppose the Vessels in which we are to put the Water, and place the
+Solids, to be inviron'd and included with sides erected perpendicular
+to the Plane of the Horizon, and the Solid that is to be put into such
+vessell to be either a streight Cylinder, <a name="tnd_9" id="tnd_9"></a><a href="#tn_9" class="tnlink" title="missing full stop added to end of paragraph">or else an upright Prisme.</a></p>
+
+<p><i>The which proposed and declared, I proceed to demonstrate the truth
+of what hath been hinted, forming the ensuing Theoreme.</i></p>
+
+
+
+
+<h2><a name="THEOREME_I" id="THEOREME_I"></a><i>THEOREME I.</i></h2>
+
+<div class="sidenote">The Proportion of the water raised to the Solid
+submerged.</div>
+
+<p class="def_head">The Mass of the Water which ascends in the submerging of a Solid,
+Prisme or Cylinder, or that abaseth in taking it out, is less
+than the Mass of the said Solid, so depressed or advanced: and
+hath to it the same proportion, that the Surface of the Water
+circumfusing the Solid, hath to the same circumfused Surface,
+together with the Base of the Solid.</p>
+
+<p class="cap">L<i>et the Vessell be A B C D, and in it the Water raised up to the
+Levell E F G, before the Solid Prisme H I K be therein immerged; but
+after that it is depressed under Water, let the Water be raised as
+high as the Levell L M, the Solid H I K shall then be all under Water,
+and the Mass of the elevated Water shall be L G, which is less than
+<span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span>
+<span class="figleft" style="width: 220px;">
+  <img src="images/i012.png" width="220" height="237" alt="" title="" />
+</span>
+the Masse of the Solid depressed, namely of H I K, being equall to the
+only part E I K, which is contained under the first Levell E F G.
+Which is manifest, because if the Solid H I K be taken out, the Water
+I G shall return into the place occupied by the Mass E I K, where it
+was continuate before the submersion of the Prisme. And the Mass L G
+being equall to the Mass E K: adde thereto the Mass E N, and it shall
+be the whole Mass E M, composed of the parts of the Prisme E N, and of
+the Water N F, equall to the whole Solid H I K: And, therefore, the
+Mass L G shall have the same proportion to E M, as to the Mass H I K:
+But the Mass L G hath the same proportion to the Mass E M, as the
+Surface L M hath to the Surface M H: Therefore it is manifest, that
+the Mass of Water repulsed L G, is in proportion to the Mass of the
+Solid submerged H I K; as the Surface L M, namely, that of the Water
+ambient about the Sollid, to the whole Surface H M, compounded of the
+said ambient water, and the Base of the Prisme H N. But if we suppose
+the first Levell of the Water the according to the Surface H M, and
+the Prisme allready submerged H I K; and after to be taken out and
+raised to E A O, and the Water to be faln from the first Levell H L M
+as low as E F G; It is manifest, that the Prisme E A O being the same
+with H I K, its superiour part H O, shall be equall to the inferiour E
+I K: and remove the common part E N, and, consequently, the Mass of
+the Water L G is equall to the Mass H O; and, therefore, less than the
+Solid, which is without the Water, namely, the whole Prisme E A O, to
+which likewise, the said Mass of Water abated L G, hath the same
+proportion, that the Surface of the Waters circumfused L M hath to the
+same circumfused Surface, together with the Base of the Prisme A O:
+which hath the same demonstration with the former case above.</i></p>
+
+<p><i>And from hence is inferred, that the Mass of the Water, that riseth
+in the immersion of the Solid, or that ebbeth in elevating it, is not
+equall to all the Mass of the Solid, which is submerged or elevated,
+but to that part only, which in the immersion is under the first
+Levell of the Water, and in the elevation remaines above the first
+Levell: Which is that which was to be demonstrated. We will now pursue
+the things that remain.</i></p>
+
+<p>And first we will demonstrate that,</p>
+<p><span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span></p>
+
+
+
+
+
+<h2><a name="THEOREME_II" id="THEOREME_II"></a>THEOREME II.</h2>
+
+<div class="sidenote">The proportion of the water abated, to the Solid
+raised.</div>
+
+<p class="def_head"><i>When in one of the above said Vessels, of what ever breadth,
+whether wide or narrow, there is placed such a Prisme or
+Cylinder, inviron'd with Water, if we elevate that Solid
+perpendicularly, the Water circumfused shall abate, and the
+Abatement of the Water, shall have the same proportion to the
+Elevation of the Prisme, as one of the Bases of the Prisme, hath
+to the Surface of the Water Circumfused.</i></p>
+
+
+<div class="figright" style="width: 246px;">
+<img src="images/i013.png" width="246" height="198" alt="" title="" />
+</div>
+
+<p class="cap">Imagine in the Vessell, as is aforesaid, <a name="tnd_11" id="tnd_11"></a><a href="#tn_11" class="tnlink" title="printer's error, missing letter C in illustration">the Prisme A C D B to be</a>
+placed, and in the rest of the Space the Water to be diffused as far
+as the Levell E A: and raising the Solid, let it be transferred to G
+M, and let the Water be abased from E A to N O: I say, that the
+descent of the Water, measured by the Line A O, hath the same
+proportion to the rise of the Prisme, measured by the Line G A, as the
+Base of the Solid G H hath to the Surface of the Water N O. The which
+is manifest: because the Mass of the Solid G A B H, raised above the
+first Levell E A B, is equall to the Mass of Water that is abased E N
+O A. Therefore, E N O A and G A B H are two equall Prismes; for of
+equall Prismes, the Bases answer contrarily to their heights:
+Therefore, as the Altitude A O is to the Altitude A G, so is the
+Superficies or Base G H to the Surface of the Water N O. If therefore,
+for example, a Pillar were erected in a waste Pond full of Water, or
+else in a Well, capable of little more then the Mass of the said
+Pillar, in elevating the said Pillar, and taking it out of the Water,
+according as it riseth, the Water that invirons it will gradually
+abate, and the abasement of the Water at the instant of lifting out
+the Pillar, shall have the same proportion, that the thickness of the
+Pillar hath to the excess of the breadth of the said Pond or Well,
+above the thickness of the said Pillar: so that if the breadth of the
+Well were an eighth part larger than the thickness of the Pillar, and
+the breadth of the Pond twenty five times as great as the said
+thickness, in the Pillars ascending one foot, the water in the Well
+shall descend seven foot, and that in the Pond only 1/25 of a foot.</p>
+
+<div class="sidenote">Why a Solid less grave <i>in specie</i> than water, stayeth
+not under water, in very small depths:</div>
+
+<p>This Demonstrated, it will not be difficult to show the true cause,
+how it comes to pass, that,</p>
+<p><span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span></p>
+
+
+
+
+<h2><a name="THEOREME_III" id="THEOREME_III"></a>THEOREME III.</h2>
+
+<p class="def_head"><i>A Prisme or regular Cylinder, of a substance specifically less
+grave than Water, if it should be totally submerged in Water,
+stayes not underneath, but riseth, though the Water circumfused
+be very little, and in absolute Gravity, never so much inferiour
+to the Gravity of the said Prisme.</i></p>
+
+
+<p class="cap">Let then the Prisme A E F B, be put into the Vessell C D F B, the same
+being less grave <i>in specie</i> than the Water: and let the Water infused
+rise to the height of the Prisme: I say, that the Prisme left at
+liberty, it shall rise, being born up by the Water circumfused C D E
+<span class="figleft" style="width: 190px;">
+<img src="images/i014.png" width="190" height="162" alt="" title="" />
+</span>
+A. For the Water C E being specifically more grave than the Solid A F,
+the absolute weight of the water C E, shall have greater proportion to
+the absolute weight of the Prisme A F, than the Mass C E hath to the
+Mass A F (in regard the Mass hath the same proportion to the Mass,
+that the weight absolute hath to the weight absolute, in case the
+Masses are of the same Gravity <i>in specie</i>.) But the Mass C E is to
+the Mass A F, as the Surface of the water A C, is to the Superficies,
+or Base of the Prisme A B; which is the same proportion as the ascent
+of the Prisme when it riseth, hath to the descent of the Water
+circumfused C E.</p>
+
+<p>Therefore, the absolute Gravity of the water C E, hath greater
+proportion to the absolute Gravity of the Prisme A F; than the Ascent
+of the Prisme A F, hath to the descent of the said water C E. The
+Moment, therefore, compounded of the absolute Gravity of the water C
+E, and of the Velocity of its descent, whilst it forceably repulseth
+and raiseth the Solid A F, is greater than the Moment compounded of
+the absolute Gravity of the Prisme A F, and of the Tardity of its
+ascent, with which Moment it contrasts and resists the repulse and
+violence done it by the Moment of the water: Therefore, the Prisme
+shall be raised.</p>
+
+<div class="sidenote">The Proportion according to which the Submersion &amp;
+Natation of Solids is made.</div>
+
+<p>It followes, now, that we proceed forward to demonstrate more
+particularly, how much such Solids shall be inferiour in Gravity to
+the water elevated; namely, what part of them shall rest submerged,
+and what shall be visible above the Surface of the water: but first it
+is necessary to demonstrate the subsequent Lemma.</p>
+<p><span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span></p>
+
+
+
+
+<h2><a name="LEMMA_I" id="LEMMA_I"></a>LEMMA I.</h2>
+
+<div class="sidenote">The absolute Gravity of Solids, are in a proportion
+compounded of their Specifick Gravities, and of their Masses.</div>
+
+<p class="def_head"><i>The absolute Gravities of Solids, have a proportion compounded of
+the proportions of their specificall Gravities, and of their
+Masses.</i></p>
+
+
+<p class="cap">Let A and B be two Solids. I say, that the Absolute Gravity of A,
+hath to the Absolute Gravity of B, a proportion compounded of the
+proportions of the specificall Gravity of A, to the Specificall
+<span class="figright" style="width: 157px;">
+<img src="images/i015.png" width="157" height="167" alt="" title="" />
+</span>
+Gravity of B, and of the Mass A to the Mass B. Let the Line D have the
+same proportion to E, that the specifick Gravity of A, hath to the
+specifick Gravity of B; and let E be to F, as the Mass A to the Mass
+B: It is manifest, that the proportion of D to F, is compounded of the
+proportions D and E; and E and F. It is requisite, therefore, to
+demonstrate, that as D is to F, so the absolute Gravity of A, is to
+the absolute Gravity of B. Take the Solid C, equall in Mass to the
+Solid A, and of the same Gravity <i>in specie</i> with the Solid B.
+Because, therefore, A and C are equall in Mass, the absolute Gravity
+of A, shall have to the absolute Gravity of C, the same proportion, as
+the specificall Gravity of A, hath to the specificall Gravity of C, or
+of B, which is the same <i>in specie</i>; that is, as D is to E. And,
+because, C and B are of the same Gravity <i>in specie</i>, it shall be,
+that as the absolute weight of C, is to the absolute weight of B, so
+the Mass C, or the Mass A, is to the Mass B; that is, as the Line E to
+the Line F. As therefore, the absolute Gravity of A, is to the
+absolute Gravity of C, so is the Line D to the Line E: and, as the
+absolute Gravity of C, is to the absolute Gravity of B, so is the Line
+E to the Line F: Therefore, by Equality of proportion, the absolute
+Gravity of A, is to the absolute Gravity of B, as the Line D to the
+Line F: which was to be demonstrated. I proceed now to demonstrate,
+how that,</p>
+<p><span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span></p>
+
+
+
+
+<h2><a name="THEOREME_IV" id="THEOREME_IV"></a>THEOREME IV.</h2>
+
+<div class="sidenote">The proportion of water requisite to make a Solid
+swim:</div>
+
+<p class="def_head"><i>If a Solid, Cylinder, or Prisme, lesse grave specifically than the
+Water, being put into a Vessel, as above, of whatsoever
+greatnesse, and the Water, be afterwards infused, the Solid shall
+rest in the bottom, unraised, till the Water arrive to that part
+of the Altitude, of the said Prisme, to which its whole Altitude
+hath the same proportion, that the Specificall Gravity of the
+Water, hath to the Specificall Gravity of the said Solid: but
+infusing more Water, the Solid shall ascend.</i></p>
+
+
+<p class="cap">Let the Vessell be M L G N of any bigness, and let there be placed in
+it the Solid Prisme D F G E, less grave <i>in specie</i> than the water;
+and look what proportion the Specificall Gravity of the water, hath to
+that of the Prisme, such let the Altitude D F, have to the Altitude F
+B. I say, that infusing water to the Altitude F B, the Solid D G shall
+not float, but shall stand in <i>Equilibrium</i>, so, that that every
+little quantity of water, that is infused, shall raise it. Let the
+water, therefore, be infused to the Levell A B C; and; because the
+Specifick Gravity of the Solid D G, is to the Specifick Gravity of the
+water, as the altitude B F is to the altitude F D; that is, as the
+Mass B G to the Mass G D; as the proportion of the Mass B G is to the
+Mass G D, as the proportion of the Mass G D is to the Mass A F, they
+compose the Proportion of the Mass B G to the Mass A F. Therefore, the
+Mass B G is to the Mass A F, in a proportion compounded of the
+proportions of the Specifick Gravity of the Solid G D, to the
+<span class="figleft" style="width: 183px;">
+<img src="images/i016.png" width="183" height="176" alt="" title="" />
+</span>
+Specifick Gravity of the water, and of the Mass G D to the Mass A F:
+But the same proportions of the Specifick Gravity of G D, to the
+Specifick Gravity of the water, and of the Mass G D to the Mass A F,
+do also by the precedent <i>Lemma</i>, compound the proportion of the
+absolute Gravity of the Solid D G, to the absolute Gravity of the Mass
+of the water A F: Therefore, as the Mass B G is to the Mass A F, so is
+the Absolute Gravity of the Solid D G, to the Absolute Gravity of the
+Mass of the water A F. But as the Mass B G is to the Mass A F; so is
+the Base of the Prisme D E, to the Surface of the water A B; and so is
+the descent of the water A B, to the Elevation of the Prisme D G;
+<span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span>
+Therefore, the descent of the water is to the elevation of the Prisme,
+as the absolute Gravity of the Prisme, is to the absolute Gravity of
+the water: Therefore, the Moment resulting from the absolute Gravity
+of the water A F, and the Velocity of the Motion of declination, with
+which Moment it forceth the Prisme D G, to rise and ascend, is equall
+to the Moment that results from the absolute Gravity of the Prisme D
+G, and from the Velocity of the Motion, wherewith being raised, it
+would ascend: with which Moment it resists its being raised: because,
+therefore, such Moments are equall, there shall be an <i>Equilibrium</i>
+between the water and the Solid. And, it is manifest, that putting a
+little more water unto the other A F, it will increase the Gravity and
+Moment, whereupon the Prisme D G, shall be overcome, and elevated till
+that the only part B F remaines submerged. Which is that that was to
+be demonstrated.</p>
+
+
+<h3>COROLLARY I.</h3>
+
+<div class="sidenote"><i>H</i>ow far Solids less grave <i>in specie</i> than water, do
+submerge.</div>
+
+<p class="cor_head"><i>By what hath been demonstrated, it is manifest, that Solids less
+grave</i> in specie <i>than the water, submerge only so far, that as
+much water in Mass, as is the part of the Solid submerged, doth
+weigh absolutely as much as the whole Solid.</i></p>
+
+<p>For, it being supposed, that the Specificall Gravity of the water, is
+to the Specificall Gravity of the Prisme D G, as the Altitude D F, is
+to the Altitude F B; that is, as the Solid D G is to the Solid B G; we
+might easily demonstrate, that as much water in Mass as is equall to
+the Solid B G, doth weigh absolutely as much as the whole Solid D G;
+For, by the <i>Lemma</i> foregoing, the Absolute Gravity of a Mass of
+water, equall to the Mass B G, hath to the Absolute Gravity of the
+Prisme D G, a proportion compounded of the proportions, of the Mass B
+G to the Mass G D, <a name="tnd_15" id="tnd_15"></a><a href="#tn_15" class="tnlink" title="printer's error or archaic lettering, final y looking like a 7 in original text">and of the Specifick Gravit{y}</a> of the water, to the
+Specifick Gravity of the Prisme: But the Gravity <i>in specie</i> of the
+water, to the Gravity <i>in specie</i> of the Prisme, is supposed to be as
+the Mass G D to the Mass G B. Therefore, the Absolute Gravity of a
+Mass of water, equall to the Mass B G, is to the Absolute Gravity of
+the Solid D G, in a proportion compounded of the proportions, of the
+Mass B G to the Mass G D, and of the Mass D G to the Mass G B; which
+is a proportion of equalitie. The Absolute Gravity, therefore, of a
+Mass of Water equall to the part of the Mass of the Prisme B G, is
+equall to the Absolute Gravity of the whole Solid D G.</p>
+<p><span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span></p>
+
+
+<h3>COROLLARY II.</h3>
+
+<div class="sidenote"><i>A</i> Rule to equilibrate Solids in the water.</div>
+
+<p class="cor_head"><i>It followes, moreover, that a Solid less grave than the water,
+being put into a Vessell of any imaginable greatness, and water
+being circumfused about it to such a height, that as much water
+in Mass, as is the part of the Solid submerged, do weigh
+absolutely as much as the whole Solid; it shall by that water be
+justly sustained, be the circumfused Water in quantity greater or
+lesser.</i></p>
+
+<p>For, if the Cylinder or Prisme M, less grave than the water, <i>v. gra.</i>
+in Subsequiteriall proportion, shall be put into the capacious Vessell
+A B C D, and the water raised about it, to three quarters of its
+<span class="figleft" style="width: 411px;">
+<img src="images/i018.png" width="411" height="69" alt="" title="" />
+</span>
+height, namely, to its Levell A D: it shall be sustained and exactly
+poysed in <i>Equilibrium</i>. The same will happen; <a name="tnd_16b" id="tnd_16b"></a><a href="#tn_16b" class="tnlink" title="letter N for T in text to refer to
+illustration">if the Vessell E N S F</a>
+were very small, so, that between the Vessell and the Solid M, there
+were but a very narrow space, and only capable of so much water, as
+the hundredth part of the Mass M, by which it should be likewise
+raised and erected, as before it had been elevated to three fourths of
+the height of the Solid: which to many at the first sight, may seem a
+notable Paradox, and beget a conceit, that the Demonstration of these
+effects, were sophisticall and fallacious: but, for those who so
+repute it, the Experiment is a means that may fully satisfie them. But
+he that shall but comprehend of what Importance Velocity of Motion is,
+and how it exactly compensates the defect and want of Gravity, will
+cease to wonder, in considering that at the elevation of the Solid M,
+the great Mass of water A B C D abateth very little, but the little
+Mass of water E N S F decreaseth very much, and in an instant, as the
+Solid M before did rise, howbeit for a very short space: Whereupon the
+Moment, compounded of the small Absolute Gravity of the water E N S F,
+and of its great Velocity in ebbing, <a name="tnd_16" id="tnd_16"></a><a href="#tn_16" class="tnlink" title="printer's error, duplicate word in text">equalizeth the Force and and
+Moment,</a> that results from the composition of the immense Gravity of
+the water A B C D, with its great slownesse of ebbing; since that in
+the Elevation of the Sollid M, the abasement of the lesser water E S,
+is performed just so much more swiftly than the great Mass of water A
+C, as this is more in Mass than that which we thus demonstrate.</p>
+
+<div class="sidenote"><i>T</i>he proportion according to which water riseth and
+falls in different Vessels at the Immersion and Elevation of
+Solids.</div>
+
+<p>In the rising of the Solid M, its elevation hath the same proportion
+to the circumfused water E N S F, that the Surface of the said water,
+hath to the Superficies or Base of the said Solid M; which Base hath
+the same proportion to the Surface of the water A D, that the
+<span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span>
+abasement or ebbing of the water A C, hath to the rise or elevation of
+the said Solid M. Therefore, by Perturbation of proportion, in the
+ascent of the said Solid M, the abasement of the water A B C D, to the
+abasement of the water E N S F, hath the same proportion, that the
+Surface of the water E F, hath to the Surface of the water A D; that
+is, that the whole Mass of the water E N S F, hath to the whole Mass A
+B C D, being equally high: It is manifest, therefore, that in the
+expulsion and elevation of the Solid M, the water E N S F shall exceed
+in Velocity of <i>M</i>otion the water A B C D, asmuch as it on the other
+side is exceeded by that in quantity: whereupon their Moments in such
+operations, are mutually equall.</p>
+
+<p><i>And, for ampler confirmation, and clearer explication of this, let
+us consider the present Figure, (which if I be not deceived, may
+serve to detect the errors of some Practick Mechanitians who upon a
+false foundation some times attempt impossible enterprizes,) in
+which, unto the large Vessell E I D F, the narrow Funnell or Pipe I
+C A B is continued, and suppose water infused into them, unto the
+Levell L G H, which water shall rest in this position, not without
+admiration in some, who cannot conceive how it can be, that the
+<span class="figright" style="width: 146px;">
+<img src="images/i019.png" width="146" height="287" alt="" title="" />
+</span>
+heavie charge of the great Mass of water G D, pressing downwards,
+should not elevate and repulse the little quantity of the other,
+contained in the Funnell or Pipe C L, by which the descent of it is
+resisted and hindered: But such wonder shall cease, if we begin to
+suppose the water G D to be abased only to Q D, and shall
+afterwards consider, what the water C L hath done, which to give
+place to the other, which is descended from the Levell G H, to the
+Levell Q O, shall of necessity have ascended in the same time, from
+the Levell L unto A B. And the ascent L B, shall be so much greater
+than the descent G Q, by how much the breadth of the Vessell G D,
+is greater than that of the Funnell I C; which, in summe, is as
+much as the water G D, is more than the water L C: but in regard
+that the Moment of the Velocity of the Motion, in one Moveable,
+compensates that of the Gravity of another what wonder is it, if
+the swift ascent of the lesser Water C L, shall resist the slow
+descent of the greater G D?</i></p>
+
+<p>The same, therefore, happens in this operation, <a name="tnd_17a" id="tnd_17a"></a><a href="#tn_17a" class="tnlink" title="printer's error, rhe for the">as in rhe Stilliard,</a>
+in which a weight of two pounds counterpoyseth an other of 200,
+<a name="tnd_17b" id="tnd_17b"></a><a href="#tn_17b" class="tnlink" title="missing space between words">asoften as that</a> shall move in the same time, a space 100 times greater
+than this: which falleth out when one Arme of the Beam is an hundred
+<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span>
+times as long as the other. Let the erroneous opinion of those
+therefore cease, who hold that a Ship is better, and easier born up in
+<span class="sidenote">A ship flotes as well in ten Tun of Water as in an
+Ocean.</span>
+a great abundance of water, then in a lesser quantity, (<i>this was
+believed by</i> Aristotle <i>in his Problems, Sect. 23, Probl. 2.</i>) it being
+on the contrary true, that its possible, that a Ship may as well float
+in ten Tun of water, as in an Ocean.</p>
+
+<div class="sidenote">A Solid  <a name="tnd_18" id="tnd_18"></a><a href="#tn_18" class="tnlink" title="printer's error, specifiaclly for specifically">specifiaclly</a> graver than the water, cannot be
+born up by any quantity of it.</div>
+
+<p>But following our matter, I say, that by what hath been hitherto
+demonstrated, we may understand how, that</p>
+
+
+<h3>COROLLARY III.</h3>
+
+<p class="cor_head"><i>One of the above named Solids, when more grave</i> in specie <i>than the
+water, can never be sustained, by any whatever quantity of it.</i></p>
+
+<p>For having seen how that the Moment wherewith such a Solid, as grave
+<i>in specie</i> as the water, contrasts with the Moment of any Mass of
+water whatsoever, is able to retain it, even to its totall Submersion,
+without its ever ascending; it remaineth, manifest, that the water is
+far less able to raise it up, when it exceeds the same <i>in specie</i>:
+so, that though you infuse water till its totall Submersion, it shall
+still stay at the Bottome, and with such Gravity, and Resistance to
+Elevation, as is the excess of its Absolute Gravity, above the
+Absolute Gravity of a Mass equall to it, made of water, or of a Matter
+<i>in specie</i> equally grave with the water: and, though you should
+moreover adde never so much water above the Levell of that which
+equalizeth the Altitude of the Solid, it shall not, for all that,
+encrease the Pression, or Gravitation, of the parts circumfused about
+the said Solid, by which greater pression, it might come to be
+repulsed; because, the Resistance is not made, but only by those parts
+of the water, which at the Motion of the said Solid do also move, and
+these are those only, which are comprehended by the two Superficies
+equidistant to the Horizon, and their parallels, that comprehend the
+Altitude of the Solid immerged in the water.</p>
+
+<p>I conceive, I have by this time sufficiently declared and opened the
+way to the contemplation of the true, intrinsecall and proper Causes
+of diverse Motions, and of the Rest of many Solid Bodies in diverse
+<i>Mediums</i>, and particularly in the water, shewing how all in effect,
+depend on the mutuall excesses of the Gravity of the Moveables and of
+the <i>Mediums</i>: and, that which did highly import, removing the
+Objection, which peradventure would have begotten much doubting, and
+scruple in some, about the verity of my Conclusion, namely, how that
+notwithstanding, that the excess of the Gravity of the water, above
+the Gravity of the Solid, demitted into it, be the cause of its
+floating and rising from the Bottom to the Surface, yet a quantity of
+water, that weighs not ten pounds, can raise a Solid that weighs above
+<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span>
+100 pounds: in that we have demonstrated, That it sufficeth, that such
+difference be found between the Specificall Gravities of the <i>Mediums</i>
+and Moveables, let the particular and absolute Gravities be what they
+will: insomuch, that a Solid, provided that it be Specifically less
+grave than the water, although its absolute weight were 1000 pounds,
+yet may it be born up and elevated by ten pounds of water, and less:
+and on the contrary, another Solid, so that it be Specifically more
+grave than the water, though in absolute Gravity it were not above a
+pound, yet all the water in the Sea, cannot raise it from the Bottom,
+or float it. This sufficeth me, for my present occasion, to have, by
+the above declared Examples, discovered and demonstrated, without
+extending such matters farther, and, as I might have done, into a long
+Treatise: yea, but that there was a necessity of resolving the above
+proposed doubt, I should have contented my self with that only, which
+is demonstrated by <i>Archimedes</i>, in his first <i>Book De Insidentibus
+humido</i>: where in generall termes he infers and confirms the same
+<span class="sidenote"><i>Of Natation</i> (a) <i>Lib. 1, Prop. 4.</i> (b) <i>Id. Lib. 1.
+Prop. 3.</i> (c) <i>Id. Lib. 1. Prop. 3.</i></span>
+Conclusions, namely, that Solids (<i>a</i>) less grave than water, swim or
+float upon it, the (<i>b</i>) more grave go to the Bottom, and the (<i>c</i>)
+equally grave rest indifferently in all places, yea, though they
+should be wholly under water.</p>
+
+<div class="sidenote">The Authors defence of <i>Archimedes</i> his Doctrine,
+against the oppositions of <i>Buonamico</i>.</div>
+
+<p>But, because that this Doctrine of Archimedes, perused, transcribed
+and examined by <i>Signor Francesco Buonamico</i>, in his <i>fifth Book of
+Motion, Chap. 29</i>, and afterwards by him confuted, might by the
+Authority of so renowned, and famous a Philosopher, be rendered
+dubious, and suspected of falsity; I have judged it necessary to
+defend it, if I am able so to do, and to clear <i>Archimedes</i>, from
+those censures, with which he appeareth to be charged. <i>Buonamico</i>
+rejecteth the Doctrine of <i>Archimedes</i>, first, as not consentaneous
+<span class="sidenote">His first Objection against the Doctrine of
+<i>Archimedes</i>.</span>
+with the Opinion of <i>Aristotle</i>, adding, that it was a strange thing
+to him, that the Water should exceed the Earth in Gravity, seeing on
+<span class="sidenote">His Second Objection.</span>
+the contrary, that the Gravity of water, increaseth, by means of the
+participation of Earth. And he subjoyns presently after, that he was
+<span class="sidenote">His third Objection.</span>
+not satisfied with the Reasons of <i>Archimedes</i>, as not being able with
+that Doctrine, to assign the cause whence it comes, that a Boat and a
+Vessell, which otherwise, floats above the water, doth sink to the
+Bottom, if once it be filled with water; that by reason of the
+equality of Gravity, between the water within it, and the other water
+without, it should stay a top; but yet, nevertheless, we see it to go
+to the Bottom.</p>
+
+<p>He farther addes, that <i>Aristotle</i> had clearly confuted the Ancients,
+<span class="sidenote">His fourth Objection.</span>
+who said, that light Bodies moved upwards, driven by the impulse of
+<span class="sidenote">The <i>A</i>ncients denyed <i>A</i>bsolute Levity.</span>
+the more grave Ambient: which if it were so, it should seem of
+necessity to follow, that all naturall Bodies are by nature heavy, and
+<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span>
+none light: For that the same would befall the Fire and Air, if put in
+the Bottom of the water. And, howbeit, <i>Aristotle</i> grants a Pulsion in
+the Elements, by which the Earth is reduced into a Sphericall Figure,
+yet nevertheless, in his judgement; it is not such that it can remove
+grave Bodies from their naturall places, but rather, that it send them
+toward the Centre, to which (as he somewhat obscurely continues to
+say,) the water principally moves, if it in the interim meet not with
+something that resists it, and, by its Gravity, thrusts it out of its
+place: in which case, if it cannot directly, yet at least as well as
+it can, it tends to the Centre: but it happens, that light Bodies by
+such Impulsion, do all ascend upward: <a name="tnd_20b" id="tnd_20b"></a><a href="#tn_20b" class="tnlink" title="potential printer's error, properly for property">but this properly they have</a> by
+nature, as also, that other of swimming. He concludes, lastly, that he
+<span class="sidenote">The causes of Natation &amp; Submersion, according to the
+Peripateticks.</span>
+concurs with <i>Archimedes</i> in his Conclusions; but not in the Causes,
+which he would referre to the facile and difficult Separation of the
+<i>Medium</i>, and to the predominance of the Elements, so that when the
+Moveable superates the power of the <i>Medium</i>; as for example, Lead
+doth the Continuity of water, it shall move thorow it, else not.</p>
+
+<p>This is all that I have been able to collect, as produced against
+<i>Archimedes</i> by <i>Signor Buonamico</i>: who hath not well observed the
+Principles and Suppositions of <i>Archimedes</i>; which yet must be false,
+if the Doctrine be false, which depends upon them; but is contented to
+alledge therein some Inconveniences, and some Repugnances to the
+Doctrine and Opinion of <i>Aristotle</i>. In answer to which Objections, I
+say, first, That the being of <i>Archimedes</i> Doctrine, simply different
+<span class="sidenote">The Authors answer to the first Objection.</span>
+from the Doctrine of <i>Aristotle</i>, ought not to move any to suspect it,
+there being no cause, why the Authority of this should be preferred to
+the Authority of the other: but, because, where the decrees of Nature
+are indifferently exposed to the intellectuall eyes of each, the
+Authority of the one and the other, <a name="tnd_20" id="tnd_20"></a><a href="#tn_20" class="tnlink" title="printer's error, n for u">loseth all a{u}thenticalness</a> of
+Perswasion, the absolute power residing in Reason; therefore I pass to
+that which he alledgeth in the second place, as an absurd consequent
+<span class="sidenote">The Authors answer to the second Objection.</span>
+of the Doctrine of <i>Archimedes</i>, namely, That water should be more
+grave than Earth. But I really find not, that ever <i>Archimedes</i> said
+such a thing, or that it can be rationally deduced from his
+Conclusions: and if that were manifest unto me, I verily believe, I
+should renounce his Doctrine, as most erroneous. Perhaps this
+Deduction of <i>Buonamico</i>, is founded upon that which he citeth of the
+Vessel, which swims as long as its voyd of water, but once full it
+sinks to the Bottom, and understanding it of a Vessel of Earth, he
+infers against <i>Archimedes</i> thus: Thou sayst that the Solids which
+swim, are less grave than water: this Vessell swimmeth: therefore,
+this Vessell is lesse grave than water. If this be the Illation. I
+<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span>
+easily answer, granting that this Vessell is lesse grave than water,
+and denying the other consequence, namely, that Earth is less Grave
+than Water. The Vessel that swims occupieth in the water, not only a
+place equall to the Mass of the Earth, of which it is formed; but
+equall to the Earth and to the Air together, contained in its
+concavity. And, if such a Mass compounded of Earth and Air, shall be
+less grave than such another quantity of water, it shall swim, and
+shall accord with the Doctrine of <i>Archimedes</i>; but if, again,
+removing the Air, the Vessell shall be filled with water, so that the
+Solid put in the water, be nothing but Earth, nor occupieth other
+place, than that which is only possest by Earth, it shall then go to
+the Bottom, by reason that the Earth is heavier than the water: and
+this corresponds well with the meaning of <i>Archimedes</i>. See the same
+effect illustrated, with such another Experiment, In pressing a Viall
+Glass to the Bottom of the water, when it is full of Air, it will meet
+with great resistance, because it is not the Glass alone, that is
+pressed under water, but together with the Glass a great Mass of Air,
+and such, that if you should take as much water, as the Mass of the
+Glass, and of the Air contained in it, you would have a weight much
+greater than that of the Viall, and of its Air: and, therefore, it
+will not submerge without great violence: but if we demit only the
+Glass into the water, which shall be when you shall fill the Glass
+with water, then shall the Glass descend to the Bottom; as superiour
+in Gravity to the water.</p>
+
+<p>Returning, therefore, to our first purpose; I say, that Earth is more
+grave than water, and that therefore, a Solid of Earth goeth to the
+bottom of it; but one may possibly make a composition of Earth and
+Air, which shall be less grave than a like Mass of Water; and this
+shall swim: and yet both this and the other experiment shall very well
+accord with the Doctrine of <i>Archimedes</i>. But because that in my
+judgment it hath nothing of difficulty in it, I will not positively
+affirme that <i>Signor Buonamico</i>, would by such a discourse object unto
+<i>Archimedes</i> the absurdity of inferring by his doctrine, that Earth
+was less grave than Water, though I know not how to conceive what
+other accident he could have induced thence.</p>
+
+<p>Perhaps such a Probleme (in my judgement false) was read by <i>Signor
+Buonamico</i> in some other Author, by whom peradventure it was
+attributed as a singular propertie, of some particular Water, and so
+comes now to be used with a double errour in confutation of
+<i>Archimedes</i>, since he saith no such thing, nor by him that did say it
+was it meant of the common Element of Water.</p>
+
+<div class="sidenote">The Authors answer to the third Objection.</div>
+
+<p>The third difficulty in the doctrine of <i>Archimedes</i> was, that he
+could not render a reason whence it arose, that a piece of Wood, and a
+Vessell of Wood, which otherwise floats, goeth to the bottom, if
+filled with Water. <i>Signor Buonamico</i> hath supposed that a Vessell of
+Wood, and of Wood that by nature swims, as before is said, goes to the
+<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span>
+bottom, if it be filled with water; of which he in the following
+Chapter, which is the 30 of the fifth Book copiously discourseth: but
+I (speaking alwayes without diminution of his singular Learning) dare
+in defence of <i>Archimedes</i> deny this experiment, being certain that a
+piece of Wood which by its nature sinks not in Water, shall not sinke
+though it be turned and converted into the forme of any Vessell
+whatsoever, and then filled with Water: and he that would readily see
+the Experiment in some other tractable Matter, and that is easily
+reduced into several Figures, may take pure Wax, and making it first
+into a Ball or other solid Figure, let him adde to it so much Lead as
+shall just carry it to the bottome, so that being a graine less it
+could not be able to sinke it, and making it afterwards into the forme
+of a Dish, and filling it with Water, he shall finde that without the
+said Lead it shall not sinke, and that with the Lead it shall descend
+with much slowness: &amp; in short he shall satisfie himself, that the
+Water included makes no alteration. I say not all this while, but that
+its possible of Wood to make Barkes, which being filled with water,
+sinke; but that proceeds not through its Gravity, encreased by the
+Water, but rather from the Nailes and other Iron Workes, so that it no
+longer hath a Body less grave than Water, but one mixt of Iron and
+Wood, more grave than a like Masse of Water. Therefore let <i>Signor
+Buonamico</i> desist from desiring a reason of an effect, that is not in
+nature: yea if the sinking of the Woodden Vessell when its full of
+Water, may call in question the Doctrine of <i>Archimedes</i>, which he
+would not have you to follow, is on the contrary consonant and
+agreeable to the Doctrine of the Peripateticks, since it aptly
+assignes a reason why such a Vessell must, when its full of Water,
+descend to the bottom; converting the Argument the other way, we may
+with safety say that the Doctrine of <i>Archimedes</i> is true, since it
+aptly agreeth with true experiments, and question the other, whose
+Deductions are fastened upon erroneouss Conclusions. As for the other
+point hinted in this same Instance, where it <a name="tnd_22" id="tnd_22"></a><a href="#tn_22" class="tnlink" title="printer's error or variation in spelling, Benonamico for Buonamico">seemes that <i>Benonamico</i></a>
+understands the same not only of a piece of wood, shaped in the forme
+of a Vessell, but also of massie Wood, which filled, <i>scilicet</i>, as I
+believe, he would say, soaked and steeped in Water, goes finally to
+the bottom that happens in some porose Woods, which, while their
+Porosity is replenished with Air, or other Matter less grave than
+Water, are Masses specificially less grave than the said Water, like
+as is that Viall of Glass whilest it is full of Air: but when, such
+light Matter departing, there succeedeth Water into the same
+Porosities and Cavities, there results a compound of Water and Glass
+more grave than a like Mass of Water: but the excess of its Gravity
+consists in the Matter of the Glass, and not in the Water, which
+cannot be graver than it self: so that which remaines of the Wood, the
+<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>
+Air of its Cavities departing, if it shall be more grave <i>in specie</i>
+than Water, fil but its Porosities with Water, and you shall have a
+Compost of Water and of Wood more grave than Water, but not by vertue
+of the Water received into and imbibed by the Porosities, but of that
+Matter of the Wood which remains when the Air is departed: and being
+such it shall, according to the Doctrine of <i>Archimedes</i>, goe to the
+bottom, like as before, according to the same Doctrine it did swim.</p>
+
+<div class="sidenote">The Authors answer to the fourth Objection.</div>
+
+<p>As to that finally which presents itself in the fourth place,
+namely, that the <i>Ancients</i> have been heretofore confuted by
+<i>Aristotle</i>, who denying Positive and Absolute Levity, and truely
+esteeming all Bodies to be grave, said, that that which moved upward
+was driven by the circumambient Air, and therefore that also the
+Doctrine of <i>Archimedes</i>, as an adherent to such an Opinion was
+convicted and confuted: I answer first, that <i>Signor Buonamico</i> in my
+judgement hath imposed upon <i>Archimedes</i>, and deduced from his words
+more than ever he intended by them, or may from his Propositions be
+collected, in regard that <i>Archimedes</i> neither denies, nor admitteth
+Positive Levity, nor doth he so much as mention it: so that much less
+ought <i>Buonamico</i> to inferre, that he hath denyed that it might be the
+Cause and Principle of the Ascension of Fire, and other Light Bodies:
+<span class="sidenote">Of Natation, Lib. 1. Prop. 7.</span>
+having but only demonstrated, that Solid Bodies more grave than Water
+descend in it, according to the excess of their Gravity above the
+Gravity of that, he demonstrates likewise, how the less grave ascend
+in the same Water, <a name="tnd_23" id="tnd_23"></a><a href="#tn_23" class="tnlink" title="printer's error, missing i">accordng to its excess</a> of Gravity, above the
+<span class="sidenote">Of Natation, Lib. 1. Prop. 4.</span>
+Gravity of them. So that the most that can be gathered from the
+Demonstration of <i>Archimedes</i> is, that like as the excess of the
+Gravity of the Moveable above the Gravity of the Water, is the Cause
+that it descends therein, so the excess of the Gravity of the water
+above that of the Moveable, is a sufficient Cause why it descends not,
+but rather betakes it self to swim: not enquiring whether of moving
+upwards there is, or is not any other Cause contrary to Gravity: nor
+doth <i>Archimedes</i> discourse less properly than if one should say: If
+the South Winde shall assault the Barke with greater <i>Impetus</i> than is
+the violence with which the Streame of the River carries it towards
+the South, the motion of it shall be towards the North: but if the
+<i>Impetus</i> of the Water shall overcome that of the Winde, its motion
+shall be towards the South. The discourse is excellent and would be
+unworthily contradicted by such as should oppose it, saying: Thou
+mis-alledgest as Cause of the motion of the Bark towards the South,
+the <i>Impetus</i> of the Stream of the Water above that of the South
+Winde; mis-alledgest I say, for it is the Force of the North Winde
+opposite to the South, that is able to drive the Bark towards the
+South. Such an Objection would be superfluous, because he which
+alledgeth for Cause of the Motion the Stream of the Water, denies not
+<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span>
+but that the Winde opposite to the South may do the same, but only
+affirmeth that the force of the Water prevailing over the South Wind,
+the Bark shall move towards the South: and saith no more than is true.
+And just thus when <i>Archimedes</i> saith, that the Gravity of the Water
+prevailing over that by which the moveable descends to the Bottom,
+such moveable shall be raised from the Bottom to the Surface alledgeth
+a very true Cause of such an Accident, nor doth he affirm or deny that
+there is, or is not, a vertue contrary to Gravity, called by some
+Levity, that hath also a power of moving some Matters upwards. Let
+therefore the Weapons of <i>Signor Buonamico</i> be directed against
+<i>Plato</i>, and other <i>Ancients</i>, who totally denying <i>Levity</i>, and
+<span class="sidenote"><i>Plato</i> denyeth Positive Levity.</span>
+taking all Bodies to be grave, say that the Motion upwards is made,
+not from an intrinsecal Principle of the Moveable, but only by the
+Impulse of the <i>Medium</i>; and let <i>Archimedes</i> and his Doctrine escape
+him, since he hath given him no Cause of quarelling with him. But if
+this Apologie, produced in defence of <i>Archimedes</i>, should seem to
+some insufficient to free him from the Objections and Arguments,
+produced by <i>Aristotle</i> against <i>Plato</i>, and the other <i>Ancients</i>, as if
+they did also fight against <i>Archimedes</i>, alledging the Impulse of the
+Water as the Cause of the swimming of some Bodies less grave than it,
+<span class="sidenote">The Authors defence of the doctrine of <i>Plato</i> and the
+<i>Ancients</i>, who absolutely deny Levity:</span>
+I would not question, but that I should be able to maintaine the
+Doctrine of <i>Plato</i> and those others to be most true, who absolutely
+deny Levity, and affirm no other Intrinsecal Principle of Motion to be
+in Elementary Bodies save only that towards the Centre of the Earth,
+<span class="sidenote">According to <i>Plato</i> there is no Principle of the
+Motion, of descent in Naturall Bodies, save that to the Centre.</span>
+nor no other Cause of moving upwards, speaking of that which hath the
+resemblance of natural Motion, but only the repulse of the <i>Medium</i>,
+fluid, and exceeding the Gravity of the Moveable: and as to the
+<span class="sidenote">No cause of the motion of Ascent, save the Impulse of
+the <i>Medium</i>, exceeding the Moveable in Gravitie.</span>
+Reasons of <i>Aristotle</i> on the contrary, I believe that I could be able
+fully to answer them, and I would assay to do it, if it were
+absolutely necessary to the present Matter, or were it not too long a
+Digression for this short Treatise. I will only say, that if there
+were in some of our Ellementary Bodies an Intrinsecall Principle and
+Naturall Inclination to shun the Centre of the Earth, and to move
+towards the Concave of the Moon, such Bodies, without doubt, would
+more swiftly ascend through those <i>Mediums</i> that least oppose the
+Velocity of the Moveable, and these are the more tenuous and subtle;
+as is, for example, the Air in comparison of the Water, we daily
+proving that we can with farre more expeditious Velocity move a Hand
+or a Board to and again in one than in the other: nevertheless, we
+<span class="sidenote">Bodies ascend much swifter in the Water, than in the
+Air.</span>
+never could finde any Body, that did not ascend much more swiftly in
+the water than in the Air. Yea of Bodies which we see continually to
+ascend in the Water, there is none that having arrived to the confines
+of the Air, do not wholly lose their Motion; even the Air it self,
+<span class="sidenote">All Bodies ascending through Water, lose their Motion,
+comming to the confines of the Air.</span>
+which rising with great Celerity through the Water, being once come to
+ <a name="tnd_24" id="tnd_24"></a><a href="#tn_24" class="tnlink" title="missing line at the end of page in original text">its Region it loseth all</a></p>
+
+<p><span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span></p>
+<div class="sidenote">The lighter Bodies ascend more swiftly through Water.</div>
+
+<p>And, howbeit, Experience shewes, that the Bodies, successively less
+grave, do most expeditiously ascend in water, it cannot be doubted,
+but that the Ignean Exhalations do ascend more swiftly through the
+water, than doth the Air: which Air is seen by Experience to ascend
+more swiftly through the Water, than the Fiery Exhalations through the
+Air: Therefore, we must of necessity conclude, that the said
+<span class="sidenote">Fiery Exhalations ascend thorow the Water more swiftly
+than doth the Air; &amp; the Air ascends more swiftly thorow the
+Water, than Fire thorow the Air.</span>
+Exhalations do much more expeditiously ascend through the Water, than
+through the Air; and that, consequently, they are moved by the Impulse
+of the Ambient <i>Medium</i>, and not by an intrinsick Principle that is in
+them, of avoiding the Centre of the Earth; to which other grave Bodies
+tend.</p>
+
+<div class="sidenote"><i>T</i>he Authors confutation of the Peripateticks Causes
+of Natation &amp; Submersion.</div>
+
+<p>To that which for a finall conclusion, <i>Signor Buonamico</i> produceth
+of going about to reduce the descending or not descending, to the
+easie and uneasie Division of the <i>Medium</i>, and to the predominancy of
+the Elements: I answer, as to the first part, that that cannot in any
+manner be admitted as a Cause, being that in none of the Fluid
+<i>Mediums</i>, as the Air, the Water, and other Liquids, there is any
+Resistance against Division, but all by every the least Force, are
+<span class="sidenote">Water &amp; other fluids void of Resistance against
+Division.</span>
+divided and penetrated, as I will anon demonstrate: so, that of such
+Resistance of Division there can be no Act, since it self is not in
+being. As to the other part, I say, that the predominancy of the
+Elements in Moveables, is to be considered, as far as to the excesse
+<span class="sidenote"><i>T</i>he predominancy of Elements in Moveables to be
+considered only in relation to their excess or defect of Gravity
+in reference to the <i>Medium</i>.</span>
+or defect of Gravity, in relation to the <i>Medium</i>: for in that Action,
+the Elements operate not, but only, so far as they are grave or light:
+therefore, to say that the Wood of the Firre sinks not, because Air
+predominateth in it, is no more than to say, because it is less grave
+than the Water. Yea, even the immediate Cause, is its being less grave
+than the Water: and it being under the predominancy of the Air, is the
+<span class="sidenote"><i>T</i>he immediate Cause of Natation is that the Moveable
+is less grave than the Water.</span>
+Cause of its less Gravity: Therefore, he that alledgeth the
+predominancy of the Element for a Cause, brings the Cause of the
+Cause, and not the neerest and immediate Cause. Now, who knows not
+that the true Cause is the immediate, and not the mediate? Moreover,
+<span class="sidenote"><i>T</i>he Peripateticks alledge for the reason of Natation
+the Cause of the Cause.</span>
+he that alledgeth Gravity, brings a Cause most perspicuous to Sence:
+<span class="sidenote">Gravity a Cause most perspicuous to sence.</span>
+The cause we may very easily assertain our selves; whether Ebony, for
+example, and Firre, be more or less grave than water: but whether
+Earth or Air predominates in them, who shall make that manifest?
+Certainly, no Experiment can better do it than to observe whether they
+swim or sink. So, that he who knows, not whether such a Solid swims,
+unless when he knows that Air predominates in it, knows not whether it
+swim, unless he sees it swim, for then he knows that it swims, when he
+knows that it is Air that predominates, but knows not that Air hath
+the predominance, unless he sees it swim: therefore, he knows not if
+it swims, till such time as he hath seen it swim.</p>
+
+<p><span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span></p>
+<p>Let us not then despise those Hints, though very dark, which Reason,
+after some contemplation, offereth to our Intelligence, and lets be
+content to be taught by <i>Archimedes</i>, that then any Body shall
+submerge in water, when it shall be specifically more grave than it,
+<span class="sidenote">Lib 1. of Natation Prop. 7</span>
+and that if it shall be less grave, it shall of necessity swim, and
+<span class="sidenote">Id. Lib. 1. Prop. 4.</span>
+that it will rest indifferently in any place under water, if its
+Gravity be perfectly like to that of the water.</p>
+
+<p>These things explained and proved, I come to consider that which
+<span class="sidenote">Id. Lib 1. Prop. 3.</span>
+offers it self, touching what the Diversity of figure given unto the
+said Moveable hath to do with these Motions and Rests; and proceed to
+affirme, that,</p>
+
+
+
+
+<h2><a name="THEOREME_V" id="THEOREME_V"></a>THEOREME V.</h2>
+
+<div class="sidenote">Diversity of Figure no Cause of its absolute Natation
+or Submersion.</div>
+
+<p class="def_head"><i>The diversity of Figures given to this or that Solid, cannot any
+way be a Cause of its absolute Sinking or Swimming.</i></p>
+
+
+<p class="cap">So that if a Solid being formed, for example, into a Sphericall
+Figure, doth sink or swim in the water, I say, that being formed into
+any other Figure, the same figure in the same water, shall sink or
+swim: nor can such its Motion by the Expansion or by other mutation of
+Figure, be impeded or taken away.</p>
+
+<div class="sidenote">The Expansion of Figure, retards the Velocity of the
+ascent or descent of the Moveable in the water; but doth not
+deprive it of all Motion.</div>
+
+<p>The Expansion of the Figure may indeed retard its Velocity, aswell of
+ascent as descent, and more and more according as the said Figure is
+reduced to a greater breadth and thinness: but that it may be reduced
+to such a form as that that same matter be wholly hindred from moving
+in the same water, that I hold to be impossible. In this I have met
+with great contradictors, who producing some Experiments, and in
+perticular a thin Board of Ebony, and a Ball of the same Wood, and
+shewing how the Ball in Water descended to the bottom, and the Board
+being put lightly upon the Water submerged not, but rested; have held,
+and with the Authority of <i>Aristotle</i>, confirmed themselves in their
+Opinions, that the Cause of that Rest was the breadth of the Figure,
+<a name="tnd_26" id="tnd_26"></a><a href="#tn_26" class="tnlink" title="missing letter n">u{n}able by its small weight</a> to pierce and penetrate the Resistance of
+the Waters Crassitude, which Resistance is readily overcome by the
+other Sphericall Figure.</p>
+
+<p>This is the Principal point in the present Question, in which I
+perswade my self to be on the right side.</p>
+
+<p>Therefore, beginning to investigate with the examination of exquisite
+Experiments that really the Figure doth not a jot alter the descent or
+Ascent of the same Solids, and having already demonstrated that the
+greater or less Gravity of the Solid in relation to the Gravity of the
+<i>Medium</i> is the cause of Descent or Ascent: when ever we would make
+<span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span>
+proof of that, which about this Effect the diversity of Figure
+worketh, its necessary to make the Experiment with Matter wherein
+variety of Gravities hath no place. For making use of Matters which
+may be different in their Specifical Gravities, and meeting with
+varieties of effects of Ascending and Descending, we shall alwayes be
+left unsatisfied whether that diversity derive it self really from the
+sole Figure, or else from the divers Gravity also. We may remedy this
+by takeing one only Matter, that is tractable and easily reduceable
+into every sort of Figure. Moreover, it will be an excellent expedient
+to take a kinde of Matter, exactly alike in Gravity unto the Water:
+for that Matter, as far as pertaines to the Gravity, is indifferent
+either to Ascend or Descend; so that we may presently observe any the
+least difference that derives it self from the diversity of Figure.</p>
+
+<div class="sidenote">An Experiment in Wax, that proveth Figure to have no
+Operation in Natation &amp; Submersion.</div>
+
+<p>Now to do this, Wax is most apt, which, besides its incapacity of
+receiveing any sensible alteration from its imbibing of Water, is
+ductile or pliant, and the same piece is easily reduceable into all
+Figures: and being <i>in Specie</i> a very inconsiderable matter inferiour
+in Gravity to the Water, by mixing therewith a little of the fileings
+of Lead it is reduced to a Gravity exactly equall to that of the
+Water.</p>
+
+<p>This Matter prepared, and, for example, a Ball being made thereof as
+bigge as an Orange or biger, and that made so grave as to sink to the
+bottom, but so lightly, that takeing thence one only Grain of Lead, it
+returns to the top, and being added, it submergeth to the bottom, let
+the same Wax afterwards be made into a very broad and thin Flake or
+Cake; and then, returning to make the same Experiment, you shall see
+that it being put to the bottom, it shall, with the Grain of Lead rest
+below, and that Grain deducted, it shall ascend to the very Surface,
+and added again it shall dive to the bottom. And this same effect
+shall happen alwaies in all sort of Figures, as wel regular as
+irregular: nor shall you ever finde any that will swim without the
+removall of the Grain of Lead, or sinke to the bottom unless it be
+added: and, in short, about the going or not going to the Bottom, you
+shall discover no diversity, although, indeed, you shall about the
+quick and slow descent: for the more expatiated and distended Figures
+move more slowly aswel in the diveing to the bottom as in the rising
+to the top; and the other more contracted and compact Figures, more
+speedily. Now I know not what may be expected from the diversity of
+Figures, if the most contrary to one another operate not so much as
+doth a very small Grain of Lead, added or removed.</p>
+
+<div class="sidenote">An objection against the Experiment in Water.</div>
+
+<p>Me thinkes I hear some of the Adversaries to raise a doubt upon my
+produced Experiment. And first that they offer to my consideration,
+that the Figure, as a Figure simply, and disjunct from the Matter
+workes not any effect, but requires to be conjoyned with the Matter;
+<span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span>
+and, furthermore, not with every Matter, but with those only,
+wherewith it may be able to execute the desired operation. Like as we
+see it verified by Experience, that the Acute and sharp Angle is more
+apt to cut, than the Obtuse; yet alwaies provided, that both the one
+and the other, be joyned with a Matter apt to cut, as for example,
+with Steel. Therefore, a Knife with a fine and sharp edge, cuts Bread
+or Wood with much ease, which it will not do, if the edge be blunt and
+thick: but he that will instead of Steel, take Wax, and mould it into
+a Knife, undoubtedly shall never know the effects of sharp and blunt
+edges: because neither of them will cut, the Wax being unable by
+reason of its flexibility, to overcome the hardness of the Wood and
+Bread. And, therefore, applying the like discourse to our purpose,
+they say, that the difference of Figure will shew different effects,
+touching Natation and Submersion, but not conjoyned with any kind of
+Matter, but only with those Matters which, by their Gravity, are apt
+to resist the Velocity of the water, whence he that would elect for
+the Matter, Cork or other light wood, unable, through its Levity, to
+superate the Crassitude of the water, and of that Matter should forme
+Solids of divers Figures, would in vain seek to find out what
+operation Figure hath in Natation or Submersion; because all would
+swim, and that not through any property of this or that Figure, but
+through the debility of the Matter, wanting so much Gravity, as is
+requisite to superate and overcome the Density and Crassitude of the
+water.</p>
+
+<p>Its needfull, therefore, if wee would see the effect wrought by the
+Diversity of Figure, first to make choice of a Matter of its nature
+apt to penetrate the Crassitude of the water. And, for this effect,
+<span class="sidenote">An Experiment in Ebany, brought to disprove the
+Experiment in Wax.</span>
+they have made choice of such a Matter, as fit, that being readily
+reduced into Sphericall Figure, goes to the Bottom; and it is Ebony,
+of which they afterwards making a small Board or Splinter, as thin as
+a Lath, have illustrated how that this, put upon the Surface of the
+water, rests there without descending to the Bottom: and making, on
+the otherside, of the same wood a Ball, no less than a hazell Nut,
+they shew, that this swims not, but descendes. From which Experiment,
+they think they may frankly conclude, that the Breadth of the Figure
+in the flat Lath or Board, is the cause of its not descending to the
+Bottom, for as much as a Ball of the same Matter, not different from
+the Board in any thing but in Figure, submergeth in the same water to
+the Bottom. The discourse and the Experiment hath really so much of
+probability and likelyhood of truth in it, that it would be no wonder,
+if many perswaded by a certain cursory observation, should yield
+credit to it; nevertheless, I think I am able to discover, how that it
+is not free from falacy.</p>
+
+<p>Beginning, therefore, to examine one by one, all the particulars that
+<span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span>
+have been produced, I say, that Figures, as simple Figures, not only
+operate not in naturall things, but neither are they ever seperated
+from the Corporeall substance: nor have I ever alledged them stript of
+<span class="sidenote">Figure is unseperable from Corporeall Substance.</span>
+sensible Matter, like as also I freely admit, that in our endeavouring
+to examine the Diversity of Accidents, dependant upon the variety of
+Figures, it is necessary to apply them to Matters, which obstruct not
+the various operations of those various Figures: and I admit and
+grant, that I should do very ill; if I would experiment the influence
+of Acutenesse of edge with a Knife of Wax, applying it to cut an Oak,
+because there is no Acuteness in Wax able to cut that very hard wood.
+But yet such an Experiment of this Knife, would not be besides the
+purpose, to cut curded Milk, or other very yielding Matter: yea, in
+such like Matters, the Wax is more commodious than Steel; for finding
+the diversity depending upon Angles, more or less Acute, for that Milk
+is indifferently cut with a Raisor, and with a Knife, that hath a
+blunt edge. It needs, therefore, that regard be had, not only to the
+hardness, solidity or Gravity of Bodies, which under divers figures,
+are to divide and penetrate some Matters, but it forceth also, that
+regard be had, on the other side, to the Resistance of the Matters, to
+be divided and penetrated. But since I have in making the Experiment
+concerning our Contest; chosen a Matter which penetrates the
+Resistance of the water; and in all figures descendes to the Bottome,
+the Adversaries can charge me with no defect; yea, I have propounded
+so much a more excellent Method than they, in as much as I have
+removed all other Causes, of descending or not descending to the
+Bottom, and retained the only sole and pure variety of Figures,
+demonstrating that the same Figures all descende with the only
+alteration of a Grain in weight: which Grain being removed, they
+return to float and swim; it is not true, therefore, (resuming the
+Example by them introduced) <a name="tnd_29" id="tnd_29"></a><a href="#tn_29" class="tnlink" title="missing letter e">that I have gon{e} about</a> to experiment the
+efficacy of Acuteness, in cutting with Matters unable to cut, but with
+Matters proportioned to our occasion, since they are subjected to no
+other variety, then that alone which depends on the Figure more or
+less acute.</p>
+
+<div class="sidenote">The answer to the Objection against the Experiment of
+the Wax.</div>
+
+<p>But let us proceed a little farther, and observe, how that indeed the
+Consideration, which, they say, ought to be had about the Election of
+the Matter, to the end, that it may be proportionate for the making of
+our experiment, is needlessly introduced, declaring by the example of
+Cutting, that like as Acuteness is inefficient to cut, unless when it
+is in a Matter hard and apt to superate the Resistance of the wood or
+other Matter, which we intend to cut; so the aptitude of descending or
+not descending in water, ought and can only be known in those Matters,
+that are able to overcome the Renitence, and superate the Crassitude
+of the water. Unto which, I say, that to make distinction and
+election, more of this than of that Matter, on which to impress the
+<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>
+Figures for cutting or penetrating this or that Body, as the solidity
+or obdurateness of the said Bodies shall be greater or less, is very
+necessary: but withall I subjoyn, that such distinction, election and
+caution would be superfluous and unprofitable, if the Body to be cut
+or penetrated, should have no Resistance, or should not at all
+withstand the Cutting or Penitration: and if the Knife were to be used
+in cutting a Mist or Smoak, one of Paper would be equally serviceable
+with one of <i>Damascus</i> Steel: and so by reason the water hath not any
+Resistance against the Penitration of any Solid Body, all choice of
+Matter is superfluous and needless, and the Election which I said
+above to have been well made of a Matter reciprocall in Gravity to
+water, was not because it was necessary, for the overcoming of the
+crassitude of the water, but its Gravity, with which only it resists
+the sinking of Solid Bodies: and for what concerneth the Resistance of
+the crassitude, if we narrowly consider it, we shall find that all
+Solid Bodies, as well those that sink, as those that swim, are
+indifferently accomodated and apt to bring us to the knowledge of the
+truth in question. Nor will I be frighted out of the belief of these
+Conclusions, by the Experiments which may be produced against me, of
+many severall Woods, Corks, Galls, and, moreover, of subtle slates and
+plates of all sorts of Stone and Mettall, apt by means of their
+Naturall Gravity, to move towards the Centre of the Earth, the which,
+nevertheless, being impotent, either through the Figure (as the
+Adversaries thinke) or through Levity, to break and penetrate the
+Continuity of the parts of the water, and to distract its union, do
+continue to swimm without submerging in the least: nor on the other
+side, shall the Authority of <i>Aristotle</i> move me, who in more than one
+place, affirmeth the contrary to this, which Experience shews me.</p>
+
+<div class="sidenote">No Solid of such Levity, nor of such Figure, but that
+it doth penetrate the Crassitude of the Water.</div>
+
+<div class="sidenote">Bodies of all Figures, laid upon the water, do
+penetrate its Crassitude, and in what proportion.</div>
+
+<p>I return, therefore, to assert, that there is not any Solid of such
+Levity, nor of such Figure, that being put upon the water, doth not
+divide and penetrate its Crassitude: yea if any with a more
+perspicatious eye, shall return to observe more exactly the thin
+Boards of Wood, he shall see them to be with part of their thickness
+under water, and not only with their inferiour Superficies, to kisse
+the Superiour of the water, as they of necessity must have believed,
+who have said, that such Boards submerge not, as not being able to
+divide the Tenacity of the parts of the water: and, moreover, he shall
+see, that subtle shivers of Ebony, Stone or Metall, when they float,
+have not only broak the Continuity of the water, but are with all
+their thickness, under the Surface of it; and more and more, according
+as the Matters are more grave: so that a thin Plate of Lead, shall be
+lower than the Surface of the circumfused water, by at least twelve
+times the thickness of the Plate, and Gold shall dive below the Levell
+<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span>
+of the water, almost twenty times the thickness of the Plate, as I
+shall anon declare.</p>
+
+<p>But let us proceed to evince, that the water yields and suffers it
+self to be penetrated by every the lightest Body; and therewithall
+demonstrate, how, even by Matters that submerge not, we may come to
+know that Figure operates nothing about the going or not going to the
+Bottom, seeing that the water suffers it self to be penetrated equally
+by every Figure.</p>
+
+<div class="sidenote">The Experiment of a Cone, demitted with its Base, and
+after with its Point downwards.</div>
+
+<p>Make a Cone, or a Piramis of Cypress, of Firre, or of other Wood of
+like Gravity, or of pure Wax, and let its height be somewhat great,
+namely a handfull, or more, and put it into the water with the Base
+downwards: first, you shall see that it will penetrate the water, nor
+shall it be at all impeded by the largeness of the Base, nor yet shall
+it sink all under water, but the part towards the point shall lye
+above it: by which shall be manifest, first, that that Solid forbeares
+not to sink out of an inability to divide the Continuity of the water,
+having already divided it with its broad part, that in the opinion of
+the Adversaries is the less apt to make the division. The Piramid
+being thus fixed, note what part of it shall be submerged, and revert
+it afterwards with the point downwards, and you shall see that it
+shall not dive into the water more than before, but if you observe how
+far it shall sink, every person expert in Geometry, may measure, that
+those parts that remain out of the water, both in the one and in the
+other Experiment are equall to an hair: whence he may manifestly
+conclude, that the acute Figure which seemed most apt to part and
+penetrate the water, doth not part or penetrate it more than the large
+and spacious.</p>
+
+<p>And he that would have a more easie Experiment, let him take two
+Cylinders of the same Matter, one long and small, and the other short,
+but very broad, and let him put them in the water, not distended, but
+erect and endways: he shall see, if he diligently measure the parts of
+the one and of the other, that in each of them the part submerged,
+retains exactly the same proportion to that out of the water, and that
+no greater part is submerged of that long and small one, than of the
+other more spacious and broad: howbeit, this rests upon a very large,
+and that upon a very little Superficies of water: therefore the
+diversity of Figure, occasioneth neither facility, nor difficulty, in
+parting and penetrating the Continuity of the water, and,
+consequently, cannot be the Cause of the Natation or Submersion. He
+may likewise discover the non operating of variety of Figures, in
+arising from the Bottom of the water, towards the Surface, by taking
+Wax, and tempering it with a competent quantity of the filings of
+Lead, so that it may become a considerable matter graver than the
+<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span>
+water: then let him make it into a Ball, and thrust it unto the Bottom
+of the water; and fasten to it as much Cork, or other light matter, as
+just serveth to raise it, and draw it towards the Surface: for
+afterwards changing the same Wax into a thin Cake, or into any other
+Figure, that same Cork shall raise it in the same manner to a hair.</p>
+
+<p>This silenceth not my Antagonists, but they say, that all the
+discourse hitherto made by me little importeth to them, and that it
+serves their turn, that they have demonstrated in one only particular,
+and in what matter, and under what Figure pleaseth them, namely, in a
+Board and in a Ball of Ebony, that this put in the water, descends to
+the Bottom, and that stays atop to swim: and the Matter being the
+same, and the two Bodies differing in nothing but in Figure, they
+affirm, that they have with all perspicuity demonstrated and sensibly
+manifested what they undertook; and lastly, that they have obtained
+their intent. Nevertheless, I believe, and thinke, I can demonstrate,
+that that same Experiment proveth nothing against my Conclusion.</p>
+
+<div class="sidenote">In Experiments of Natation, the Solid is to be put
+into, not upon the water.</div>
+
+<p>And first, it is false, that the Ball descends, and the Board not: for
+the Board shall also descend, if you do to both the Figures, as the
+words of our Question requireth; that is, if you put them both into
+the water.</p>
+
+<div class="sidenote">The Question of Natation stated.</div>
+
+<p><i>The words were these. That the Antagonists having an opinion, that
+the Figure would alter the Solid Bodies, in relation to the
+descending or not descending, ascending or not ascending in the
+same</i> Medium, <i>as</i> v. gr. <i>in the same water, in such sort, that, for
+Example, a Solid that being of a Sphericall Figure, shall descend
+to the Bottom, being reduced into some other Figure, shall not
+descend: I holding the contrary, do affirm, that a Corporeall Solid
+Body, which reduced into a Sphericall Figure, or any other, shall
+go to the Bottom, shall do the like under whatsoever <a name="tnd_32" id="tnd_32"></a><a href="#tn_32" class="tnlink" title="unclear symbol in original text">other Figure,
+{&amp;}c.</a></i></p>
+
+<div class="sidenote">Place defined according to Aristotle.</div>
+
+<p>But to be in the water, implies to be placed in the water, and by
+<i>Aristotles</i> own Definition of place, to be placed, importeth to be
+invironed by the Superficies of the Ambient Body, therefore, then
+shall the two Figures be in the water, when the Superficies of the
+water, shall imbrace and inviron them: but when the Adversaries shew
+the Board of Ebony not descending to the Bottom, they put it not into
+the water, but upon the water, where being by a certain impediment (as
+by and by we will shew) retained, it is invironed, part by water, and
+part by air, which thing is contrary to our agreement, that was, that
+the Bodies should be in the water, and not part in water, and part in
+air.</p>
+
+<p><span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span></p>
+<p><i>The which is again made manifest, by the questions being put as
+well about the things which go to the Bottom, as those which arise
+from the Bottom to swimme, and who sees not that things placed in
+the Bottom, must have water about them.</i></p>
+
+<div class="sidenote">The confutation of the Experiment in the Ebany.</div>
+
+<p>It is now to be noted, that the Board of Ebany and the Ball, put into
+the water, both sink, but the Ball more swiftly, and the Board more
+slowly; and slower and slower, according as it shall be more broad and
+thin, and of this Tardity the breadth of the Figure is the true Cause:
+But these broad Boards that slowly descend, are the same, that being
+put lightly upon the water, do swimm: Therefore, if that were true
+which the Adversaries affirm, the same numerical Figure, would in the
+same numericall water, cause one while Rest, and another while Tardity
+of Motion, which is impossible: for every perticular Figure which
+descends to the Bottom, hath of necessity its own determinate Tardity
+<span class="sidenote">Every perticular Figure hath its own peculiar Tardity.</span>
+and slowness, proper and naturall unto it, according to which it
+moveth, so that every other Tardity, greater or lesser is improper to
+its nature: if, therefore, a Board, as suppose of a foot square,
+descendeth naturally with six degrees of Tardity, it is impossible,
+that it should descend with ten or twenty, unless some new impediment
+do arrest it. Much less can it, by reason of the same Figure rest, and
+wholly cease to move; but it is necessary, that when ever it resteth,
+there do some greater impediment intervene than the breadth of the
+Figure. Therefore, it must be somewhat else, and not the Figure, that
+stayeth the Board of Ebany above water, of which Figure the only
+Effect is the retardment of the Motion, according to which it
+descendeth more slowly than the Ball. Let it be confessed, therefore,
+rationally discoursing, that the true and sole Cause of the Ebanys
+going to the Bottom, is the excess of its Gravity above the Gravity of
+the water: and the Cause of the greater or less Tardity, the breadth
+of this Figure, or the contractedness of that: but of its Rest, it can
+by no means be allowed, that the quallity of the Figure, is the Cause
+thereof: aswell, because, making the Tardity greater, according as the
+Figure more dilateth, there cannot be so immense a Dilatation, to
+which there may not be found a correspondent immence Tardity without
+redusing it to Nullity of Motion; as, because the Figures produced by
+the Antagonists for effecters of Rest, are the self same that do also
+go to the Bottom.</p>
+
+<div class="sidenote">* The Figure &amp; Resistance of the Medium against
+Division, have nothing to do with the Effect of Natation or
+Submersion, by an Experiment in Wallnut tree.</div>
+
+<p>I will not omit another reason, founded also upon Experience, and if
+I deceive not my self, manifestly concluding, how that the
+Introduction of the breadth or amplitude of Figure, and the Resistance
+of the water against penetration, have nothing to do in the Effect of
+descending, or ascending, or resting in the water. *Take a piece of
+wood or other Matter, of which a Ball ascends from the Bottom of the
+<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span>
+water to the Surface, more slowly than a Ball of Ebony of the same
+bignesse, so that it is manifest, that the Ball of Ebony more readily
+divideth the water in descending, than the other in ascending; as for
+Example, let the Wood be Walnut-tree. Then take a Board of
+Walnut-tree, like and equall to that of Ebony of the Antagonists,
+which swims; and if it be true, that this floats above water, by
+reason of the Figure, unable through its breadth, to pierce the
+Crassitude of the same, the other of Wallnut-tree, without all
+question, being thrust unto the Bottom, will stay there, as less apt,
+through the same impediment of Figure, to divide the said Resistance
+of the water. But if we shall find, and by experience see, that not
+only the thin Board, but every other Figure of the same Wallnut-tree
+will return to float, as undoubtedly we shall, then I must desier my
+opposers to forbear to attribute the floating of the Ebony, unto the
+Figure of the Board, in regard that the Resistance of the water is the
+same, as well to the ascent, as to the descent, and the force of the
+Wallnut-trees ascension, is lesse than the Ebonys force in going to
+the Bottom.</p>
+
+<div class="sidenote">An Experiment in Gold, to prove the non-operating of
+Figure in Natation and Submersion.</div>
+
+<p>Nay, I will say more, that if we shall consider Gold in comparison of
+water, we shall find, that it exceeds it in Gravity almost twenty
+times, so that the Force and Impetus, wherewith a Ball of Gold goes to
+the Bottom, is very great. On the contrary, there want not matters, as
+Virgins Wax, and some Woods, which are not above a fiftieth part less
+grave than water, whereupon their Ascension therein is very slow, and
+a thousand times weaker than the <i>Impetus</i> of the Golds descent: yet
+notwithstanding, a plate of Gold swims without descending to the
+Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin
+Board of Wood, which put in the Bottom of the Water, shall rest there
+without ascending. Now if the Figure can obstruct the Penetration, and
+impede the descent of Gold, that hath so great an <i>Impetus</i>, how can
+it choose but suffice to resist the same Penetration of the other
+matter in ascending, when as it hath scarce a thousandth part of the
+<i>Impetus</i> that the Gold hath in descending? Its therefore, necessary,
+that that which suspends the thin Plate of Gold, or Board of Ebony,
+upon the water, be some thing that is wanting to the other Cakes and
+Boards of Matters less grave than the water; since that being put to
+the Bottom, and left at liberty, they rise up to the Surface, without
+any obstruction: But they want not for flatness and breadth of Figure:
+Therefore, the *spaciousnesse of the Figure, is not that which makes
+the Gold and Ebony to swim.</p>
+
+<p>And, because, that the excess of their Gravity above the Gravity of
+the water, is questionless the Cause of the sinking of the flat piece
+of Ebony, and the thin Plate of Gold, when they go to the Bottom,
+therefore, of necessity, when they float, the Cause of their staying
+above water, proceeds from Levity, which in that case, by some
+<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span>
+Accident, peradventure not hitherto observed, cometh to meet with the
+said Board, rendering it no longer as it was before, whilst it did
+sink more ponderous than the water, but less.</p>
+
+<p>Now, let us return to take the thin Plate of Gold, or of Silver, or
+the thin Board of Ebony, and let us lay it lightly upon the water, so
+that it stay there without sinking, and diligently observe its effect.
+And first, see how false the assertion of <i>Aristotle</i>, and our
+oponents is, to wit, that it stayeth above water, through its
+unability to pierce and penetrate the Resistance of the waters
+Crassitude: for it will manifestly appear, not only that the said
+Plates have penetrated the water, but also that they are a
+considerable matter lower than the Surface of the same, the which
+continueth eminent, and maketh as it were a Rampert on all sides,
+round about the said Plates, the profundity of which they stay
+swimming: and, according as the said Plates shall be more grave than
+the water, two, four, ten or twenty times, it is necessary, that their
+Superficies do stay below the universall Surface of the water, so much
+more, than the thickness of those Plates, as we shal more distinctly
+shew anon. In the mean space, for the more easie understanding of what
+<span class="figright" style="width: 277px;">
+<img src="images/i037.png" width="277" height="136" alt="" title="" />
+</span>
+I say, observe with me a little the present Scheme: in which let us
+suppose the Surface of the water to be distended, according to the
+Lines F L D B, upon which if one shall put a board of matter
+specifically more grave than water, but so lightly that it submerge
+not, it shall not rest any thing above, but shall enter with its whole
+thickness into the water: and, moreover, shall sink also, as we see by
+the Board A I, O I, whose breadth is wholly sunk into the water, the
+little Ramperts of water L A and D O incompassing it, whose
+Superficies is notably higher than the Superficies of the Board. See
+now whether it be true, that the said Board goes not to the Bottom, as
+being of Figure unapt to penetrate the Crassitude of the water.</p>
+
+<div class="sidenote">Why solids having penitrated the Water, do not proceed
+to a totall Submersion.</div>
+
+<p>But, if it hath already penetrated, and overcome the Continuity of
+the water, &amp; is of its own nature more grave than the said water, why
+doth it not proceed in its sinking, but stop and suspend its self
+within that little dimple or cavitie, which with its ponderosity it
+hath made in the water? I answer; because that in submerging it self,
+so far as till its Superficies come to the Levell with that of the
+water, it loseth a part of its Gravity, and loseth the rest of it as
+it submergeth &amp; descends beneath the Surface of the water, which
+maketh Ramperts and Banks round about it, and it sustaines this loss
+by means of its drawing after it, and carrying along with it, the Air
+that is above it, and by Contact adherent to it, which Air succeeds to
+fill the Cavity that is invironed by the Ramperts of water; so that
+that which in this case descends and is placed in the water, is not
+only the Board of Ebony or Plate of Iron, but a composition of Ebony
+<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span>
+and Air, from which resulteth a Solid no longer superiour in Gravity
+to the water, as was the simple Ebony, or the simple Gold. And, if we
+exactly consider, what, and how great the Solid is, that in this
+Experiment enters into the water, and contrasts with the Gravity of
+the same, it will be found to be all that which we find to be beneath
+the Surface of the water, the which is an aggregate and Compound of a
+Board of Ebony, and of almost the like quantity of Air, or a Mass
+compounded of a Plate of Lead, and ten or twelve times as much Air.
+But, Gentlemen, you that are my Antagonists in our Question, we
+require the Identity of Matter, and the alteration only of the Figure;
+therefore, you must remove that Air, which being conjoyned with the
+Board, makes it become another Body less grave than the Water, and put
+only the Ebony into the Water, and you shall certainly see the Board
+descend to the Bottom; and, if that do not happen, you have got the
+day. And to seperate the Air from the Ebony, there needs no more but
+<span class="sidenote">How to seperate the Air from Solids in demitting them
+into the water.</span>
+only to bath the Superficies of the said Board with the same Water:
+for the Water being thus interposed between the Board and the Air, the
+other circumfused Water shall run together without any impediment, and
+shall receive into it the sole and bare Ebony, as it was to do.</p>
+
+<p>But, me thinks I hear some of the Adversaries cunningly opposing this,
+and telling me, that they will not yield, by any means, that their
+Board be wetted, because the weight added thereto by the Water, by
+making it heavier than it was before, draws it to the Bottom, and that
+the addition of new weight is contrary to our agreement, which was,
+that the Matter be the same.</p>
+
+<p>To this, I answer, first; that treating of the operation of Figure
+in Bodies put into the Water, none can suppose them to be put into the
+Water without being wet; nor do I desire more to be done to the Board,
+then I will give you leave to do to the Ball. Moreover, it is untrue,
+that the Board sinks by vertue of the new Weight added to it by the
+Water, in the single and slight bathing of it: for I will put ten or
+twenty drops of Water upon the same Board, whilst it is sustained upon
+the water; which drops, because not conjoyned with the other Water
+circumfused, shall not so encrease the weight of it, as to make it
+sink: but if the Board being taken out, and all the water wiped off
+that was added thereto, I should bath all its Superficies with one
+only very small drop, and put it again upon the water, without doubt
+it shall sink, the other Water running to cover it, not being retained
+by the superiour Air; which Air by the interposition of the thin vail
+of water, that takes away its Contiguity unto the Ebony, shall without
+Renitence be seperated, nor doth it in the least oppose the succession
+of the other Water: but rather, to speak better, it shall descend
+freely; because it shall be all invironed and covered with water, as
+<span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span>
+soon as its superiour Superficies, before vailed with water, doth
+arrive to the Levell of the universall Surface of the said water. To
+say, in the next place, that water can encrease the weight of things
+that are demitted into it, is most false; for water hath no Gravity in
+water, since it descends not: yea, if we would well consider what any
+<span class="sidenote">Water hath no Gravity in Water.</span>
+immense Mass of water doth put upon a grave Body; that is placed in
+it, we shall find experimentally, that it, on the contrary, will
+rather in a great part deminish the weight of it, and that we may be
+<span class="sidenote">Water deminisheth the Gravity of Solids immerged
+therein.</span>
+able to lift an huge Stone from the Bottom of the water, which the
+water being removed, we are not able to stir. Nor let them tell me by
+way of reply, that although the superposed water augment not the
+Gravity of things that are in it, yet it increaseth the ponderosity of
+those that swim, and are part in the water and part in the Air, as is
+seen, for Example, in a Brass Ketle, which whilst it is empty of
+<span class="sidenote">The Experiment of a brass Ketle swiming when empty, &amp;
+sinking when full, alledged to prove that water gravitates in
+water, answered.</span>
+water, and replenished only with Air shall swim, but pouring of Water
+therein, it shall become so grave, that it shall sink to the Bottom,
+and that by reason of the new weight added thereto. To this I will
+return answer, as above, that the Gravity of the Water, contained in
+the Vessel is not that which sinks it to the Bottom, but the proper
+Gravity of the Brass, superiour to the Specificall Gravity of the
+Water: for if the Vessel were less grave than water, the Ocean would
+not suffice to submerge it. And, give me leave to repeat it again, as
+<span class="sidenote">An Ocean sufficeth not to sink a Vessel specifically
+less grave than water.</span>
+the fundamentall and principall point in this Case, that the Air
+contained in this Vessel before the infusion of the Water, was that
+which kept it a-float, since that there was made of it, and of the
+<span class="sidenote">Air, the Cause of the Natation of empty Vessels of
+Matters graver <i>in specie</i> than the water.</span>
+Brass, a Composition less grave than an equall quantity of Water: and
+the place that the Vessel occupyeth in the Water whilst it floats, is
+not equall to the Brass alone, but to the Brass and to the Air
+together, which filleth that part of the Vessel that is below the
+Levell of the water: Moreover, when the Water is infused, the Air is
+removed, and there is a composition made of Brass and of water, more
+grave <i>in specie</i> than the simple water, but not by vertue of the
+water infused, as having greater Specifick Gravity than the other
+water, but through the proper Gravity of the Brass, and through the
+alienation of the Air. Now, as he that should say that Brass, that by
+its nature goes to the Bottom, being formed into the Figure of a
+Ketle, acquireth from that Figure a vertue of lying in the Water
+<span class="sidenote">Neither Figure, nor the breadth of Figure, is the Cause
+of Natation.</span>
+without sinking, would say that which is false; because that Brass
+fashioned into any <a name="tnd_37" id="tnd_37"></a><a href="#tn_37" class="tnlink" title="potential printer's error, comma in unusual position">whatever Figure, goeth always</a> to the Bottom,
+provided, that that which is put into the water be simple Brass; and
+it is not the Figure of the Vessel that makes the Brass to float, but
+it is because that that is not purely Brass which is put into the
+water, but an aggregate of Brass and of Air: so is it neither more nor
+<span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span>
+less false, that a thin Plate of Brass or of Ebony, swims by vertue of
+its dilated &amp; broad Figure: for the truth is, that it bares up without
+submerging, because that that which is put in the water, is not pure
+Brass or simple Ebony, but an aggregate of Brass and Air, or of Ebony
+and Air. And, this is not contrary unto my Conclusion, the which,
+(having many a time seen Vessels of Mettall, and thin pieces of
+diverse grave Matters float, by vertue of the Air conjoyned with them)
+did affirm, That Figure was not the Cause of the Natation or
+Submersion of such Solids as were placed in the water. Nay more, I
+cannot omit, but must tell my Antagonists, that this new conceit of
+denying that the Superficies of the Board should be bathed, may beget
+in a third person an opinion of a poverty of Arguments of defence on
+their part, since that such bathing was never insisted upon by them in
+the beginning of our Dispute, and was not questioned in the least,
+being that the Originall of the discourse arose upon the swiming of
+Flakes of Ice, wherein it would be simplicity to require that their
+<a name="tnd_38" id="tnd_38"></a><a href="#tn_38" class="tnlink" title="missing space between words">Superficies might bedry:</a> besides, that whether these pieces of Ice be
+wet or dry they alwayes swim, and as the Adversaries say, by reason of
+the Figure.</p>
+
+<p>Some peradventure, by way of defence, may say, that wetting the Board
+of Ebony, and that in the superiour Superficies, it would, though of
+it self unable to pierce and penetrate the water, be born downwards,
+if not by the weight of the additionall water, at least by that desire
+and propension that the superiour parts of the water have to re-unite
+and rejoyn themselves: by the Motion of which parts, the said Board
+cometh in a certain manner, to be depressed downwards.</p>
+
+<div class="sidenote">The Bathed Solid descends not out of any affectation
+of union in the upper parts of the water.</div>
+
+<p>This weak Refuge will be removed, if we do but consider, that the
+repugnancy of the inferiour parts of the water, is as great against
+Dis-union, as the Inclination of its superiour parts is to union: nor
+can the uper unite themselves without depressing the board, nor can it
+descend without disuniting the parts of the nether Water: so that it
+doth follow, by necessary consequence, that for those respects, it
+shall not descend. Moreover, the same that may be said of the upper
+parts of the water, may with equall reason be said of the nether,
+namely, that desiring to unite, they shall force the said Board
+upwards.</p>
+
+<p>Happily, some of these Gentlemen that dissent from me, will wonder,
+that I affirm, that the contiguous superiour Air is able to sustain
+that Plate of Brass or of Silver, that stayeth above water; as if I
+would in a certain sence allow the Air, a kind of Magnetick vertue of
+<span class="sidenote"><i>A</i> Magnetisme in the <i>A</i>ir, by which it bears up
+those Solids in the water, that are contiguous with it.</span>
+sustaining the grave Bodies, with which it is contiguous. To satisfie
+all I may, to all doubts, I have been considering how by some other
+sensible Experiment I might demonstrate, how truly that little
+contiguous and superiour Air sustaines those Solids, which being by
+<span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>
+nature apt to descend to the Bottom, being placed lightly on the water
+submerge not, unless they be first thorowly bathed; and have found,
+that one of these Bodies having descended to the Bottom, by
+conveighing to it (without touching it in the least) a little Air,
+which conjoyneth with the top of the same, it becometh sufficient, not
+only, as before to sustain it, but also to raise it, and to carry it
+back to the top, where it stays and abideth in the same manner, till
+such time, as the assistance of the conjoyned Air is taken away. And
+to this effect, I have taken a Ball of Wax, and made it with a little
+Lead, so grave, that it leasurely descends to the Bottom, making with
+all its Superficies very smooth and pollite: and this being put gently
+into the water, almost wholly submergeth, there remaining vissible
+only a little of the very top, the which so long as it is conjoyned
+<span class="sidenote">The Effect of the Airs Contiguity in the Natation of
+Solids.</span>
+with the Air, shall retain the Ball a-top, but the Contiguity of the
+Air taken away by wetting it, it shall descend to the Bottom and there
+remain. Now to make it by vertue of the Air, that before sustained it
+to return again to the top, and stay there, thrust into the water a
+Glass reversed with the mouth downwards, the which shall carry with it
+the Air it contains, and move this towards the Ball, abasing it till
+such time that you see, by the transparency of the Glass, that the
+contained Air do arrive to the summity of the <i>B</i>all: then gently
+<span class="sidenote">The force of Contact.</span>
+withdraw the Glass upwards, and you shall see the <i>B</i>all to rise, and
+afterwards stay on the top of the water, if you carefully part the
+<span class="sidenote"><i>A</i>n Affectation of Conjunction betwixt Solids and the
+Air contiguous to them.</span>
+Glass and the water without overmuch commoving and disturbing it.
+There is, therefore, a certain affinity between the Air and other
+Bodies, <a name="tnd_39" id="tnd_39"></a><a href="#tn_39" class="tnlink" title="missing letter t, unied for united">which holds them unied,</a> so, that they seperate not without a
+kind of violence. The same likewise is seen in the water; for if we
+<span class="sidenote">The like affectation of Conjunction betwixt Solids &amp;
+the water.</span>
+shall wholly submerge some Body in it, so that it be thorowly bathed,
+in the drawing of it afterwards gently out again, we shall see the
+water follow it, and rise notably above its Surface, before it
+seperates from it. Solid Bodies, also, if they be equall and alike in
+<span class="sidenote">Also the like affectation and Conjunction betwixt
+Solids themselves.</span>
+Superficies, so, that they make an exact Contact without the
+interposition of the least Air, that may part them in the seperation
+and yield untill that the ambient <i>Medium</i> succeeds to replenish the
+place, do hold very firmly conjoyned, and are not to be seperated
+without great force but, because, the Air, Water, and other Liquids,
+very expeditiously shape themselves to contact with any Solid
+<i>B</i>odies, so that their Superficies do exquisitely adopt themselves to
+that of the Solids, without any thing remaining between them,
+therefore, the effect of this Conjunction and Adherence is more
+manifestly and frequently observed in them, than in hard and
+inflexible Bodies, whose Superficies do very rarely conjoyn with
+exactness of Contact. This is therefore that Magnetick vertue, which
+<span class="sidenote">Contact may be the Cause of the Continuity of Naturall
+Bodies.</span>
+with firm Connection conjoyneth all Bodies, that do touch without the
+interposition of flexible fluids; and, who knows, but that that a
+Contact, when it is very exact, may be a sufficient Cause of the Union
+and Continuity of the parts of a naturall <i>B</i>ody?</p>
+<p><span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span></p>
+
+<p>Now, pursuing my purpose, I say; that it needs not, that we have
+recourse to the Tenacity, that the parts of the water have amongst
+themselves, by which they resist and oppose Division, Distraction, and
+Seperation, because there is no such Coherence and Resistance of
+Division for if there were, it would be no less in the internall parts
+than in those nearer the superiour or externall Surface, so that the
+same Board, finding alwayes the same Resistance and Renitence, would
+no less stop in the middle of the water than about the Surface, which
+is false. Moreover, what Resistance can we place in the Continuity of
+the water, if we see that it is impossible to find any Body of
+whatsoever Matter, Figure or Magnitude, which being put into the
+water, shall be obstructed and impeded by the Tenacity of the parts of
+the water to one another, so, but that it is moved upwards or
+downwards, according as the Cause of their Motion transports it? And,
+what greater proof of it can we desier, than that which we daily see
+in Muddy waters, which being put into Vessels to be drunk, and being,
+after some hours setling, still, as we say, thick in the end, after
+<span class="sidenote">The settlement of <i>M</i>uddy Water, proveth that that
+Element hath no aversion to Division.</span>
+four or six dayes they are wholly setled, and become pure and clear?
+Nor can their Resistance of Penetration stay those impalpable and
+insensible Atomes of Sand, which by reason of their exceeding small
+force, spend six dayes in descending the space of half a yard.</p>
+
+<p><i>Nor let them say, that the seeing of such small Bodies, consume
+six dayes in descending so little a way, is a sufficient Argument
+of the Waters Resistance of Division; because that is no resisting
+of Division, but a retarding of Motion; and it would be simplicity
+to say, that a thing opposeth Division, and that in the same
+<span class="sidenote">Water cannot oppose division, and at the same time
+permit it self to be divided.</span>
+instant, it permits it self to be divided: nor doth the Retardation
+of Motion at all favour the Adversaries cause, for that they are to
+instance in a thing that wholly prohibiteth Motion, and procureth
+Rest; it is necessary, therefore, to find out Bodies that stay in
+the water, if one would shew its repugnancy to Division, and not
+such as move in it, howbeit but slowly.</i></p>
+
+<p>What then is this Crassitude of the water, with which it resisteth
+Division? What, I beseech you, should it be, if we (as we have said
+above) with all diligence attempting the reduction of a Matter into so
+like a Gravity with the water, that forming it into a dilated Plate it
+rests suspended as we have said, between the two waters, it be
+impossible to effect it, though we bring them to such an
+Equiponderance, that as much Lead as the fourth part of a Grain of
+Musterd-seed, added to the same expanded Plate, that in Air [<i>i. e.
+out of the water</i>] shall weigh four or six pounds, sinketh it to the
+Bottom, and being substracted, it ascends to the Surface of the water?
+I cannot see, (if what I say be true, as it is most certain) what
+minute vertue and force we can possibly find or imagine, to which the
+Resistance of the water against Division and Penetration is not
+<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span>
+inferiour; whereupon, we must of necessity conclude that it is
+nothing: because, if it were of any sensible power, some large Plate
+might be found or compounded of a Matter alike in Gravity to the
+water, which not only would stay between the two waters; but,
+moreover, should not be able to descend or ascend without notable
+force. We may likewise collect the same from an other Experiment,
+<span class="sidenote">An hair will draw a great Mass thorow the Water; which
+proveth, that it hath no Resistance against transversall
+Division.</span>
+shewing that the Water gives way also in the same manner to
+transversall Division; for if in a setled and standing water we should
+place any great Mass that goeth not to the bottom, drawing it with a
+single Womans Hair, we might carry it from place to place without any
+opposition, and this whatever Figure it hath, though that it possess a
+great space of water, as for instance, a great Beam would do moved
+side-ways. Perhaps some might oppose me and say, that if the
+Resistance of water against Division, as I affirm, were nothing; Ships
+should not need such a force of Oars and Sayles for the moving of them
+from place to place in a tranquile Sea, or standing Lake. To him that
+should make such an objection, I would reply, that the water
+<span class="sidenote">How ships are moved in the water.</span>
+contrasteth not against, nor simply resisteth Division, but a sudden
+Division, and with so much greater Renitence, by how much greater the
+Velocity is: and the Cause of this Resistance depends not on
+Crassitude, or any other thing that absolutely opposeth Division, but
+because that the parts of the water divided, in giving way to that
+Solid that is moved in it, are themselves also necessitated locally to
+move, some to the one side, and some to the other, and some downwards:
+and this must no less be done by the waves before the Ship, or other
+Body swimming through the water, than by the posteriour and
+subsequent; because, the Ship proceeding forwards, to make it self a
+way to receive its Bulk, it is requisite, that with the Prow it
+repulse the adjacent parts of the water, as well on one hand as on the
+other, and that it move them as much transversly, as is the half of
+the breadth of the Hull: and the like removall must those waves make,
+that succeeding the Poump do run from the remoter parts of the Ship
+towards those of the middle, successively to replenish the places,
+which the Ship in advancing forwards, goeth, leaving vacant. Now,
+because, <a name="tnd_41" id="tnd_41"></a><a href="#tn_41" class="tnlink" title="printer's error, Motitions for Motions">all Motitions are made</a> in Time, and the longer in greater
+<span class="sidenote">Bodies moved a certain space in a certain Time, by a
+certain power, cannot be moved the same space and in a shorter
+time, but by a greater power.</span>
+time: and it being moreover true, that those Bodies that in a certain
+time are moved by a certain power such a certain space, shall not be
+moved the same space, and in a shorter Time, unless by a greater
+Power: therefore, the broader Ships move slower than the narrower,
+being put on by an equall Force: and the same Vessel requires so much
+greater force of Wind, or Oars, the faster it is to move.</p>
+<p><span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span></p>
+
+<p><i>But yet for all this, any great Mass swimming in a standing Lake,
+may be moved by any petit force; only it is true, that a lesser
+force more slowly moves it: but if the waters Resistance of
+Division, were in any manner sensible, it would follow, that the
+said Mass, should, notwithstanding the percussion of some sensible
+force, continue immoveable, which is not so. Yea, I will say
+<span class="sidenote">The parts of Liquids, so farre from resisting
+Division, that they contain not any thing that may be divided.</span>
+farther, that should we retire our selves into the more internall
+contemplation of the Nature of water and other Fluids, perhaps we
+should discover the Constitution of their parts to be such, that
+they not only do not oppose Division, but that they have not any
+thing in them to be divided: so that the Resistance that is
+observed in moving through the water, is like to that which we meet
+<span class="sidenote">The Resistance a Solid findeth in moving through the
+water, like to that we meet with in passing through a throng of
+people:</span>
+with in passing through a great Throng of People, wherein we find
+impediment, and not by any difficulty in the Division, for that
+none of those persons are divided whereof the Croud is composed,
+but only in moving of those persons side-ways which were before
+divided and disjoyned: and thus we find Resistance in thrusting a
+Stick into an heap of Sand, not because any part of the Sand is to
+be cut in pieces, but only to be moved and raised. Two manners of
+<span class="sidenote">Or in thrusting a Stick into an heap of Sand.</span>
+Penetration, therefore, offer themselves to us, one in Bodies,
+whose parts were continuall, and here Division seemeth necessary,
+the other in the aggregates of parts not continuall, but contiguous
+only, and here there is no necessity of dividing but of moving
+<span class="sidenote">Two kinds of Penetration, one in Bodies continuall, the
+other in Bodies only contiguous.</span>
+only. Now, I am not well resolved, whether water and other Fluids
+may be esteemed to be of parts continuall or contiguous only; yet I
+<span class="sidenote">Water consists not of continuall, but only of
+contiguous parts.</span>
+find my self indeed inclined to think that they are rather
+contiguous (if there be in Nature no other manner of aggregating,
+than by the union, or by the touching of the extreams:) and I am
+induced thereto by the great difference that I see between the
+Conjunction of the parts of an hard or Solid Body, and the
+<span class="sidenote"><i><a name="tnd_42" id="tnd_42"></a><a href="#tn_42" class="tnlink" title="possible missing letter e">Se{e} what satisfaction</a> he hath given, as to this
+point, in Lib. de Motu. Dial. 2.</i></span>
+Conjunction of the same parts when the same Body shall be made
+Liquid and Fluid: for if, for example, I take a Mass of Silver or
+other Solid and hard Mettall, I shall in dividing it into two
+parts, find not only the resistance that is found in the moving of
+it only, but an other incomparably greater, dependent on that
+<span class="sidenote">Great difference betwixt the Conjunction of the parts
+of a Body when Solid, and when fluid.</span>
+vertue, whatever it be, which holds the parts united: and so if we
+would divide again those two parts into other two, and successively
+into others and others, we should still find a like Resistance, but
+ever less by how much smaller the parts to be divided shall be; but
+if, lastly, employing most subtile and acute Instruments, such as
+are the most tenuous parts of the Fire, we shall resolve it
+(perhaps) into its last and least Particles, there shall not be
+left in them any longer either Resistance of Division, or so much
+as a capacity of being farther divided, especially by Instruments
+more grosse than the acuities of Fire: and what Knife or Rasor put
+into well melted Silver can we finde, that will divide a thing
+which surpasseth the separating power of Fire? Certainly none:
+because either the whole shall be reduced to the most minute and
+ultimate Divisions, or if there remain parts capable still of other
+<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span>
+<a name="tnd_43" id="tnd_43"></a><a href="#tn_43" class="tnlink" title="printer's error, Subdidivisions for Subdivisions">Subdidivisions,</a> they cannot receive them, but only from acuter
+Divisors than Fire; but a Stick or Rod of Iron, moved in the melted
+Metall, is not such a one. Of a like Constitution and Consistence,
+I account the parts of Water, and other Liquids to be, namely,
+<span class="sidenote">Water consists of parts that admit of no farther
+division.</span>
+incapable of Division by reason of their Ienuity; or if not
+absolutely indivisible, yet at least not to be divided by a Board,
+or other Solid Body, palpable unto the hand, the Sector being
+alwayes required to be more sharp than the Solid to be cut. Solid
+Bodies, therefore, do only move, and not divide the Water, when put
+<span class="sidenote">Solids dimitted into the water, do onely move, and not
+divide it.</span>
+into it; whose parts being before divided to the extreamest
+minuity, and therefore capable of being moved, either many of them
+at once, or few, or very few, they soon give place to every small
+Corpuscle, that descends in the same: for that, it being little and
+light, descending in the Air, and arriving to the Surface of the
+Water, it meets with Particles of Water more small, and of less
+Resistance against Motion and Extrusion, than is its own prement
+and extrusive force; whereupon it submergeth, and moveth such a
+portion of them, as is proportionate to its Power. There is not,
+therefore, any Resistance in Water against Division, nay, there is
+not in it any divisible parts. I adde; moreover, that in case yet
+there should be any small Resistance found (which is absolutely
+false) haply in attempting with an Hair to move a very great natant
+<span class="sidenote">If there were any Resistance of Division in water, it
+must needs be small, in that it is overcome by an Hair, a Grain of
+Lead, or a slight bathing of the Solid.</span>
+Machine, or in essaying by the addition of one small Grain of Lead
+to sink, or by removall of it to raise a very broad Plate of
+Matter, equall in Gravity with Water, (which likewise will not
+happen, in case we proceed with dexterity) we may observe that that
+Resistance is a very different thing from that which the
+Adversaries produce for the Cause of the Natation of the Plate of
+Lead or Board of Ebony, for that one may make a Board of Ebony,
+which being put upon the Water swimmeth, and cannot be submerged,
+no not by the addition of an hundred Grains of Lead put upon the
+same, and afterwards being bathed, not only sinks, though the said
+Lead be taken away, but though moreover a quantity of Cork, or of
+some other light Body fastened to it, sufficeth not to hinder it
+from sinking unto the bottome: so that you see, that although it
+were granted that there is a certain small Resistance of Division
+found in the substance of the Water, yet this hath nothing to do
+with that Cause which supports the Board above the Water, with a
+Resistance an hundred times greater than that which men can find in
+the parts of the Water: nor let them tell me, that only the Surface
+of the Water hath such Resistance, and not the internall parts, or
+<span class="sidenote">The uper parts of the Water, do no more resist Division
+than the middle or lower parts.</span>
+that such Resistance is found greatest in the beginning of the
+Submersion, as it also seems that in the beginning, Motion meets
+with greater opposition, than in the continuance of it; because,
+first, I will permit, that the Water be stirred, and that the
+superiour parts be mingled with the middle, and inferiour parts, or
+<span class="sidenote">Waters Resistance of division, not greater in the
+beginning of the Submersion.</span>
+that those above be wholly removed, and those in the middle only
+made use off, and yet you shall see the effect for all that, to be
+<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span>
+still the same: Moreover, that Hair which draws a Beam through the
+Water, is likewise to divide the upperparts, and is also to begin
+the Motion, and yet it begins it, and yet it divides it: and
+finally, let the Board of Ebony be put in the midway, betwixt the
+bottome and the top of the Water, and let it there for awhile be
+suspended and setled, and afterwards let it be left at liberty, and
+it will instantly begin its Motion, and will continue it unto the
+bottome. Nay, more, the Board so soon as it is dimitted upon the
+Water, hath not only begun to move and divide it, but is for a good
+space dimerged into it.</i></p>
+
+<p>Let us receive it, therefore, for a true and undoubted Conclusion,
+That the Water hath not any Renitence against simple Division, and
+that it is not possible to find any Solid Body, be it of what Figure
+it will, which being put into the Water, its Motion upwards or
+downwards, according as it exceedeth, or shall be exceeded by the
+Water in Gravity (although such excesse and difference be insensible)
+shall be prohibited, and taken away, by the Crassitude of the said
+Water. When, therefore, we see the Board of Ebony, or of other Matter,
+more grave than the Water, to stay in the Confines of the Water and
+Air, without submerging, we must have recourse to some other
+Originall, for the investing the Cause of that Effect, than to the
+breadth of the Figure, unable to overcome the Renitence with which the
+Water opposeth Division, since there is no Resistance; and from that
+which is not in being, we can expect no Action. It remains most true,
+therefore, as we have said before, that this so succeds, for that that
+which in such manner put upon the water, not the same Body with that
+which is put <i>into</i> the Water: because this which is put <i>into</i> the
+Water, is the pure Board of Ebony, which for that it is more grave
+than the Water, sinketh, and that which is put <i>upon</i> the Water, is a
+Composition of Ebony, and of so much Air, that both together are
+specifically less grave than the Water, and therefore they do not
+descend.</p>
+
+<p>I will farther confirm this which I say. Gentlemen, my Antagonists, we
+are agreed, that the excess or defect of the Gravity of the Solid,
+unto the Gravity of the Water, is the true and proper Cause of
+Natation or Submersion.</p>
+
+<div class="sidenote">Great Caution to be had in experimenting the operation
+of Figure in Natation.</div>
+
+<p>Now, if you will shew that besides the former Cause, there is another
+which is so powerfull, that it can hinder and remove the Submersion of
+those very Solids, that by their Gravity sink, and if you will say,
+that this is the breadth or ampleness of Figure, you are oblieged,
+when ever you would shew such an Experiment, first to make the
+circumstances certain, that that Solid which you put into the Water,
+be not less grave <i>in specie</i> than it, for if you should not do so,
+any one might with reason say, that not the Figure, but the Levity was
+the cause of that Natation. But I say, that when you shall dimit a
+<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span>
+Board of Ebony into the Water, you do not put therein a Solid more
+grave <i>in specie</i> than the Water, but one lighter, for besides the
+Ebony, there is in the Water a Mass of Air, united with the Ebony, and
+such, and so light, that of both there results a Composition less
+grave than the Water: See, therefore, that you remove the Air, and put
+the Ebony alone into the Water, for so you shall immerge a Solid more
+grave then the Water, and if this shall not go to the Bottom, you have
+well Philosophized and I ill.</p>
+
+<p>Now, since we have found the true Cause of the Natation of those
+Bodies, which otherwise, as being graver than the Water, would descend
+to the bottom, I think, that for the perfect and distinct knowledge of
+this business, it would be good to proceed in a way of discovering
+demonstratively those particular Accidents that do attend these
+effects, and,</p>
+
+
+
+<h2><a name="PROBL_I" id="PROBL_I"></a>PROBL. I.</h2>
+
+<div class="sidenote">To finde the proportion Figures ought to have to the
+waters Gravity, that by help of the contiguous Air, they may
+swim.</div>
+
+<p class="def_head"><i>To finde what proportion severall Figures of different Matters
+ought to have, unto the Gravity of the Water, that so they may be
+able by vertue of the Contiguous Air to stay afloat.</i></p>
+
+
+<p class="cap">Let, therefore, for better illustration, D F N E be a Vessell,
+wherein the water is contained, and suppose a Plate or Board, whose
+thickness is comprehended between the Lines I C and O S, and let it be
+of Matter exceeding the water in Gravity, so that being put upon the
+water, it dimergeth and abaseth below the Levell of the said water,
+leaving the little Banks A I and B C, which are at the greatest height
+they can be, so that if the Plate I S should but descend any little
+space farther, the little Banks or Ramparts would no longer consist,
+<span class="figright" style="width: 195px;">
+<img src="images/i047.png" width="195" height="77" alt="" title="" />
+</span>
+but expulsing the Air A I C B, they would diffuse themselves over the
+Superficies I C, and would submerge the Plate. The height A I B C is
+therefore the greatest profundity that the little Banks of water admit
+of. Now I say, that from this, and from the proportion in Gravity,
+that the Matter of the Plate hath to the water, we may easily finde of
+what thickness, at most, we may make the said Plates, to the end, they
+may be able to bear up above water: for if the Matter of the Plate or
+Board I S were, for Example, as heavy again as the water, a Board of
+that Matter shall be, at the most of a thickness equall to the
+greatest height of the Banks, that is, as thick as A I is high: which
+we will thus demonstrate. Let the Solid I S be double in Gravity to
+the water, and let it be a regular Prisme, or Cylinder, to wit, that
+<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span>
+hath its two flat Superficies, superiour and inferiour, alike and
+equall, and at Right Angles with the other laterall Superficies, and
+let its thickness I O be equall to the greatest Altitude of the Banks
+<span class="figleft" style="width: 198px;">
+<img src="images/i048.png" width="198" height="81" alt="" title="" />
+</span>
+of water: I say, that if it be put upon the water, it will not
+submerge: for the Altitude A I being equall to the Altitude I O, the
+Mass of the Air A B C I shall be equall to the Mass of the Solid C I O
+S: and the whole Mass A O S B double to the Mass I S; And since the
+Mass of the Air A C, neither encreaseth nor diminisheth the Gravity of
+the Mass I S, and the Solid I S was supposed double in Gravity to the
+water; Therefore as much water as the Mass submerged A O S B,
+compounded of the Air A I C B, and of the Solid I O S C, weighs just
+as much as the same submerged Mass A O S B: but when such a Mass of
+water, as is the submerged part of the Solid, weighs as much as the
+said Solid, it descends not farther, but resteth, as by (<i>a</i>)
+<i>Archimedes</i>, and above by us, hath been demonstrated: Therefore, I S
+<span class="sidenote">Of Natation Lib. 1. Prop. 3.</span>
+shall descend no farther, but shall rest. And if the Solid I S shall
+be Sesquialter in Gravity to the water, it shall float, as long as its
+thickness be not above twice as much as the greatest Altitude of the
+Ramparts of water, that is, of A I. For I S being Sesquialter in
+Gravity to the water, and the Altitude O I, being double to I A, the
+Solid submerged A O S B, shall be also Sesquialter in Mass to the
+Solid I S. And because the Air A C, neither increaseth nor diminisheth
+the ponderosity of the Solid I S: Therefore, as much water in quantity
+as the submerged Mass A O S B, weighs as much as the said Mass
+submerged: And, therefore, that Mass shall rest. And briefly in
+generall.</p>
+
+
+
+
+<h2><a name="THEOREME_VI" id="THEOREME_VI"></a>THEOREME. VI.</h2>
+
+<div class="sidenote">The proportion of the greatest thickness of Solids,
+beyond which encreased they sink.</div>
+
+<p class="def_head"><i>When ever the excess of the Gravity of the Solid above the Gravity
+of the Water, shall have the same proportion to the Gravity of
+the Water, that the Altitude of the Rampart, hath to the
+thickness of the Solid, that Solid shall not sink, but being
+never so little thicker it shall.</i></p>
+
+
+<p class="cap">Let the Solid I S be superior in Gravity to the water, and of such
+thickness, that the Altitude of the Rampart A I, be in proportion to
+the thickness of the Solid I O, as the excess of the Gravity of the
+said Solid I S, above the Gravity of a Mass of water equall to the
+Mass I S, is to the Gravity of the Mass of water equall to the Mass I
+<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span>
+<span class="figright" style="width: 196px;">
+<img src="images/i049.png" width="196" height="80" alt="" title="" />
+</span>
+S. I say, that the Solid I S shall not sinke, but being never so
+little thicker it shall go to the bottom: For being that as A I is to
+I O, so is the Excess of the Gravity of the Solid I S, above the
+Gravity of a Mass of water equall to the Mass I S, to the Gravity of
+the said Mass of water: Therefore, compounding, as A O is to O I, so
+shall the Gravity of the Solid I S, be to the Gravity of a Mass of
+water equall to the Mass I S: And, converting, as I O is to O A, so
+shall the Gravity of a Mass of water equall to the Mass I S, be to the
+Gravity of the Solid I S: But as I O is to O A, so is a Mass of water
+I S, to a Mass of water equall to the Mass A B S O: and so is the
+Gravity of a Mass of water I S, to the Gravity of a Mass of water A S:
+Therefore as the Gravity of a Mass of water, equall to the Mass I S,
+is to the Gravity of the Solid I S, so is the same Gravity of a Mass
+of water I S, to the Gravity of a Mass of Water A S: Therefore the
+Gravity of the Solid I S, is equall to the Gravity of a Mass of water
+equall to the Mass A S: But the Gravity of the Solid I S, is the same
+with the Gravity of the Solid A S, compounded of the Solid I S, and of
+the Air A B C I. Therefore the whole compounded Solid A O S B, weighs
+as much as the water that would be comprised in the place of the said
+Compound A O S B: And, therefore, it shall make an <i>Equilibrium</i> and
+rest, and that same Solid I O S C shall sinke no farther. But if its
+thickness I O should be increased, it would be necessary also to
+encrease the Altitude of the Rampart A I, to maintain the due
+proportion: But by what hath been supposed, the Altitude of the
+Rampart A I, is the greatest that the Nature of the Water and Air do
+admit, without the waters repulsing the Air adherent to the
+Superficies of the Solid I C, and possessing the space A I C B:
+Therefore, a Solid of greater thickness than I O, and of the same
+Matter with the Solid I S, shall not rest without submerging, but
+shall descend to the bottome: which was to be demonstrated. In
+consequence of this that hath been demonstrated, sundry and various
+Conclusions may be gathered, by which the truth of my principall
+Proposition comes to be more and more confirmed, and the imperfection
+of all former Argumentations touching the present Question cometh to
+be discovered.</p>
+
+<p><i>And first we gather from the things demonstrated, that,</i></p>
+<p><span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span></p>
+
+
+<h2><a name="THEOREME_VII" id="THEOREME_VII"></a>THEOREME VII.</h2>
+
+<div class="sidenote">The heaviest Bodies may swimme.</div>
+
+<p class="def_head"><i>All Matters, how heavy soever, even to Gold it self, the heaviest
+of all Bodies, known by us, may float upon the Water.</i></p>
+
+
+<p class="cap">Because its Gravity being considered to be almost twenty times greater
+than that of the water, and, moreover, the greatest Altitude that the
+Rampart of water can be extended to, without breaking the Contiguity
+of the Air, adherent to the Surface of the Solid, that is put upon the
+water being predetermined, if we should make a Plate of Gold so thin,
+that it exceeds not the nineteenth part of the Altitude of the said
+Rampart, this put lightly upon the water shall rest, without going to
+the bottom: and if Ebony shall chance to be in sesquiseptimall
+proportion more grave than the water, the greatest thickness that can
+be allowed to a Board of Ebony, so that it may be able to stay above
+water without sinking, would be seaven times more than the height of
+the Rampart Tinn, <i>v. gr.</i> eight times more grave than water, shall
+swimm as oft as the thickness of its Plate, exceeds not the 7th part
+of the Altitude of the Rampart.</p>
+
+<div class="sidenote"><i>He elsewhere cites this as a Proposition, therefore I
+make it of that number.</i></div>
+
+<p>And here I will not omit to note, as a second Corrollary dependent
+upon the things demonstrated, that,</p>
+
+
+
+<h2><a name="THEOREME_VIII" id="THEOREME_VIII"></a>THEOREME VIII.</h2>
+
+<div class="sidenote">Natation and Submersion, collected from the thickness,
+excluding the length and breadth of Plates.</div>
+
+<p class="def_head"><i>The Expansion of Figure not only is not the Cause of the Natation
+of those grave Bodies, which otherwise do submerge, but also the
+determining what be those Boards of Ebony, or Plates of Iron or
+Gold that will swimme, depends not on it, rather that same
+determination is to be collected from the only thickness of those
+Figures of Ebony or Gold, wholly excluding the consideration of
+length and breadth, as having no wayes any share in this Effect.</i></p>
+
+
+<p class="cap">It hath already been manifested, that the only cause of the Natation
+of the said Plates, is the reduction of them to be less grave than the
+water, by means of the connexion of that Air, which descendeth
+together with them, and possesseth place in the water; which place so
+occupyed, if before the circumfused water diffuseth it self to fill
+it, it be capable of as much water, as shall weigh equall with the
+Plate, the Plate shall remain suspended, and sinke no farther.</p>
+<p><span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span></p>
+
+<p>Now let us see on which of these three dimensions of the Solid
+depends the terminating, what and how much the Mass of that ought to
+be, that so the assistance of the Air contiguous unto it, may suffice
+to render it specifically less grave than the water, whereupon it may
+rest without Submersion. It shall undoubtedly be found, that the
+length and breadth have not any thing to do in the said determination,
+but only the height, or if you will the thickness: for, if we take a
+Plate or Board, as for Example, of Ebony, whose Altitude hath unto the
+greatest possible Altitude of the Rampart, the proportion above
+declared, for which cause it swims indeed, but yet not if we never so
+little increase its thickness; I say, that retaining its thickness,
+and encreasing its Superficies to twice, four times, or ten times its
+bigness, <a name="tnd_49" id="tnd_49"></a><a href="#tn_49" class="tnlink" title="missing letter i, dminishing for diminishing">or dminishing it by dividing</a> it into four, or six, or twenty,
+or a hundred parts, it shall still in the same manner continue to
+float: but encreasing its thickness only a Hairs breadth, it will
+alwaies submerge, although we should multiply the Superficies a
+hundred and a hundred times. Now forasmuch as that this is a Cause,
+which being added, we adde also the Effect, and being removed, it is
+removed; and by augmenting or lessening the length or breadth in any
+manner, the effect of going, or not going to the bottom, is not added
+or removed: I conclude, that the greatness and smalness of the
+Superficies hath no influence upon the Natation or Submersion. And
+that the proportion of the Altitude of the Ramparts of Water, to the
+Altitude of the Solid, being constituted in the manner aforesaid, the
+greatness or smalness of the Superficies, makes not any variation, is
+manifest from that which hath been above demonstrated, and from this,
+that, <i>The Prisms and Cylinders which have the same Base, are in
+proportion to one another as their heights.</i> Whence Cylinders or
+Prismes, namely, the Board, be they great or little, so that they be
+<span class="sidenote">Prismes and Cylinders having the same Base, are to one
+another as their heights.</span>
+all of equall thickness, have the same proportion to their
+Conterminall Air, which hath for Base the said Superficies of the
+Board, and for height the Ramparts of water; so that alwayes of that
+Air, and of the Board, Solids, are compounded, that in Gravity equall
+a Mass of water equall to the Mass of the Solids, compounded of Air,
+and of the Board: whereupon all the said Solids do in the same manner
+continue afloat. We will conclude in the third place, that,</p>
+<p><span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span></p>
+
+
+
+<h2><a name="THEOREME_IX" id="THEOREME_IX"></a>THEOREME. IX.</h2>
+
+<div class="sidenote">All Figures of all Matters, <a name="tnd_50" id="tnd_50"></a><a href="#tn_50" class="tnlink" title="printer's error, missing letter l, hep for help">float by hep of</a> the
+Rampart replenished with Air, and some but only touch the water.</div>
+
+<p class="def_head"><i>All sorts of Figures of whatsoever Matter, albeit more grave than
+the Water, do by Benefit of the said Rampart, not only float, but
+some Figures, though of the gravest Matter, do stay wholly above
+Water, wetting only the inferiour Surface that toucheth the
+Water.</i></p>
+
+
+<p class="cap">And these shall be all Figures, which from the inferiour Base upwards,
+grow lesser and lesser; the which we shall exemplifie for this time in
+Piramides or Cones, of which Figures the passions are common. We will
+demonstrate therefore, that,</p>
+
+<p><i>It is possible to form a Piramide, of any whatsoever Matter
+preposed, which being put with its Base upon the Water, rests not
+only without submerging, but without wetting it more then its
+Base.</i></p>
+
+<p>For the explication of which it is requisite, that we first
+demonstrate the subsequent Lemma, namely, that,</p>
+
+
+
+
+<h2><a name="LEMMA_II" id="LEMMA_II"></a>LEMMA II.</h2>
+
+<div class="sidenote">Solids whose Masses are in contrary proportion to
+their Specifick Gravities are equall in absolute Gravity.</div>
+
+<p class="def_head"><i>Solids whose Masses answer in proportion contrarily to their
+Specificall Gravities, are equall in Absolute Gravities.</i></p>
+
+
+<p class="cap">Let A C and B be two Solids, and let the Mass A C be to the Mass B,
+as the Specificall Gravity of the Solid B, is to the Specificall
+Gravity of the Solid A C: I say, the Solids A C and B are equall in
+<span class="figleft" style="width: 156px;">
+<img src="images/i052.png" width="156" height="103" alt="" title="" />
+</span>
+absolute weight, that is, equally grave. For if the Mass A C be equall
+to the Mass B, then, by the Assumption, the Specificall Gravity of B,
+shall be equall to the Specificall Gravity of A C, and being equall in
+Mass, and of the same Specificall Gravity they shall absolutely weigh
+one as much as another. But if their Masses shall be unequall, let the
+Mass A C be greater, and in it take the part C, equall to the Mass B.
+And, because the Masses B and C are equall; the Absolute weight of B,
+shall have the same proportion to the Absolute weight of C, that the
+Specificall Gravity of B, hath to the Specificall Gravity of C; or of
+C A, which is the same <i>in specie</i>: But look what proportion the
+Specificall Gravity of B, hath to the Specificall Gravity of C A, the
+like proportion, by the Assumption, hath the Mass C A, to the Mass B,
+<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>
+that is, to the Mass C: Therefore, the absolute weight of B, to the
+absolute weight of C, is as the Mass A C to the Mass C: But as the
+Mass A C, is to the Mass C, so is the absolute weight of A C, to the
+absolute weight of C: Therefore the absolute weight of B, hath the
+same proportion to the absolute weight of C, that the absolute weight
+of A C, hath to the absolute weight of C: Therefore, the two Solids A
+C and B are equall in absolute Gravity: which was to be demonstrated.
+Having demonstrated this, I say,</p>
+
+
+
+
+<h2><a name="THEOREME_X" id="THEOREME_X"></a>THEOREME X.</h2>
+
+<div class="sidenote">There may be Cones and Piramides of any Matter, which
+demitted into the water, rest only their Bases.</div>
+
+<p class="def_head"><i>That it is possible of any assigned Matter, to form a Piramide or
+Cone upon any Base, which being put upon the Water shall not
+submerge, nor wet any more than its Base.</i></p>
+
+
+<p class="cap">Let the greatest possible Altitude of the Rampart be the Line D B,
+and the Diameter of the Base of the Cone to be made of any Matter
+assigned B C, at right angles to D B: And as the Specificall Gravity
+<span class="figright" style="width: 173px;">
+<img src="images/i053.png" width="173" height="213" alt="" title="" />
+</span>
+of the Matter of the Piramide or Cone to be made, is to the
+Specificall Gravity of the water, so let the Altitude of the Rampart D
+B, be to the third part of the Piramide or Cone A B C, described upon
+the Base, whose Diameter is B C: I say, that the said Cone A B C, and
+any other Cone, lower then the same, shall rest upon the Surface of
+the water B C without sinking. Draw D F parallel to B C, and suppose
+the Prisme or Cylinder E C, which shall be tripple to the Cone A B C.
+And, because the Cylinder D C hath the same proportion to the Cylinder
+C E, that the Altitude D B, hath to the Altitude B E: But the Cylinder
+C E, is to the Cone A B C, as the Altitude E B is to the third part of
+the Altitude of the Cone: Therefore, by Equality of proportion, the
+Cylinder D C is to the Cone A B C, as D B is to the third part of the
+Altitude B E: But as D B is to the third part of B E, so is the
+Specificall Gravity of the Cone A B C, to the Specificall Gravity of
+the water: Therefore, as the Mass of the Solid D C, is to the Mass of
+the Cone A <i>B</i> C, so is the Specificall Gravity of the said Cone, to
+the Specificall Gravity of the water: Therefore, by the precedent
+Lemma, the Cone A B C weighs in absolute Gravity, as much as a Mass of
+Water equall to the Mass D C: But the water which by the imposition of
+the Cone A B C, is driven out of its place, is as much as would
+precisely lie in the place D C, and is equall in weight to the Cone
+that displaceth it: Therefore, there shall be an <i>Equilibrium</i>, and
+the Cone shall rest without farther submerging. And its manifest,</p>
+<p><span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span></p>
+
+<h3>COROLARY I.</h3>
+
+<div class="sidenote">Amongst Cones of the same Base, those of least
+Altitude shall sink the least.</div>
+
+<p class="cor_head"><i>That making upon the same Basis, a Cone of a less Altitude, it
+shall be also less grave, and shall so much the more rest without
+Submersion.</i></p>
+
+
+<h3>COROLARY II.</h3>
+
+<div class="sidenote">There may be Cones and Piramides of any Matter, which
+demitted with the Point downwards do float atop.</div>
+
+<p class="cor_head"><i>It is manifest, also, that one may make Cones and Piramids of any
+Matter whatsoever, more grave than the water, which being put
+into the water, with the Apix or Point downwards, rest without
+Submersion.</i></p>
+
+<p class="cap">Because if we reassume what hath been above demonstrated, of Prisms
+and Cylinders, and that on Bases equall to those of the said
+Cylinders, we make Cones of the same Matter, and three times as high
+as the Cylinders, they shall rest afloat, for that in Mass and Gravity
+they shall be equall to those Cylinders, and by having their Bases
+equall to those of the Cylinders, they shall leave equall Masses of
+Air included within the Ramparts. This, which for Example sake hath
+been demonstrated, in Prisms, Cylinders, Cones and Piramids, might be
+proved in all other Solid Figures, but it would require a whole Volume
+(such is the multitude and variety of their Symptoms and Accidents) to
+comprehend the particuler demonstration of them all, and of their
+severall Segments: but I will to avoid prolixity in the present
+Discourse, content my self, that by what I have declared every one of
+ordinary Capacity may comprehend, that there is not any Matter so
+grave, no not Gold it self, of which one may not form all sorts of
+Figures, which by vertue of the superiour Air adherent to them, and
+not by the Waters Resistance of Penetration, do remain afloat, so that
+they sink not. Nay, farther, I will shew, for removing that Error,
+that,</p>
+
+
+
+
+<h2><a name="THEOREME_XI" id="THEOREME_XI"></a>THEOREME XI.</h2>
+
+<div class="sidenote">A Piramide or Cone, demitted with the Point downwards
+shal swim, with its Base downward shall sink.</div>
+
+<p class="def_head"><i>A Piramide or Cone put into the Water, with the Point downward
+shall swimme, and the same put with the Base downwards shall
+sinke, and it shall be impossible to make it float.</i></p>
+
+
+<p class="cap">Now the quite contrary would happen, if the difficulty of Penetrating
+the water, were that which had hindred the descent, for that the said
+Cone is far apter to pierce and penetrate with its sharp Point, than
+with its broad and spacious Base.</p>
+
+<p>And, to demonstrate this, let the Cone be <i>A B C</i>, twice as grave as
+the water, and let its height be tripple to the height of the Rampart
+<i>D A E C</i>: I say, first, that being put lightly into the water with
+<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>
+<span class="figright" style="width: 173px;">
+<img src="images/i055a.png" width="173" height="98" alt="" title="" />
+</span>
+the Point downwards, it shall not descend to the bottom: for the
+Aeriall Cylinder contained betwixt the Ramparts <i>D A C E</i>, is equall
+in Mass to the Cone <i>A B C</i>; so that the whole Mass of the Solid
+compounded of the Air <i>D A C E</i>, and of the Cone <i>A B C</i>, shall be
+double to the Cone <i>A C B</i>: And, because the Cone <i>A B C</i> is supposed
+to be of Matter double in Gravity to the water, therefore as much
+water as the whole Masse <i>D A B C E</i>, placed beneath the Levell of the
+water, weighs as much as the Cone <i>A B C</i>: and, therefore, there shall
+be an <i>Equilibrium</i>, and the Cone <i>A B C</i> shall descend no lower. Now,
+I say farther, that the same Cone placed with the Base downwards,
+shall sink to the bottom, without any possibility of returning again,
+by any means to swimme.</p>
+
+<p>Let, therefore, the Cone be <i>A B D</i>, double in Gravity to the water,
+<span class="figright" style="width: 164px;">
+<img src="images/i055b.png" width="164" height="203" alt="" title="" />
+</span>
+and let its height be tripple the height of the Rampart of water L B:
+It is already manifest, that it shall not stay wholly out of the
+water, because the Cylinder being comprehended betwixt the Ramparts <i>L
+B D P</i>, equall to the Cone <i>A B D</i>, and the Matter of the Cone, <a name="tnd_53" id="tnd_53"></a><a href="#tn_53" class="tnlink" title="printer's error, missing letter n, beig for being">beig
+double in Gravity</a> to the water, it is evident that the weight of the
+said Cone shall be double to the weight of the Mass of water equall to
+the Cylinder <i>L B D P</i>: Therefore it shall not rest in this state, but
+shall descend.</p>
+
+
+<h3>COROLARY I.</h3>
+
+<div class="sidenote">Much less shall the said Cone swim, if one immerge a
+part thereof.</div>
+
+<p class="cor_head"><i>I say farther; that much lesse shall the said Cone stay afloat, if
+one immerge a part thereof.</i></p>
+
+<p class="cap">Which you may see, comparing with the water as well the part that
+shall immerge as the other above water. Let us therefore of the Cone A
+B D, submergeth part N T O S, and advance the Point N S F above water.
+The Altitude of the Cone F N S, shall either be more than half the
+whole Altitude of the Cone F T O, or it shall not be more: if it shall
+be more than half, the Cone F N S shall be more than half of the
+Cylinder E N S C: for the Altitude of the Cone F N S, shall be more
+than Sesquialter of the Altitude of the Cylinder E N S C: And, because
+the Matter of the Cone is supposed to be double in Specificall Gravity
+to the water, the water which would be contained within the Rampart E
+N S C, would be less grave absolutely than the Cone F N S; so that the
+whole Cone F N S cannot be sustained by the Rampart: But the part
+immerged N T O S, by being double in Specificall Gravity to the water,
+shall tend to the bottom: Therefore, the whole <i>C</i>one F T O, as well
+in respect of the part submerged, as the part above water shall
+<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span>
+descend to the bottom. But if the Altitude of the Point F N S, shall
+be half the Altitude of the whole Cone F T O, the same Altitude of the
+said Cone F N S shall be Sesquialter to the Altitude E N: and,
+therefore, E N S C shall be double to the Cone F N S; and as much
+water in Mass as the <i>C</i>ylinder E N S C, would weigh as much as the
+part of the <i>C</i>one F N S. But, because the other immerged part N T O
+S, is double in Gravity to the water, a Mass of water equall to that
+compounded of the <i>C</i>ylinder E N S C, and of the Solid N T O S, shall
+weigh less than the <i>C</i>one F T O, by as much as the weight of a Mass
+of water equall to the Solid N T O S: Therefore, the <i>C</i>one <a name="tnd_54" id="tnd_54"></a><a href="#tn_54" class="tnlink" title="printer's error, missing letter l">sha{l}l
+also descend.</a> Again, because the Solid N T O S, is septuple to the
+Cone F N S, to which the <i>C</i>ylinder E S is double, the proportion of
+the Solid N T O S, shall be to the <i>C</i>ylinder E N S C, as seaven to
+two: Therefore, the whole Solid compounded of the <i>C</i>ylinder E N S C,
+and of the Solid N T O S, is much less than double the Solid N T O S:
+Therefore, the single Solid N T O S, is much graver than a Mass of
+water equall to the Mass, compounded of the <i>C</i>ylinder E N S C, and of
+N T O S.</p>
+
+
+<h3>COROLARY II.</h3>
+
+<div class="sidenote">Part of the Cones towards the Cuspis removed, it shall
+still sink.</div>
+
+<p class="cor_head"><i>From whence it followeth, that though one should remove and take
+away the part of the Cone F N S, the sole remainder N T O S would
+go to the bottom.</i></p>
+
+
+<h3>COROLARY III.</h3>
+
+<div class="sidenote">The more the Cone is immerged, the more impossible is
+its floating.</div>
+
+<p class="cor_head"><i>And if we should more depress the Cone F T O, it would be so much
+the more impossible that it should sustain it self afloat, the
+part submerged N T O S still encreasing, and the Mass of Air
+contained in the Rampart diminishing, which ever grows less, the
+more the Cone submergeth.</i></p>
+
+<p class="cap">That Cone, therefore, that with its Base upwards, and its <i>Cuspis</i>
+downwards doth swimme, being dimitted with its Base downward must of
+necessity sinke. They have argued farre from the truth, therefore, who
+have ascribed the cause of Natation to waters resistance of Division,
+as to a passive principle, and to the breadth of the Figure, with
+which the division is to be made, as the Efficient.</p>
+
+<p>I come in the fourth place, to collect and conclude the reason of
+that which I have proposed to the Adversaries, namely,</p>
+<p><span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span></p>
+
+
+
+<h2><a name="THEOREME_XII" id="THEOREME_XII"></a>THEOREME XII.</h2>
+
+<div class="sidenote">Solids of any Figure &amp; greatnesse, that naturally
+sink, may by help of the Air in the Rampart swimme.</div>
+
+<p class="def_head"><i>That it is possible <a name="tnd_55" id="tnd_55"></a><a href="#tn_55" class="tnlink" title="printer's error, missing letter r">to fo{r}m Solid Bodies,</a> of what Figure and
+greatness soever, that of their own Nature goe to the Bottome;
+But by the help of the Air contained in the Rampart, rest without
+submerging.</i></p>
+
+
+<p class="cap">The truth of this Proposition is sufficiently manifest in all those
+Solid Figures, that determine in their uppermost part in a plane
+Superficies: for making such Figures of some Matter specifically as
+grave as the water, putting them into the water, so that the whole
+Mass be covered, it is manifest, that they shall rest in all places,
+provided, that such a Matter equall in weight to the water, may be
+exactly adjusted: and they shall by consequence, rest or lie even with
+the Levell of the water, without making any Rampart. If, therefore, in
+respect of the Matter, such Figures are apt to rest without
+submerging, though deprived of the help of the Rampart, it is
+manifest, that they may admit so much encrease of Gravity, (without
+encreasing their Masses) as is the weight of as much water as would be
+contained within the Rampart, that is made about their upper plane
+Surface: by the help of which being sustained, they shall rest afloat,
+but being bathed, they shall descend, having been made graver than the
+water. In Figures, therefore, that determine above in a plane, we may
+cleerly comprehend, that the Rampart added or removed, may prohibit or
+permit the descent: but in those Figures that go lessening upwards
+towards the top, some Persons may, and that not without much seeming
+Reason, doubt whether the same may be done, and especially by those
+which terminate in a very acute Point, such as are your Cones and
+small Piramids. Touching these, therefore, as more dubious than the
+rest, I will endeavour to demonstrate, that they also lie under the
+same Accident of going, or not going to the Bottom, be they of any
+whatever bigness. Let therefore the Cone be A B D, made of a matter
+<span class="figright" style="width: 187px;">
+<img src="images/i057.png" width="187" height="231" alt="" title="" />
+</span>
+specifically as grave as the water; it is manifest that being put all
+under water, it shall rest in all places (alwayes provided, that it
+shall weigh exactly as much as the water, which is almost impossible
+to effect) and that any small weight being added to it, it shall sink
+to the bottom: but if it shall descend downwards gently, I say, that
+it shall make the Rampart E S T O, and that there shall stay out of
+the water the point A S T, tripple in height to the Rampart E S: which
+<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span>
+is manifest, for the Matter of the Cone weighing equally with the
+water, the part submerged <i>S B D T</i>, becomes indifferent to move
+downwards or upwards; and the Cone <i>A S T</i>, being equall in Mass to
+the water that would be contained in the concave of the Rampart <i>E S T
+O</i>, shall be also equall unto it in Gravity: and, therefore, there
+shall be a perfect <i>Equilibrium</i>, and, consequently, a Rest. Now here
+ariseth a doubt, whether the Cone <i>A B D</i> may be made heavier, in such
+sort, that when it is put wholly under water, it goes to the bottom,
+but yet not in such sort, as to take from the Rampart the vertue of
+sustaining it that it sink not, and, the reason of the doubt is this:
+that although at such time as the Cone <i>A B D</i> is specifically as
+grave as the water, the Rampart <i>E S T O</i> sustaines it, not only when
+the point <i>A S T</i> is tripple in height to the Altitude of the Rampart
+<i>E S</i>, but also when a lesser part is above water; [for although in
+the Descent of the Cone the Point <i>A S T</i> by little and little
+<span class="figleft" style="width: 191px;">
+<img src="images/i058.png" width="191" height="227" alt="" title="" />
+</span>
+diminisheth, and so likewise the Rampart <i>E S T O</i>, yet the Point
+diminisheth in greater proportion than the Rampart, in that it
+diminisheth according to all the three Dimensions, but the Rampart
+according to two only, the Altitude still remaining the same; or, if
+you will, because the <a name="tnd_56" id="tnd_56"></a><a href="#tn_56" class="tnlink" title="printer's error, missing letter A">Cone <i>S {A} T</i></a> goes diminishing, according to
+the proportion of the cubes of the Lines that do successively become
+the Diameters of the Bases of emergent Cones, and the Ramparts
+diminish according to the proportion of the Squares of the same Lines;
+whereupon the proportions of the Points are alwayes Sesquialter of the
+proportions of the Cylinders, contained within the Rampart; so that
+if, for Example, the height of the emergent Point were double, or
+equall to the height of the Rampart, in these cases, the Cylinder
+contained within the Rampart, would be much greater than the said
+Point, because it would be either sesquialter or tripple, by reason of
+which it would perhaps serve over and above to sustain the whole Cone,
+since the part submerged would no longer weigh any thing;] yet,
+nevertheless, when any Gravity is added to the whole Mass of the Cone,
+so that also the part submerged is not without some excesse of Gravity
+above the Gravity of the water, it is not manifest, whether the
+Cylinder contained within the Rampart, in the descent that the Cone
+shall make, can be reduced to such a proportion unto the emergent
+Point, and to such an excesse of Mass above the Mass of it, as to
+compensate the excesse of the Cones Specificall Gravity above the
+Gravity of the water: and the Scruple ariseth, because that howbeit in
+the descent made by the Cone, the emergent Point <i>A S T</i> diminisheth,
+whereby there is also a diminution of the excess of the Cones Gravity
+<span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span>
+above the Gravity of the water, yet the case stands so, that the
+Rampart doth also contract it self, and the Cylinder contained in it
+doth deminish. Nevertheless it shall be demonstrated, how that the
+Cone <i>A B D</i> being of any supposed bignesse, and made at the first of
+a Matter exactly equall in Gravity to the Water, if there may be
+affixed to it some Weight, by means <a name="tnd_57" id="tnd_57"></a><a href="#tn_57" class="tnlink" title="printer's error, missing letter t">of which i{t} may descend</a> to the
+bottom, when submerged under water, it may also by vertue of the
+Rampart stay above without sinking.</p>
+
+<p>Let, therefore, the Cone <i>A B D</i> be of any supposed greatnesse, and
+alike in specificall Gravity to the water. It is manifest, that being
+put lightly into the water, it shall rest without descending; and it
+<span class="figright" style="width: 189px;">
+<img src="images/i059.png" width="189" height="226" alt="" title="" />
+</span>
+shall advance above water, the Point <i>A S T</i>, tripple in height to the
+height of the Rampart <i>E S</i>: Now, suppose the Cone <i>A B D</i> more
+depressed, so that it advance above water, only the Point <i>A I R</i>,
+higher by half than the Point <i>A S T</i>, with the Rampart about it <i>C I
+R N</i>. And, because, the Cone <i>A B D</i> is to the Cone <i>A I R</i>, as the
+cube of the Line <i>S T</i> is to the cube of the Line <i>I R</i>, but the
+Cylinder <i>E S T O</i>, is to the Cylinder <i>C I R N</i>, as the Square of <i>S
+T</i> to the Square of <i>I R</i>, the Cone <i>A S T</i> shall be Octuple to the
+Cone <i>A I R</i>, and the Cylinder <i>E S T O</i>, quadruple to the Cylinder <i>C
+I R N</i>: But the Cone <i>A S T</i>, is equall to the Cylinder <i>E S T O</i>:
+Therefore, the Cylinder <i>C I R N</i>, shall be double to the Cone <i>A I
+R</i>: and the water which might be contained in the Rampart <i>C I R N</i>,
+would be double in Mass and in Weight to the Cone <i>A I R</i>, and,
+therefore, would be able to sustain the double of the Weight of the
+Cone <i>A I R</i>: Therefore, if to the whole Cone <i>A B D</i>, there be added
+as much Weight as the Gravity of the Cone <i>A I R</i>, that is to say, the
+eighth part of the weight of the Cone <i>A S T</i>, it also shall be
+sustained by the Rampart <i>C I R N</i>, but without that it shall go to
+the bottome: the Cone <i>A B D</i>, being, by the addition of the eighth
+part of the weight of the Cone <i>A S T</i>, made specifically more grave
+than the water. But if the Altitude of the Cone <i>A I R</i>, were two
+thirds of the Altitude of the Cone <i>A S T</i>, the Cone <i>A S T</i> would be
+to the Cone <i>A I R</i>, as twenty seven to eight; and the Cylinder <i>E S T
+O</i>, to the Cylinder <i>C I R N</i>, as nine to four, that is, as twenty
+seven to twelve; and, therefore, the Cylinder <i>C I R N</i>, to the Cone
+<i>A I R</i>, as twelve to eight; and the excess of the Cylinder <i>C I R N</i>,
+above the Cone <i>A I R</i>, to the Cone <i>A S T</i>, as four to twenty seven:
+therefore if to the Cone <i>A B D</i> be added so much weight as is the
+four twenty sevenths of the weight of the Cone <i>A S T</i>, which is a
+little more then its seventh part, it also shall continue to swimme,
+<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span>
+and the height of the emergent Point shall be double to the height of
+the Rampart. This that hath been demonstrated in Cones, exactly holds
+in Piramides, although the one or the other should be very sharp in
+their Point or Cuspis: From whence we conclude, that the same Accident
+<span class="sidenote"><a name="tnd_58" id="tnd_58"></a><a href="#tn_58" class="tnlink" title="printer's error, inverted n">Natatio{n} easiest effected</a> in Figures broad toward
+the top.</span>
+shall so much the more easily happen in all other Figures, by how much
+the less sharp the Tops shall be, in which they determine, being
+assisted by more spacious Ramparts.</p>
+
+
+
+
+<h2><a name="THEOREME_XIII" id="THEOREME_XIII"></a>THEOREME XIII.</h2>
+
+<div class="sidenote">All Figures sink or swim, upon bathing or not bathing
+of their tops.</div>
+
+<p class="def_head"><i>All Figures, therefore, of whatever greatnesse, may go, and not
+go, to the Bottom, according as their Sumities or Tops shall be
+bathed or not bathed.</i></p>
+
+
+<p class="cap">And this Accident being common to all sorts of Figures, without
+exception of so much as one. Figure hath, therefore, no part in the
+production of this Effect, of sometimes sinking, and sometimes again
+not sinking, but only the being sometimes conjoyned to, and sometimes
+seperated from, the supereminent Air: which cause, in fine, who so
+shall rightly, and, as we say, with both his Eyes, consider this
+business, will find that it is reduced to, yea, that it really is the
+same with, the true, Naturall and primary cause of Natation or
+Submersion; to wit, the excess or deficiency of the Gravity of the
+water, in relation to the Gravity of that Solid Magnitude, that is
+demitted into the water. For like as a Plate of Lead, as thick as the
+back of a Knife, which being put into the water by it self alone goes
+to the bottom, if upon it you fasten a piece of Cork four fingers
+thick, doth continue afloat, for that now the Solid that is demitted
+in the water, is not, as before, more grave than the water, but less,
+so the Board of Ebony, of its own nature more grave than water; and,
+therefore, descending to the bottom, when it is demitted by it self
+alone into the water, if it shall be put upon the water, conjoyned
+with an Expanded vail of Air, that together with the Ebony doth
+descend, and that it be such, as that it doth make with it a compound
+less grave than so much water in Mass, as equalleth the Mass already
+submerged and depressed beneath the Levell of the waters Surface, it
+shall not descend any farther, but shall rest, for no other than the
+universall and most common cause, which is that Solid Magnitudes, less
+grave <i>in specie</i> than the water, go not to the bottom.</p>
+
+<p>So that if one should take a Plate of Lead, as for Example, a finger
+thick, and an handfull broad every way, and should attempt to make it
+swimme, with putting it lightly on the water, he would lose his
+Labour, because that if it should be depressed an Hairs breadth beyond
+<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span>
+the possible Altitude of the Ramparts of water, it would dive and
+sink; but if whilst it is going downwards, one should make certain
+Banks or Ramparts about it, that should hinder the defusion of the
+water upon the said Plate, the which Banks should rise so high, as
+that they might be able to contain as much water, as should weigh
+equally with the said Plate, it would, <a name="tnd_59a" id="tnd_59a"></a><a href="#tn_59a" class="tnlink" title="missing letter u">witho{u}t all Question,</a> descend
+no lower, but would rest, as being sustained by vertue of the Air
+contained within the aforesaid Ramparts: and, in short, there would be
+a Vessell by this means formed with the bottom of Lead. But if the
+thinness of the Lead shall be such, that a very small height of
+Rampart would suffice to contain so much Air, as might keep it afloat,
+it shall also rest without the Artificiall Banks or Ramparts, but yet
+not without the Air, because the Air by it self makes Banks sufficient
+for a small height, to resist the Superfusion of the water: so that
+that which in this case swimmes, is as it were a Vessell filled with
+Air, by vertue of which it continueth afloat.</p>
+
+<p>I will, in the last place, <a name="tnd_59b" id="tnd_59b"></a><a href="#tn_59b" class="tnlink" title="printer's error, inverted n">with an other Experime{n}t,</a> attempt to
+remove all difficulties, if so be there should yet be any doubt left
+in any one, touching the opperation of this *Continuity of the Air,
+<span class="sidenote"><a name="tnd_59c" id="tnd_59c"></a><a href="#tn_59c" class="tnlink" title="potential printer's error, sidenote ends with comma,">* Or rather Contiguity,</a></span>
+with the thin Plate which swims, and afterwards put an end to this
+part of my discourse.</p>
+
+<p>I suppose my self to be questioning with some of my Oponents.</p>
+
+<p>Whether Figure have any influence upon the encrease or diminution of
+the Resistance in any Weight against its being raised in the Air; and
+<span class="sidenote">An Experiment of the operation of Figures, in
+encreasing or lessening of the Airs Resistance of Division.</span>
+I suppose, that I am to maintain the Affirmative, asserting that a
+Mass of Lead, reduced to the Figure of a Ball, shall be raised with
+less force, then if the same had been made into a thinne and broad
+Plate, because that it in this spacious Figure, hath a great quantity
+of Air to penetrate, and in that other, more compacted and contracted
+very little: and to demonstrate the truth of such my Opinion, I will
+hang in a small thred first the Ball or Bullet, and put that into the
+water, tying the thred that upholds it to one end of the Ballance that
+I hold in the Air, and to the other end I by degrees adde so much
+Weight, till that at last it brings up the Ball of Lead out of the
+water: to do which, suppose a Gravity of thirty Ounces sufficeth; I
+afterwards reduce the said Lead into a flat and thinne Plate, the
+which I likewise put into the water, suspended by three threds, which
+hold it parallel to the Surface of the water, and putting in the same
+manner, Weights to the other end, till such time as the Plate comes to
+be raised and drawn out of the water: I finde that thirty six ounces
+will not suffice to seperate it from the water, and raise it thorow
+the Air: and arguing from this Experiment, I affirm, that I have fully
+demonstrated the truth of my Proposition. Here my Oponents desires me
+<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span>
+to look down, shewing me a thing which I had not before observed, to
+wit, that in the Ascent of the Plate out of the water, it draws after
+it another Plate (<i>if I may so call it</i>) of water, which before it
+divides and parts from the inferiour Surface of the Plate of Lead, is
+raised above the Levell of the other water, more than the thickness of
+the back of a Knife: Then he goeth to repeat the Experiment with the
+Ball, and makes me see, that it is but a very small quantity of water,
+which cleaves to its compacted and contracted Figure: and then he
+subjoynes, that its no wonder, if in seperating the thinne and broad
+Plate from the water, we meet with much greater Resistance, than in
+seperating the Ball, since together with the Plate, we are to raise a
+great quantity of water, which occurreth not in the Ball: He telleth
+me moreover, how that our Question is, whether the Resistance of
+Elevation be greater in a dilated Plate of Lead, than in a Ball, and
+not whether more resisteth a Plate of Lead with a great quantity of
+water, or a Ball with a very little water: He sheweth me in the close,
+that the putting the Plate and the Ball first into the water, to make
+proofe thereby of their Resistance in the Air, is besides our case,
+which treats of Elivating in the Air, and of things placed in the Air,
+and not of the Resistance that is made in the Confines of the Air and
+water, and by things which are part in Air and part in water: and
+lastly, they make me feel with my hand, that when the thinne Plate is
+in the Air, and free from the weight of the water, it is raised with
+the very same Force that raiseth the Ball. Seeing, and understanding
+these things, I know not what to do, unless to grant my self
+convinced, and to thank such a Friend, for having made me to see that
+which I never till then observed: and, being advertised by this same
+Accident, to tell my Adversaries, that our Question is, whether a
+Board and a Ball of Ebony, equally go to the bottom in water, and not
+a Ball of Ebony and a Board of Ebony, joyned with another flat Body of
+Air: and, farthermore, that we speak of sinking, and not sinking to
+the bottom, in water, and not of that which happeneth in the Confines
+of the water and Air to Bodies that be part in the Air, and part in
+the water; nor much less do we treat of the greater or lesser Force
+requisite in seperating this or that Body from the Air; not omitting
+to tell them, in the last place, that the Air doth resist, and
+gravitate downwards in the water, just so much as the water (if I may
+so speak) gravitates and resists upwards in the Air, and that the same
+Force is required to sinke a Bladder under water, that is full of Air,
+as to raise it in the Air, being full of water, removing the
+consideration of the weight of that Filme or Skinne, and considering
+the water and the Air only. And it is likewise true, that the same
+Force is required to sink a Cup or such like Vessell under water,
+whilst it is full of Air, as to raise it above the Superficies of the
+<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span>
+water, keeping it with the mouth downwards; whilst it is full of
+water, which is constrained in the same manner to follow the Cup which
+contains it, and to rise above the other water into the Region of the
+Air, as the Air is forced to follow the same Vessell under the Surface
+of the water, till <a name="tnd_61" id="tnd_61"></a><a href="#tn_61" class="tnlink" title="missing letter a">that in this c{a}se the water,</a> surmounting the
+brimme of the Cup, breaks in, driving thence the Air, and in that
+case, the said brimme coming out of the water, and arriving to the
+Confines of the Air, the water falls down, and the Air sub-enters to
+fill the cavity of the Cup: upon which ensues, that he no less
+transgresses the Articles of the <i>Convention</i>, who produceth a Plate
+conjoyned with much Air, to see if it descend to the bottom in water,
+then he that makes proof of the Resistance against Elevation in Air
+with a Plate of Lead, joyned with a like quantity of water.</p>
+
+<div class="sidenote"><i>Aristotles</i> opinion touching the Operation of Figure
+examined.</div>
+
+<p>I have said all that I could at present think of, to maintain the
+Assertion I have undertook. It remains, that I examine that which
+<i>Aristotle</i> hath writ of this matter towards the end of his Book De
+Cælo; wherein I shall note two things: the one that it being true as
+<span class="sidenote"><i>Aristot. de Cælo</i> Lib. 4. Cap 6.</span>
+
+hath been demonstrated, that Figure hath nothing to do about the
+moving or not moving it self upwards or downwards, its seemes that
+<i>Aristotle</i> at his first falling upon this Speculation, was of the
+same opinion, as in my opinion may be collected from the examination
+of his words. 'Tis true, indeed, that in essaying afterwards to render
+a reason of such effect, as not having in my conceit hit upon the
+right, (which in the second place I will examine) it seems that he is
+brought to admit the largenesse of Figure, to be interessed in this
+operation. As to the first particuler, hear the precise words of
+<i>Aristotle</i>.</p>
+
+
+<p><i>Figures are not the Causes of moving simply upwards or downwards, but
+of moving more slowly or swiftly, and by what means this comes to
+<span class="sidenote"><i>Aristotle</i> makes not Figure the cause of Motion
+absolutely, but of swift or slow motion,</span>
+<span class="sidenote">Lib. 4. Cap. 6: Text. 42.</span>
+pass, it is not difficult to see.</i></p>
+
+<p>Here first I note, that the terms being four, which fall under the
+present consideration, namely, Motion, Rest, Slowly and Swiftly: And
+<i>Aristotle</i> naming figures as Causes of Tardity and Velocity,
+excluding them from being the Cause of absolute and simple Motion, it
+seems necessary, that he exclude them on the other side, from being
+the Cause of Rest, so that his meaning is this. Figures are not the
+Causes of moving or not moving absolutely, but of moving quickly or
+slowly: and, here, if any should say the mind of <i>Aristotle</i> is to
+exclude Figures from being Causes of Motion, but yet not from being
+Causes of Rest, so that the sence would be to remove from Figures,
+there being the Causes of moving simply, but yet not there being
+Causes of Rest, I would demand, whether we ought with <i>Aristotle</i> to
+understand, that all Figures universally, are, in some manner, the
+causes of Rest in those Bodies, which otherwise would move, or else
+some particular Figures only, as for Example, broad and thinne
+<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span>
+Figures: If all indifferently, then every Body shall rest: because
+every Body hath some Figure, which is false; but if some particular
+Figures only may be in some manner a Cause of Rest, as, for Example,
+the broad, then the others would be in some manner the Causes of
+Motion: for if from seeing some Bodies of a contracted Figure move,
+which after dilated into Plates rest, may be inferred, that the
+Amplitude of Figure hath a part in the Cause of that Rest; so from
+seeing such like Figures rest, which afterwards contracted move, it
+may with the same reason be affirmed, that the united and contracted
+Figure, hath a part in causing Motion, as the remover of that which
+impeded it: The which again is directly opposite to what <i>Aristotle</i>
+saith, namely, that Figures are not the Causes of Motion. Besides, if
+<i>Aristotle</i> had admitted and not excluded Figures from being Causes of
+not moving in some Bodies, which moulded into another Figure would
+move, he would have impertinently propounded in a dubitative manner,
+in the words immediately following, whence it is, that the large and
+thinne Plates of Lead or Iron, rest upon the water, since the Cause
+was apparent, namely, the Amplitude of Figure. Let us conclude,
+therefore, that the meaning of <i>Aristotle</i> in this place is to affirm,
+that Figures are not the Causes of absolutely moving or not moving,
+but only of moving swiftly or slowly: which we ought the rather to
+believe, in regard it is indeed a most true conceipt and opinion. Now
+the mind of <i>Aristotle</i> being such, and appearing by consequence,
+rather contrary at the first sight, then favourable to the assertion
+of the Oponents, it is necessary, that their Interpretation be not
+exactly the same with that, but such, as being in part understood by
+some of them, and in part by others, was set down: and it may easily
+be indeed so, being an Interpretation consonent to the sence of the
+more famous Interpretors, which is, that the Adverbe <i>Simply</i> or
+<i>Absolutely</i>, put in the Text, ought not to be joyned to the Verbe to
+<i>Move</i>, but with the Noun <i>Causes</i>: so that the purport of
+<i>Aristotles</i> words, is to affirm, That Figures are not the Causes
+absolutely of moving or not moving, but yet are Causes <i>Secundum
+quid</i>, <i>viz.</i> in some sort; by which means, they are called Auxiliary
+and Concomitant Causes: and this Proposition is received and asserted
+as true by <i>Signor Buonamico Lib. 5. Cap. 28.</i> where he thus writes.
+<i>There are other Causes concomitant, by which some things float, and
+others sink, among which the Figures of Bodies hath the first place</i>,
+&amp;c.</p>
+
+<p>Concerning this Proposition, I meet with many doubts and difficulties,
+for which me thinks the words of <i>Aristotle</i> are not capable of such a
+construction and sence, and the difficulties are these.</p>
+
+<p>First in the order and disposure of the words of <i>Aristotle</i>, the
+particle <i>Simpliciter</i>, or if you will <i>absoluté</i>, is conjoyned with
+<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span>
+the Verb <i>to move</i>, and seperated from the Noun <i>Causes</i>, the which is
+a great presumption in my favour, seeing that the writing and the Text
+saith, Figures are not the Cause of moving simply upwards or
+downwards, but of quicker or slower Motion: and, saith not, Figures
+are not simply the Causes of moving upwards or downwards, and when the
+words of a Text receive, transposed, a sence different from that which
+they sound, taken in the order wherein the Author disposeth them, it
+is not convenient to inverte them. And who will affirm that
+<i>Aristotle</i> desiring to write a Proposition, would dispose the words
+in such sort, that they should import a different, nay, a contrary
+sence? contrary, I say, because understood as they are written; they
+say, that Figures are not the Causes of Motion, but inverted, they
+say, that Figures are the Causes of Motion, &amp;c.</p>
+
+<p>Moreover, if the intent of <i>Aristotle</i> had been to say, that Figures
+are not simply the Causes of moving upwards or downwards, but only
+Causes <i>Secundum quid</i>, he would not have adjoyned those words, <i>but
+they are Causes of the more swift or slow Motion</i>; yea, the subjoining
+this would have been not only superfluous but false, for that the
+whole tenour of the Proposition would import thus much. Figures are
+not the absolute Causes of moving upwards or downwards, but are the
+absolute Cause of the swift or slow Motion; which is not true: because
+the primary Causes of greater or lesser Velocity, are by <i>Aristotle</i>
+in the 4th of his <i>Physicks</i>, <i>Text. 71.</i> attributed to the greater or
+lesser Gravity of Moveables, compared among themselves, and to the
+greater or lesser Resistance of the <i>Medium's</i>, depending on their
+greater or less Crassitude: and these are inserted by <i>Aristotle</i> as
+the primary Causes; and these two only are in that place nominated:
+and Figure comes afterwards to be considered, <i>Text. 74.</i> rather as an
+Instrumentall Cause of the force of the Gravity, the which divides
+either with the Figure, or with the <i>Impetus</i>; and, indeed, Figure by
+it self without the force of Gravity or Levity, would opperate
+nothing.</p>
+
+<p>I adde, that if <i>Aristotle</i> had an opinion that Figure had been in
+some sort the Cause of moving or not moving, the inquisition which he
+makes immediately in a doubtfull manner, whence it comes, that a Plate
+of Lead flotes, would have been impertinent; for if but just before he
+had said, that Figure was in a certain sort the Cause of moving or not
+moving, he needed not to call in Question, by what Cause the Plate of
+Lead swims, and then ascribing the Cause to its Figure; and framing a
+discourse in this manner. Figure is a Cause <i>Secundum quid</i> of not
+sinking: but, now, if it be doubted, for what Cause a thin Plate of
+Lead goes not to the bottom; it shall be answered, that that proceeds
+<span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span>
+from its Figure: a discourse which would be indecent in a Child, much
+more in <i>Aristotle</i>; For where is the occasion of doubting? And who
+sees not, that if <i>Aristotle</i> had held, that Figure was in some sort a
+Cause of Natation, he would without the least Hesitation have writ;
+That Figure is in a certain sort the Cause of Natation, and therefore
+the Plate of Lead in respect of its large and expatiated Figure swims;
+but if we take the proposition of <i>Aristotle</i> as I say, and as it is
+written, and as indeed it is true, the ensuing words come in very
+oppositely, as well in the introduction of swift and slow, as in the
+question, which very pertinently offers it self, and would say thus
+much.</p>
+
+<p>Figures are not the Cause of moving or not moving simply upwards or
+downwards, but of moving more quickly or slowly: But if it be so, the
+Cause is doubtfull, whence it proceeds, that a Plate of Lead or of
+Iron broad and thin doth swim, &amp;c. And the occasion of the doubt is
+obvious, because it seems at the first glance, that the Figure is the
+Cause of this Natation, since the same Lead, or a less quantity, but
+in another Figure, goes to the bottom, and we have already affirmed,
+that the Figure hath no share in this effect.</p>
+
+<p>Lastly, if the intent of <i>Aristotle</i> in this place had been to say,
+that Figures, although not absolutely, are at least in some measure
+the Cause of moving or not moving: I would have it considered, that he
+names no less the Motion upwards, than the other downwards: and
+because in exemplifying it afterwards, he produceth no other
+Experiments than of a Plate of Lead, and Board of Ebony, Matters that
+of their own Nature go to the bottom, but by vertue (as our
+Adversaries say) of their Figure, rest afloat; it is fit that they
+should produce some other Experiment of those Matters, which by their
+Nature swims, but retained by their Figure rest at the bottom. But
+since this is impossible to be done, we conclude, that <i>Aristotle</i> in
+this place, hath not attributed any action to the Figure of simply
+moving or not moving.</p>
+
+<p>But though he hath exquisitely Philosophiz'd, in investigating the
+solution of the doubts he proposeth, yet will I not undertake to
+maintain, rather various difficulties, that present themselves unto
+me, give me occasion of suspecting that he hath not entirely displaid
+unto us, the true Cause of the present Conclusion: which difficulties
+I will propound one by one, ready to change opinion, whenever I am
+shewed, that the Truth is different from what I say; to the confession
+whereof I am much more inclinable than to contradiction.</p>
+
+<div class="sidenote"><i>Aristotle</i> erred in affirming a Needle dimitted long
+wayes to sink.</div>
+
+<p><i>Aristotle</i> having propounded the Question, whence it proceeds, that
+broad Plates of Iron or Lead, float or swim; he addeth (as it were
+strengthening the occasion of doubting) forasmuch as other things,
+less, and less grave, be they round or long, as for instance a Needle
+<span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span>
+go to the bottom. Now I here doubt, or rather am certain that a Needle
+put lightly upon the water, rests afloat, no less than the thin Plates
+of Iron or Lead. I cannot believe, albeit it hath been told me, that
+some to defend <i>Aristotle</i> should say, that he intends a Needle
+demitted not longwayes but endwayes, and with the Point downwards;
+nevertheless, not to leave them so much as this, though very weak
+refuge, and which in my judgement <i>Aristotle</i> himself would refuse, I
+say it ought to be understood, that the Needle must be demitted,
+according to the Dimension named by <i>Aristotle</i>, which is the length:
+because, if any other Dimension than that which is named, might or
+ought to be taken, I would say, that even the Plates of Iron and Lead,
+sink to the bottom, if they be put into the water edgewayes and not
+flatwayes. But because <i>Aristotle</i> saith, broad Figures go not to the
+bottom, it is to be understood, being demitted broadwayes: and,
+therefore, when he saith, long Figures as a Needle, albeit light, rest
+not afloat, it ought to be understood of them when demitted longwayes.</p>
+
+<p><i>Moreover, to say that</i> Aristotle <i>is to be understood of the
+Needle demitted with the Point downwards, is to father upon him a
+great impertinency; for in this place he saith, that little
+Particles of Lead or Iron, if they be round or long as a Needle, do
+sink to the bottome; so that by his Opinion, a Particle or small
+Grain of Iron cannot swim: and if he thus believed, what a great
+folly would it be to subjoyn, that neither would a Needle demitted
+endwayes swim? And what other is such a Needle, but many such like
+Graines accumulated one upon another? It was too unworthy of such a
+man to say, that one single Grain of Iron could not swim, and that
+neither can it swim, though you put a hundred more upon it.</i></p>
+
+<p>Lastly, either <i>Aristotle</i> believed, that a Needle demitted longwayes
+upon the water, would swim, or he believed that it would not swim: If
+he believed it would not swim, he might well speak as indeed he did;
+but if he believed and knew that it would float, why, together with
+the dubious Problem of the Natation of broad Figures, though of
+ponderous Matter, hath he not also introduced the Question; whence it
+proceeds, that even long and slender Figures, howbeit of Iron or Lead
+do swim? And the rather, for that the occasion of doubting seems
+greater in long and narrow Figures, than in broad and thin, as from
+<i>Aristotles</i> not having doubted of it, is manifested.</p>
+
+<p>No lesser an inconvenience would they fasten upon <i>Aristotle</i>, who in
+his defence should say, that he means a Needle pretty thick, and not a
+small one; for take it for granted to be intended of a small one; and
+<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span>
+it shall suffice to reply, that he believed that it would swim; and I
+will again charge him with having avoided a more wonderfull and
+intricate Probleme, and introduced the more facile and less
+wonderfull.</p>
+
+<p>We say freely therefore, that <i>Aristotle</i> did hold, that only the
+broad Figure did swim, but the long and slender, such as a Needle,
+not. The which nevertheless is false, as it is also false in round
+Bodies: because, as from what hath been predemonstrated, may be
+gathered, little Balls of Lead and Iron, do in like manner swim.</p>
+
+<div class="sidenote"><i>Aristotle</i> affirmeth some Bodies volatile for their
+Minuity, Text. 42.</div>
+
+<p>He proposeth likewise another Conclusion, which likewise seems
+different from the truth, and it is, That some things, by reason of
+their littleness fly in the Air, as the small dust of the Earth, and
+the thin leaves of beaten Gold: but in my Opinion, Experience shews
+us, that that happens not only in the Air, but also in the water, in
+which do descend, even those Particles or Atomes of Earth, that
+disturbe it, whose minuity is such, that they are not deservable, save
+only when they are many hundreds together. Therefore, the dust of the
+Earth, and beaten Gold, do not any way sustain themselves in the Air,
+but descend downwards, and only fly to and again in the same, when
+strong Windes raise them, or other agitations of the Air commove them:
+and this also happens in the commotion of the water, which raiseth its
+Sand from the bottom, and makes it muddy. But <i>Aristotle</i> cannot mean
+this impediment of the commotion, of which he makes no mention, nor
+names other than the lightness of such Minutiæ or Atomes, and the
+Resistance of the Crassitudes of the Water and Air, by which we see,
+that he speakes of a calme, and not disturbed and agitated Air: but in
+that case, neither Gold nor Earth, be they never so small, are
+sustained, but speedily descend.</p>
+
+<div class="sidenote"><i>Democritus</i> placed the Cause of Natation in certain
+fiery Atomes.</div>
+
+<p>He passeth next to confute <i>Democritus</i>, which, by his Testimony would
+<span class="sidenote"><i>Aristot. De Cælo</i> lib. 4. cap. 6. text. 43.</span>
+have it, that some Fiery Atomes, which continually ascend through the
+water, do spring upwards, and sustain those grave Bodies, which are
+very broad, and that the narrow descend to the bottom, for that but a
+small quantity of those Atomes, encounter and resist them.</p>
+
+<div class="sidenote"><i>Democritus</i> confuted by <i>Aristotle</i>, text 43.</div>
+
+<p>I say, <i>Aristotle</i> confutes this position, saying, that that should
+much more occurre in the Air, as the same <i>Democritus</i> instances
+against himself, but after he had moved the objection, he slightly
+resolves it, with saying, that those Corpuscles which ascend in the
+Air, make not their <i>Impetus</i> conjunctly. Here I will not say, that
+the reason alledged by <i>Democritus</i> is true, but I will only say, it
+<span class="sidenote"><i>Aristotles</i> confutation of <i>Democritus</i> refuted by the
+Author.</span>
+seems in my judgement, that it is not wholly confuted by <i>Aristotle</i>,
+whilst he saith, that were it true, that the calid ascending Atomes,
+should sustain Bodies grave, but very broad, it would much more be
+done in the Air, than in Water, for that haply in the Opinion of
+<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span>
+<i>Aristotle</i>, the said calid Atomes ascend with much greater Force and
+Velocity through the Air, than through the water. And if this be so,
+as I verily believe it is, the Objection of <i>Aristotle</i> in my
+judgement seems to give occasion of suspecting, that he may possibly
+be deceived in more than one particular: First, because those calid
+Atomes, (whether they be Fiery Corpuscles, or whether they be
+Exhalations, or in short, whatever other matter they be, that ascends
+upwards through the Air) cannot be believed to mount faster through
+Air, than through water: but rather on the contrary, they peradventure
+move more impetuously through the water, than through the Air, as hath
+been in part demonstrated above. And here I cannot finde the reason,
+why <i>Aristotle</i> seeing, that the descending Motion of the same
+Moveable, is more swift in Air, than in water, hath not advertised us,
+that from the contrary Motion, the contrary should necessarily follow;
+to wit, that it is more swift in the water, than in the Air: for since
+that the Moveable which descendeth, moves swifter through the Air,
+than through the water, if we should suppose its Gravity gradually to
+diminish, it would first become such, that descending swiftly through
+the Air, it would descend but slowly through the water: and then
+again, it might be such, that descending in the Air, it should ascend
+in the water: and being made yet less grave, it shall ascend swiftly
+through the water, and yet descend likewise through the Air: and in
+short, before it can begin to ascend, though but slowly through the
+Air, it shall ascend swiftly through the water: how then is it true,
+that ascending Moveables move swifter through the Air, than through
+the water?</p>
+
+<p>That which hath made <i>Aristotle</i> believe, the Motion of Ascent to be
+swifter in Air, than in water, was first, the having referred the
+Causes of slow and quick, as well in the Motion of Ascent, as of
+Descent, only to the diversity of the Figures of the Moveable, and to
+the more or less Resistance of the greater or lesser Crassitude, or
+Rarity of the <i>Medium</i>; not regarding the comparison of the Excesses
+of the Gravities of the Moveables, and of the <i>Mediums</i>: the which
+notwithstanding, is the most principal point in this affair: for if
+the augmentation and diminution of the Tardity or Velocity, should
+have only respect to the Density or Rarity of the <i>Medium</i>, every Body
+that descends in Air, would descend in water: because whatever
+difference is found between the Crassitude of the water, and that of
+the Air, may well be found between the Velocity of the same Moveable
+in the Air, and some other Velocity: and this should be its proper
+Velocity in the water, which is absolutely false. The other occasion
+is, that he did believe, that like as there is a positive and
+intrinsecall Quality, whereby Elementary Bodies have a propension of
+moving towards the Centre of the Earth, so there is another likewise
+<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span>
+intrinsecall, whereby some of those Bodies have an <i>Impetus</i> of flying
+<span class="sidenote">Lib. 4. Cap. 5.</span>
+the Centre, and moving upwards: by Vertue of which intrinsecall
+Principle, called by him Levity, the Moveables which have that same
+Motion more easily penetrate the more subtle <i>Medium</i>, than the more
+dense: but such a Proposition appears likewise uncertain, as I have
+above hinted in part, and as with Reasons and Experiments, I could
+demonstrate, did not the present Argument importune me, or could I
+dispatch it in few words.</p>
+
+<p>The Objection therefore of <i>Aristotle</i> against <i>Democritus</i>, whilst he
+saith, that if the Fiery ascending Atomes should sustain Bodies grave,
+but of a distended Figure, it would be more observable in the Air than
+in the water, because such Corpuscles move swifter in that, than in
+this, is not good; yea the contrary would evene, for that they ascend
+more slowly through the Air: and, besides their moving slowly, they
+ascend, not united together, as in the water, but discontinue, and, as
+we say, scatter: And, therefore, as <i>Democritus</i> well replyes,
+resolving the instance they make not their push or <i>Impetus</i>
+conjunctly.</p>
+
+<p><i>Aristotle</i>, in the second place, deceives himself, whilst he will
+have the said grave Bodies to be more easily sustained by the said
+Fiery ascending Atomes in the Air than in the Water: not observing,
+that the said Bodies are much more grave in that, than in this, and
+that such a Body weighs ten pounds in the Air, which will not in the
+water weigh 1/2 an ounce; how can it then be more easily sustained in
+the Air, than in the Water?</p>
+
+<div class="sidenote"><i>Democritus</i> confuted by the Authour.</div>
+
+<p>Let us conclude, therefore, that <i>Democritus</i> hath in this particular
+better Philosophated than <i>Aristotle</i>. But yet will not I affirm, that
+<i>Democritus</i> hath reason'd rightly, but I rather say, that there is a
+manifest Experiment that overthrows his Reason, and this it is, That
+if it were true, that calid ascending Atomes should uphold a Body,
+that if they did not hinder, would go to the bottom, it would follow,
+that we may find a Matter very little superiour in Gravity to the
+water, the which being reduced into a Ball, or other contracted
+Figure, should go to the bottom, as encountring but few Fiery Atomes;
+and which being distended afterwards into a dilated and thin Plate,
+should come to be thrust upwards by the impulsion of a great Multitude
+of those Corpuscles, and at last carried to the very Surface of the
+water: which wee see not to happen; Experience shewing us, that a Body
+<i>v. gra.</i> of a Sphericall Figure, which very hardly, and with very
+great leasure goeth to the bottom, will rest there, and will also
+descend thither, being reduced into whatsoever other distended Figure.
+We must needs say then, either that in the water, there are no such
+ascending Fiery Atoms, or if that such there be, that they are not
+able to raise and lift up any Plate of a Matter, that without them
+<span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span>
+would go to the bottom: Of which two Positions, I esteem the second to
+be true, understanding it of water, constituted in its naturall
+Coldness. But if we take a Vessel of Glass, or Brass, or any other
+hard matter, full of cold water, within which is put a Solid of a flat
+or concave Figure, but that in Gravity exceeds the water so little,
+that it goes slowly to the bottom; I say, that putting some burning
+Coals under the said Vessel, as soon as the new Fiery Atomes shall
+have penetrated the substance of the Vessel, they shall without doubt,
+ascend through that of the water, and thrusting against the foresaid
+Solid, they shall drive it to the Superficies, and there detain it, as
+long as the incursions of the said Corpuscles shall last, which
+ceasing after the removall of the Fire, the Solid being abandoned by
+its supporters, shall return to the bottom.</p>
+
+<p>But <i>Democritus</i> notes, that this Cause only takes place when we
+treat of raising and sustaining of Plates of Matters, but very little
+heavier than the water, or extreamly thin: but in Matters very grave,
+and of some thickness, as Plates of Lead or other Mettal, that same
+Effect wholly ceaseth: In Testimony of which, let's observe that such
+Plates, being raised by the Fiery Atomes, ascend through all the depth
+of the water, and stop at the Confines of the Air, still staying under
+water: but the Plates of the Opponents stay not, but only when they
+have their upper Superficies dry, nor is there any means to be used,
+that when they are within the water, they may not sink to the bottom.
+The cause, therefore, of the Supernatation of the things of which
+<i>Democritus</i> speaks is one, and that of the Supernatation of the
+things of which we speak is another. But, returning to <i>Aristotle</i>,
+<span class="sidenote"><i>Aristotle</i> shews his desire of finding <i>Democritus</i>
+in an Error, to exceed that of discovering Truth.</span>
+methinks that he hath more weakly confuted <i>Democritus</i>, than
+<i>Democritus</i> himself hath done: For <i>Aristotle</i> having propounded the
+Objection which he maketh against him, and opposed him with saying,
+that if the calid ascendent Corpuscles were those that raised the thin
+Plate, much more then would such a Solid be raised and born upwards
+through the Air, it sheweth that the desire in <i>Aristotle</i> to detect
+<i>Democritus</i>, was predominate over the exquisiteness of Solid
+Philosophizing: which desire of his he hath discovered in other
+occasions, and that we may not digress too far from this place, in the
+Text precedent to this Chapter which we have in hand; where he
+<span class="sidenote">Cap. 5. Text 41.</span>
+attempts to confute the same <i>Democritus</i> for that he, not contenting
+himself with names only, had essayed more particularly to declare what
+things Gravity and Levity were; that is, the Causes of descending and
+ascending, (and had introduced Repletion and Vacuity) ascribing this
+to Fire, by which it moves upwards, and that to the Earth, by which it
+descends; afterwards attributing to the Air more of Fire, and to the
+water more of Earth. But <i>Aristotle</i> desiring a positive Cause, even
+of ascending Motion, and not as <i>Plato</i>, or these others, a simple
+<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span>
+negation, or privation, such as Vacuity would be in reference to
+Repletion, argueth against <i>Democritus</i> and saith: If it be true, as
+<span class="sidenote">Id. ibid.</span>
+you suppose, then there shall be a great Mass of water, which shall
+have more of Fire, than a small Mass of Air, and a great Mass of Air,
+which shall have more of Earth than a little Mass of water, whereby it
+would ensue, that a great Mass of Air, should come more swiftly
+downwards, than a little quantity of water: But that is never in any
+case soever: Therefore <i>Democritus</i> discourseth erroneously.</p>
+
+<p>But in my opinion, the Doctrine of <i>Democritus</i> is not by this
+allegation overthrown, but if I erre not, the manner of <i>Aristotle</i>
+deduction either concludes not, or if it do conclude any thing, it may
+with equall force be restored against himself. <i>Democritus</i> will grant
+to <i>Aristotle</i>, that there may be a great Mass of Air taken, which
+contains more Earth, than a small quantity of water, but yet will
+deny, that such a Mass of Air, shall go faster downwards than a little
+water, and that for many reasons. First, because if the greater
+quantity of Earth, contained in the great Mass of Air, ought to cause
+a greater Velocity than a less quantity of Earth, contained in a
+little quantity of water, it would be necessary, first, that it were
+true, that a greater Mass of pure Earth, should move more swiftly than
+a less: But this is false, though <i>Aristotle</i> in many places affirms
+it to be true: because not the greater absolute, but the greater
+specificall Gravity, is the cause of greater Velocity: nor doth a Ball
+<span class="sidenote">The greater Specificall, not the greater absolute
+Gravity, is the Cause of Velocity.</span>
+of Wood, weighing ten pounds, descend more swiftly than one weighing
+ten Ounces, and that is of the same Matter: but indeed a Bullet of
+Lead of four Ounces, descendeth more swiftly than a Ball of Wood of
+twenty Pounds: because the Lead is more <i>grave in specie</i> than the
+Wood. Therefore, its not necessary, that a great Mass of Air, by
+reason of the much Earth contained in it, do descend more swiftly than
+a little Mass of water, but on the contrary, any whatsoever Mass of
+<span class="sidenote">Any Mass of water shal move more swiftly, than any of
+Air, and why.</span>
+water, shall move more swiftly than any other of Air, by reason the
+participation of the terrene parts <i>in specie</i> is greater in the
+water, than in the Air. Let us note, in the second place, how that in
+multiplying the Mass of the Air, we not only multiply that which is
+therein of terrene, but its Fire also: whence the Cause of ascending,
+no less encreaseth, by vertue of the Fire, than that of descending on
+the account of its multiplied Earth. It was requisite in increasing
+the greatness of the Air, to multiply that which it hath of terrene
+only, leaving its Fire in its first state, for then the terrene parts
+of the augmented Air, overcoming the terrene parts of the small
+quantity of water, it might with more probability have been pretended,
+that the great quantity of Air, ought to descend with a greater
+<i>Impetus</i>, than the little quantity of water.</p>
+
+<p><span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span></p>
+<p>Therefore, the Fallacy lyes more in the Discourse of <i>Aristotle</i>, than
+in that of <i>Democritus</i>, who with severall other Reasons might oppose
+<i>Aristotle</i>, and alledge; If it be true, that the extreame Elements be
+one simply grave, and the other simply light, and that the mean
+Elements participate of the one, and of the other Nature; but the Air
+more of Levity, and the water more of Gravity, then there shall be a
+great Mass of Air, whose Gravity shall exceed the Gravity of a little
+quantity of water, and therefore such a Mass of Air shall descend more
+swiftly than that little water: But that is never seen to occurr:
+Therefore its not true, that the mean Elements do participate of the
+one, and the other quality. This argument is fallacious, no less than
+the other against <i>Democritus</i>.</p>
+
+<p>Lastly, <i>Aristotle</i> having said, that if the Position of <i>Democritus</i>
+were true, it would follow, that a great Mass of Air should move more
+swiftly than a small Mass of water, and afterwards subjoyned, that
+that is never seen in any Case: methinks others may become desirous to
+know of him in what place this should evene, which he deduceth against
+<i>Democritus</i>, and what Experiment teacheth us, that it never falls out
+so. To suppose to see it in the Element of water, or in that of the
+Air is vain, because neither doth water through water, nor Air through
+Air move, nor would they ever by any whatever participation others
+assign them, of Earth or of Fire: the Earth, in that it is not a Body
+fluid, and yielding to the mobility of other Bodies, is a most
+improper place and <i>Medium</i> for such an Experiment: <i>Vacuum</i>,
+according to the same <i>Aristotle</i> himself, there is none, and were
+there, nothing would move in it: there remains the Region of Fire, but
+being so far distant from us, what Experiment can assure us, or hath
+assertained <i>Aristotle</i> in such sort, that he should as of a thing
+most obvious to sence, affirm what he produceth in confutation of
+<i>Democritus</i>, to wit, that a great Mass of Air, is moved no swifter
+than a little one of water? But I will dwell no longer upon this
+matter, whereon I have spoke sufficiently: but leaving <i>Democritus</i>, I
+return to the Text of <i>Aristotle</i>, wherein he goes about to render the
+true reason, how it comes to pass, that the thin Plates of Iron or
+Lead do swim on the water; and, moreover, that Gold it self being
+beaten into thin Leaves, not only swims in water, but flyeth too and
+again in the Air. He supposeth that of Continualls, some are easily
+<span class="sidenote"><i>De Cælo</i> l. 4. c. 6. t. 44.</span>
+divisible, others not: and that of the easily divisible, some are more
+so, and some less: and these he affirms we should esteem the Causes.
+He addes that that is easily divisible, which is well terminated, and
+the more the more divisible, and that the Air is more so, than the
+water, and the water than the Earth. And, lastly, supposeth that in
+each kind, the lesse quantity is easlyer divided and broken than the
+greater.</p>
+<p><span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span></p>
+
+<p>Here I note, that the Conclusions of <i>Aristotle</i> in generall are all
+true, but methinks, that he applyeth them to particulars, in which
+they have no place, as indeed they have in others, as for Example, Wax
+is more easily divisible than Lead, and Lead than Silver, inasmuch as
+Wax receives all the terms more easlier than Lead, and Lead than
+Silver. Its true, moreover, that a little quantity of Silver is
+easlier divided than a great Mass: and all these Propositions are
+true, because true it is, that in Silver, Lead and Wax, there is
+simply a Resistance against Division, and where there is the absolute,
+there is also the respective. But if as well in water as in Air, there
+be no Renitence against simple Division, how can we say, that the
+water is easlier divided than the Air? We know not how to extricate
+our selves from the Equivocation: whereupon I return to answer, that
+Resistance of absolute Division is one thing, and Resistance of
+Division made with such and such Velocity is another. But to produce
+Rest, and to abate the Motion, the Resistance of absolute Division is
+necessary; and the Resistance of speedy Division, causeth not Rest,
+but slowness of Motion. But that as well in the Air, as in water,
+there is no Resistance of simple Division, is manifest, for that there
+is not found any Solid Body which divides not the Air, and also the
+water: and that beaten Gold, or small dust, are not able to superate
+the Resistance of the Air, is contrary to that which Experience shews
+us, for we see Gold and Dust to go waving to and again in the Air, and
+at last to descend downwards, and to do the same in the water, if it
+be put therein, and separated from the Air. And, because, as I say,
+neither the water, nor the Air do resist simple Division, it cannot be
+said, that the water resists more than the Air. Nor let any object
+unto me, the Example of most light Bodies, as a Feather, or a little
+of the pith of Elder, or water-reed that divides the Air and not the
+water, and from this infer, that the Air is easlier divisible than the
+water; for I say unto them, that if they do well observe, they shall
+see the same Body likewise divide the Continuity of the water, and
+<span class="sidenote"><i>Archimed. De Insident. humi</i> lib. 2. prop. 1.</span>
+submerge in part, and in such a part, as that so much water in Mass
+would weigh as much as the whole Solid. And if they shal yet persist
+in their doubt, that such a Solid sinks not through inability to
+divide the water, I will return them this reply, that if they put it
+under water, and then let it go, they shall see it divide the water,
+and presently ascend with no less celerity, than that with which it
+divided the Air in descending: so that to say that this Solid ascends
+in the Air, but that coming to the water, it ceaseth its Motion, and
+therefore the water is more difficult to be divided, concludes
+nothing: for I, on the contrary, will propose them a piece of Wood, or
+of Wax, which riseth from the bottom of the water, and easily divides
+its Resistance, which afterwards being arrived at the Air, stayeth
+<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>
+there, and hardly toucheth it; whence I may aswell say, that the water
+is more easier divided than the Air.</p>
+
+<p>I will not on this occasion forbear to give warning of another fallacy
+of these persons, who attribute the reason of sinking or swimming to
+the greater or lesse Resistance of the Crassitude of the water against
+Division, making use of the example of an Egg, which in sweet water
+goeth to the bottom, but in salt water swims; and alledging for the
+cause thereof, the faint Resistance of fresh water against Division,
+and the strong Resistance of salt water. But if I mistake not, from
+the same Experiment, we may aswell deduce the quite contrary; namely,
+that the fresh water is more dense, and the salt more tenuous and
+subtle, since an Egg from the bottom of salt water speedily ascends to
+the top, and divides its Resistance, which it cannot do in the fresh,
+in whose bottom it stays, being unable to rise upwards. Into such like
+perplexities, do false Principles Lead men: but he that rightly
+Philosophating, shall acknowledge the excesses of the Gravities of the
+Moveables and of the Mediums, to be the Causes of those effects, will
+say, that the Egg sinks to the bottom in fresh water, for that it is
+more grave than it, and swimeth in the salt, for that its less grave
+than it: and shall without any absurdity, very solidly establish his
+Conclusions.</p>
+
+<p>Therefore the reason totally ceaseth, that <i>Aristotle</i> subjoyns in the
+Text saying; The things, therefore, which have great breadth remain
+<span class="sidenote">Text 45.</span>
+above, because they comprehend much, and that which is greater, is not
+easily divided. Such discoursing ceaseth, I say, because its not true,
+that there is in water or in Air any Resistance of Division; besides
+that the Plate of Lead when it stays, hath already divided and
+penetrated the Crassitude of the water, and profounded it self ten or
+twelve times more than its own thickness: besides that such Resistance
+of Division, were it supposed to be in the water, could not rationally
+be affirmed to be more in its superiour parts than in the middle, and
+lower: but if there were any difference, the inferiour should be the
+more dense, so that the Plate would be no less unable to penetrate the
+lower, than the superiour parts of the water; nevertheless we see that
+no sooner do we wet the superiour Superficies of the Board or thin
+Piece of Wood, but it precipitatly, and without any retension,
+descends to the bottom.</p>
+
+<p>I believe not after all this, that any (thinking perhaps thereby to
+defend <i>Aristotle</i>) will say, that it being true, that the much water
+resists more than the little, the said Board being put lower
+descendeth, because there remaineth a less Mass of water to be divided
+by it: because if after the having seen the same Board swim in four
+Inches of water, and also after that in the same to sink, he shall try
+the same Experiment upon a profundity of ten or twenty fathom water,
+he shall see the very self same effect. And here I will take occasion
+<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span>
+to remember, for the removall of an Error that is too common; That
+that Ship or other whatsoever Body, that on the depth of an hundred or
+a thousand fathom, swims with submerging only six fathom of its own
+height, [<i>or in the Sea dialect, that draws six fathom water</i>] shall
+swim in the same manner in water, that hath but six fathom and half an
+Inch of depth. Nor do I on the other side, think that it can be said,
+<span class="sidenote">A Ship that in 100 Fathome water draweth 6 Fathome,
+shall float in 6 Fathome and 1/2 an Inch of depth.</span>
+that the superiour parts of the water are the more dense, although a
+most grave Authour hath esteemed the superiour water in the Sea to be
+so, grounding his opinion upon its being more salt, than that at the
+bottom: but I doubt the Experiment, whether hitherto in taking the
+water from the bottom, the Observatour did not light upon some spring
+of fresh water there spouting up: but we plainly see on the contrary,
+the fresh Waters of Rivers to dilate themselves for some miles beyond
+their place of meeting with the salt water of the Sea, without
+descending in it, or mixing with it, unless by the intervention of
+some commotion or turbulency of the Windes.</p>
+
+<p>But returning to <i>Aristotle</i>, I say, that the breadth of Figure hath
+nothing to do in this business more or less, because the said Plate of
+Lead, or other Matter, cut into long Slices, swim neither more nor
+less; and the same shall the Slices do, being cut anew into little
+<span class="sidenote">Thickness not breadth of Figure to be respected in
+Natation.</span>
+pieces, because its not the breadth but the thickness that operates in
+this business. I say farther, that in case it were really true, that
+the Renitence to Division were the proper Cause of swimming, the
+<span class="sidenote">Were Renitence the cause of Natation, breadth of Figure
+would hinder the swiming of Bodies.</span>
+Figures more narrow and short, would much better swim than the more
+spacious and broad, so that augmenting the breadth of the Figure, the
+facility of supernatation will be deminished, and decreasing, that
+this will encrease.</p>
+
+<p>And for declaration of what I say, consider that when a thin Plate of
+Lead descends, dividing the water, the Division and discontinuation is
+made between the parts of the water, invironing the perimeter or
+Circumference of the said Plate, and according to the bigness greater
+or lesser of that circuit, it hath to divide a greater or lesser
+quantity of water, so that if the circuit, suppose of a Board, be ten
+Feet in sinking it flatways, it is to make the seperation and
+division, and to so speak, an incission upon ten Feet of water; and
+likewise a lesser Board that is four Feet in Perimeter, must make an
+incession of four Feet. This granted, he that hath any knowledge in
+Geometry, will comprehend, not only that a Board sawed in many long
+thin pieces, will much better float than when it was entire, but that
+all Figures, the more short and narrow they be, shall so much the
+better swim. Let the Board A B C D be, for Example, eight Palmes long,
+and five broad, its circuit shall be twenty six Palmes; and so many
+must the incession be, which it shall make in the water to descend
+therein: <a name="tnd_74" id="tnd_74"></a><a href="#tn_74" class="tnlink" title="printer's error, ir for it">but if we do saw ir,</a> as suppose into eight little pieces,
+<span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span>
+according to the Lines E F, G H, <a name="tnd_75" id="tnd_75"></a><a href="#tn_75" class="tnlink" title="unclear symbol in original text">{&amp;}c. making seven Segments,</a> we must
+adde to the twenty six Palmes of the circuit of the whole Board,
+seventy others; whereupon the eight little pieces so cut and
+seperated, have to cut ninty six Palmes of water. And, if moreover, we
+<span class="figright" style="width: 199px;">
+<img src="images/i077.png" width="199" height="254" alt="" title="" />
+</span>
+cut each of the said pieces into five parts, reducing them into
+Squares, to the circuit of ninty six Palmes, with four cuts of eight
+Palmes apiece; we shall adde also sixty four Palmes, whereupon the
+said Squares to descend in the water, must divide one hundred and
+sixty Palmes of water, but the Resistance is much greater than that of
+twenty six; therefore to the lesser Superficies, we shall reduce them,
+so much the more easily will they float: and the same will happen in
+all other Figures, whose Superficies are simular amongst themselves,
+but different in bigness: because the said Superficies, being either
+deminished or encreased, always diminish or encrease their Perimeters
+in subduple proportion; to wit, the Resistance that they find in
+penetrating the water; therefore the little pieces gradually swim,
+with more and more facility as their breadth is lessened.</p>
+
+<p><i>This is manifest; for keeping still the same height of the Solid,
+with the same proportion as the Base encreaseth or deminisheth,
+doth the said Solid also encrease or diminish; whereupon the Solid
+more diminishing than the Circuit, the Cause of Submersion more
+diminisheth than the Cause of Natation: And on the contrary, the
+Solid more encreasing than the Circuit, the Cause of Submersion
+encreaseth more, that of Natation less.</i></p>
+
+<p>And this may all be deduced out of the Doctrine of <i>Aristotle</i> against
+his own Doctrine.</p>
+
+<div class="sidenote">Lib. 4. c. 6. Text 45.</div>
+
+<p>Lastly, to that which we read in the latter part of the Text, that is
+to say, that we must compare the Gravity of the Moveable with the
+Resistance of the Medium against Division, because if the force of the
+Gravity exceed the Resistance of the <i>Medium</i>, the Moveable will
+descend, if not it will float. I need not make any other answer, but
+that which hath been already delivered; namely, that its not the
+Resistance of absolute Division, (which neither is in Water nor Air)
+but the Gravity of the <i>Medium</i> that must be compared with the Gravity
+of the Moveables; and if that of the <i>Medium</i> be greater, the Moveable
+shall not descend, nor so much as make a totall Submersion, but a
+partiall only; because in the place which it would occupy in the
+water, there must not remain a Body that weighs less than a like
+quantity of water: but if the Moveable be more grave, it shall descend
+to the bottom, and possess a place where it is more conformable for it
+<span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span>
+to remain, than another Body that is less grave. And this is the only
+true proper and absolute Cause of Natation and Submersion, so that
+nothing else hath part therein: and the Board of the Adversaries
+swimmeth, when it is conjoyned with as much Air, as, together with it,
+doth form a Body less grave than so much water as would fill the place
+that the said Compound occupyes in the water; but when they shall
+demit the simple Ebony into the water, according to the Tenour of our
+Question, it shall alwayes go to the bottom, though it were as thin as
+a Paper.</p>
+
+<p>&nbsp;</p>
+
+<div class="figcenter" style="width: 609px;">
+<img src="images/i078a.png" width="609" height="46" alt="" title="" />
+</div>
+
+<p>&nbsp;</p>
+
+<p class="f_end">FINIS.</p>
+
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+
+<div class="figcenter" style="width: 368px;">
+<img src="images/i078b.png" width="368" height="295" alt="" title="" />
+</div>
+
+
+<hr style="width: 65%;" />
+
+
+<div class="bbox">
+  <p><b>Detailed Transcriber's Notes</b></p>
+
+  <p>The text has been made to match the original text as much as
+  possible including variation in spelling, punctuation, italics etc.
+  The following, details apparent printer's errors as well as changes
+  or additions to aid readability of text.</p>
+
+  <p>Page <a href="#Page_1">1</a><a name="tn_1" id="tn_1"></a>, missing full stop after abbreviation gr., <a href="#tnd_1">'0 gr 54 min.'</a>.</p>
+
+  <p>Page <a href="#Page_3">3</a><a name="tn_3a" id="tn_3a"></a>, sidenote, missing space between words, <a href="#tnd_3a">'the Authority ofan Author.'</a>.</p>
+
+  <p>Page <a href="#Page_3">3</a><a name="tn_3b" id="tn_3b"></a>, printer's error, augmentarion for augmentation, <a href="#tnd_3b">'and
+  augmentarion of Masse'</a>.</p>
+
+  <p>Page <a href="#Page_4">4</a><a name="tn_4a" id="tn_4a"></a>, missing letter t, <a href="#tnd_4a">'tha{t} that proceeded not'</a>.</p>
+
+  <p>Page <a href="#Page_4">4</a><a name="tn_4b" id="tn_4b"></a>, printer's error or inconsistent punctuation, <a href="#tnd_4b">'my paynes and
+  time. and although'</a>.</p>
+
+  <p>Page <a href="#Page_6">6</a><a name="tn_6" id="tn_6"></a>, inconsistent punctuation, full stop after axiome where as
+  there are none after those following, <a href="#tnd_6">'AXIOME. I.'</a>.</p>
+
+  <p>Page <a href="#Page_9">9</a><a name="tn_9" id="tn_9"></a>, missing full stop added to end of paragraph, <a href="#tnd_9">'or else an
+  upright Prisme.'</a>.</p>
+
+  <p>Page <a href="#Page_11">11</a><a name="tn_11" id="tn_11"></a>, printer's error, missing letter C in illustration, <a href="#tnd_11">'the
+  Prisme A C D B to be placed'</a>.</p>
+
+  <p>Page <a href="#Page_15">15</a><a name="tn_15" id="tn_15"></a>, printer's error or archaic lettering, final y looking like a
+  7 in original text, <a href="#tnd_15">'and of the Specifick Gravit{y}'</a>.</p>
+
+  <p>Page <a href="#Page_16">16</a><a name="tn_16b" id="tn_16b"></a>, letter N for T in text to refer to
+    illustration, <a href="#tnd_16b">if the Vessell E N S F'</a>.</p>
+
+  <p>Page <a href="#Page_16">16</a><a name="tn_16" id="tn_16"></a>, printer's error, duplicate word in text, <a href="#tnd_16">'equalizeth the
+  Force and and Moment,'</a>.</p>
+
+  <p>Page <a href="#Page_17">17</a><a name="tn_17a" id="tn_17a"></a>, printer's error, rhe for the, <a href="#tnd_17a">'as in rhe Stilliard,'</a>.</p>
+
+  <p>Page <a href="#Page_17">17</a><a name="tn_17b" id="tn_17b"></a>, missing space between words, <a href="#tnd_17b">'asoften as that'</a>.</p>
+
+  <p>Page <a href="#Page_18">18</a><a name="tn_18" id="tn_18"></a>, printer's error, specifiaclly for specifically, <a href="#tnd_18">'A Solid specifiaclly graver'</a>.</p>
+
+  <p>Page <a href="#Page_20">20</a><a name="tn_20b" id="tn_20b"></a>, potential printer's error, properly for property, <a href="#tnd_20b">'but
+  this properly they have'</a>.</p>
+
+  <p>Page <a href="#Page_20">20</a><a name="tn_20" id="tn_20"></a>, printer's error, n for u, <a href="#tnd_20">'loseth all a{u}thenticalness'</a>.</p>
+
+  <p>Page <a href="#Page_22">22</a><a name="tn_22" id="tn_22"></a>, printer's error or variation in spelling, Benonamico for
+  Buonamico, <a href="#tnd_22">'it seemes that Benonamico'</a>.</p>
+
+  <p>Page <a href="#Page_23">23</a><a name="tn_23" id="tn_23"></a>, printer's error, missing i, <a href="#tnd_23">'accordng to its excess'</a>.</p>
+
+  <p>Page <a href="#Page_24">24</a><a name="tn_24" id="tn_24"></a>, missing line at the end of page in original text, <a href="#tnd_24">'its Region it loseth all'</a>.</p>
+
+  <p>Page <a href="#Page_26">26</a><a name="tn_26" id="tn_26"></a>, missing letter n, <a href="#tnd_26">'u{n}able by its small weight'</a>.</p>
+
+  <p>Page <a href="#Page_29">29</a><a name="tn_29" id="tn_29"></a>, missing letter e, <a href="#tnd_29">'that I have gon{e} about'</a>.</p>
+
+  <p>Page <a href="#Page_32">32</a><a name="tn_32" id="tn_32"></a>, unclear symbol in original text, <a href="#tnd_32">'other Figure, {&amp;}c.'</a>.</p>
+
+  <p>Page <a href="#Page_37">37</a><a name="tn_37" id="tn_37"></a>, potential printer's error, comma in unusual position,
+  <a href="#tnd_37">'whatever Figure, goeth always'</a>.</p>
+
+  <p>Page <a href="#Page_38">38</a><a name="tn_38" id="tn_38"></a>, missing space between words, <a href="#tnd_38">'Superficies might bedry:'</a>.</p>
+
+  <p>Page <a href="#Page_39">39</a><a name="tn_39" id="tn_39"></a>, missing letter t, unied for united, <a href="#tnd_39">'which holds them unied,'</a>.</p>
+
+  <p>Page <a href="#Page_41">41</a><a name="tn_41" id="tn_41"></a>, printer's error, Motitions for Motions, <a href="#tnd_41">'all Motitions are
+  made'</a>.</p>
+
+  <p>Page <a href="#Page_42">42</a><a name="tn_42" id="tn_42"></a>, sidenote, possible missing letter e, <a href="#tnd_42">'Se{e} what satisfaction'</a>.</p>
+
+  <p>Page <a href="#Page_43">43</a><a name="tn_43" id="tn_43"></a>, printer's error, Subdidivisions for Subdivisions, <a href="#tnd_43">'other
+  Subdidivisions,'</a>.</p>
+
+  <p>Page <a href="#Page_49">49</a><a name="tn_49" id="tn_49"></a>, missing letter i, dminishing for diminishing, <a href="#tnd_49">'or dminishing
+  it by dividing'</a>.</p>
+
+  <p>Page <a href="#Page_50">50</a><a name="tn_50" id="tn_50"></a>, sidenote, printer's error, missing letter l, hep for help,
+  <a href="#tnd_50">'float by hep of'</a>.</p>
+
+  <p>Page <a href="#Page_53">53</a><a name="tn_53" id="tn_53"></a>, printer's error, missing letter n, beig for being, <a href="#tnd_53">'beig
+  double in Gravity'</a>.</p>
+
+  <p>Page <a href="#Page_54">54</a><a name="tn_54" id="tn_54"></a>, printer's error, missing letter l, <a href="#tnd_54">'sha{l}l also descend.'</a>.</p>
+
+  <p>Page <a href="#Page_55">55</a><a name="tn_55" id="tn_55"></a>, printer's error, missing letter r, <a href="#tnd_55">'to fo{r}m Solid Bodies,'</a>.</p>
+
+  <p>Page <a href="#Page_56">56</a><a name="tn_56" id="tn_56"></a>, printer's error, missing letter A, <a href="#tnd_56">'Cone S {A} T'</a>.</p>
+
+  <p>Page <a href="#Page_57">57</a><a name="tn_57" id="tn_57"></a>, printer's error, missing letter t, <a href="#tnd_57">'of which i{t} may
+  descend'</a>.</p>
+
+  <p>Page <a href="#Page_58">58</a><a name="tn_58" id="tn_58"></a>, sidenote, printer's error, inverted n, <a href="#tnd_58">'Natatio{n} easiest
+  effected'</a>.</p>
+
+  <p>Page <a href="#Page_59">59</a><a name="tn_59a" id="tn_59a"></a>, missing letter u, <a href="#tnd_59a">'witho{u}t all Question,'</a>.</p>
+
+  <p>Page <a href="#Page_59">59</a><a name="tn_59b" id="tn_59b"></a>, printer's error, inverted n, <a href="#tnd_59b">'with an other Experime{n}t'</a>.</p>
+
+  <p>Page <a href="#Page_59">59</a><a name="tn_59c" id="tn_59c"></a>, potential printer's error, sidenote ends with comma, <a href="#tnd_59c">'Or rather Contiguity,'</a>.</p>
+
+  <p>Page <a href="#Page_61">61</a><a name="tn_61" id="tn_61"></a>, missing letter a, <a href="#tnd_61">'that in this c{a}se the water,'</a>.</p>
+
+  <p>Page <a href="#Page_74">74</a><a name="tn_74" id="tn_74"></a>, printer's error, ir for it, <a href="#tnd_74">'but if we do saw ir,'</a>.</p>
+
+  <p>Page <a href="#Page_75">75</a><a name="tn_75" id="tn_75"></a>, unclear symbol in original text, <a href="#tnd_75">'{&amp;}c. making seven
+  Segments'</a>.</p>
+
+</div>
+
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's Discourse on Floating Bodies, by Galileo Galilei
+
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+</pre>
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+</body>
+</html>
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+Project Gutenberg's Discourse on Floating Bodies, by Galileo Galilei
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Discourse on Floating Bodies
+
+Author: Galileo Galilei
+
+Translator: Thomas Salusbury
+
+Release Date: October 12, 2011 [EBook #37729]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK DISCOURSE ON FLOATING BODIES ***
+
+
+
+
+Produced by Tim Madden and the Online Distributed
+Proofreading Team at https://www.pgdp.net (This file was
+produced from images generously made available by The
+Internet Archive)
+
+
+
+
+
+
+  [Transcriber's Notes
+
+  All apparent printer's errors retained. Variation in punctuation are
+  as in the original, but missing full stops at end of paragraphs have
+  been supplied. There are inconsistencies in the use of italics,
+  spacing of words and use of full stop after 'AXIOME', abbreviations
+  etc. All are retained to match text. There is a great variation in
+  spelling including multiple spellings of the same word, all spelling
+  has been retained to match text. There are several instances of
+  obviously missing letters or inverted n & u. These have been changed
+  or obvious letters replaced, with the changes surrounded by {}.
+
+  All instances are detailed at the end of the text. It should also be
+  noted that in the original text there is a missing line at the end of
+  page 24 in original text.
+
+  There are a number of instances in the original text where 'that' is
+  immediately followed by a second 'that' in the sentence. These could
+  be potential printer's errors or, since several of them make sense,
+  part of the author's style. They have been left in the text as they
+  appear in the original text.
+
+  The original text has many sidenotes, some are true sidenotes,
+  introductions to paragraphs etc, some acting as footnotes with some
+  marked in original text with *. These have been dealt with in three
+  ways with the footnotes placed after their relevant paragraph and
+  sidenotes place before their relevant paragraph.
+
+  1) Footnotes marked with capital letter. These were sidenotes in
+  original text marked with * in the original text and thus acting
+  like footnotes.
+
+  2) Footnotes marked with number. These were sidenotes in original
+  text that were unmarked but acting like normal footnotes. The anchor
+  in the text was placed at the most suitable relevant place in
+  comparison with the placement of the sidenote text in the margin,
+  but still should be considered only an approximate placement.
+
+  3) Sidenotes placed at start of the relevant paragraph. Some
+  sidenotes were considered not to be relevant as footnotes,
+  introductions to paragraphs etc, and were left as sidenotes before
+  their relevant paragraph.]
+
+       *       *       *       *       *
+
+
+
+
+                          A
+                      DISCOURSE
+                     _PRESENTED_
+                 TO THE MOST SERENE
+                   Don Cosimo II.
+                     GREAT DUKE
+                        _OF_
+                      TUSCANY,
+
+                     CONCERNING
+
+           The _NATATION_ of BODIES Vpon,
+                And _SUBMERSION_ In,
+                        THE
+                       WATER.
+
+        By GALILEUS GALILEI: Philosopher and
+   Mathematician unto His most Serene Highnesse.
+
+  Englished from the Second Edition of the ITALIAN,
+  compared with the Manuscript Copies, and reduced
+                 into PROPOSITIONS:
+
+             By _THOMAS SALUSBURY_, Esq;
+
+                      _LONDON_:
+
+            Printed by WILLIAM LEYBOURN:
+
+                    _M DC LXIII._
+
+       *       *       *       *       *
+
+                  [Decoration]
+
+
+
+
+                  A DISCOVRSE
+
+  Presented to the Most Serene DON COSIMO II.
+
+            GREAT DUKE of _TUSCANY_:
+
+                   CONCERNING
+
+  _The Natation of BODIES Upon, or Submersion_
+               _In, the WATER._
+
+
+
+
+Considering (Most Serene Prince) that the publishing this present
+Treatise, of so different an Argument from that which many expect, and
+which according to the intentions I proposed in my [A] Astronomicall
+_Adviso_, I should before this time have put forth, might peradventure
+make some thinke, either that I had wholly relinquished my farther
+imployment about the new Celestiall Observations, or that, at least, I
+handled them very remissely; I have judged fit to render an account,
+aswell of my deferring that, as of my writing, and publishing this
+treatise.
+
+    [A] His Nuncio Siderio.
+
+As to the first, the last discoveries of _Saturn_ to be
+tricorporeall, and of the mutations of Figure in _Venus_, like to
+those that are seen in the Moon, together with the Consequents
+depending thereupon, have not so much occasioned the demur, as the
+investigation of the times of the Conversions of each of the Four
+Medicean Planets about _Jupiter_, which I lighted upon in _April_ the
+year past, 1611, at my being in _Rome_; where, in the end, I
+assertained my selfe, that the first and neerest to _Jupiter_, moved
+about 8 _gr._ & 29 _m._ of its Sphere in an houre, makeing its whole
+revolution in one naturall day, and 18 hours, and almost an halfe. The
+second moves in its Orbe 14 _gr._ 13 _min._ or very neer, in an hour,
+and its compleat conversion is consummate in 3 dayes, 13 hours, and
+one third, or thereabouts. The third passeth in an hour, 2 _gr._ 6
+_min._ little more or less of its Circle, and measures it all in 7
+dayes, 4 hours, or very neer. The fourth, and more remote than the
+rest, goes in one houre, 0 _gr_ 54 _min._ and almost an halfe of its
+Sphere, and finisheth it all in 16 dayes, and very neer 18 hours. But
+because the excessive velocity of their returns or restitutions,
+requires a most scrupulous precisenesse to calculate their places, in
+times past and future, especially if the time be for many Moneths or
+Years; I am therefore forced, with other Observations, and more exact
+than the former, and in times more remote from one another, to correct
+the Tables of such Motions, and limit them even to the shortest
+moment: for such exactnesse my first Observations suffice not; not
+only in regard of the short intervals of Time, but because I had not
+as then found out a way to measure the distances between the said
+Planets by any Instrument: I Observed such Intervals with simple
+relation to the Diameter of the Body of _Jupiter_; taken, as we have
+said, by the eye, the which, though they admit not errors of above a
+Minute, yet they suffice not for the determination of the exact
+greatness of the Spheres of those Stars. But now that I have hit upon
+a way of taking such measures without failing, scarce in a very few
+Seconds, I will continue the observation to the very occultation of
+_JUPITER_, which shall serve to bring us to the perfect knowledge of
+the Motions, and Magnitudes of the Orbes of the said Planets, together
+also with some other consequences thence arising. I adde to these
+things the observation of some obscure Spots[1], which are discovered in
+the Solar Body, which changing, position in that, propounds to our
+consideration a great argument either that the Sun revolves in it
+selfe, or that perhaps other Starrs, in like manner as _Venus_ and
+_Mercury_, revolve about it, invisible in other times, by reason of
+their small digressions, lesse than that of _Mercury_, and only
+visible when they interpose between the Sun and our eye, or else hint
+the truth of both this and that; the certainty of which things ought
+not to be contemned, nor omitted.
+
+     [1] The Authors Observations of the Solar Spots
+
+  _Continuall observation hath at last assured me that these Spots
+  are matters contiguous to the Body of the Sun, there continually
+  produced in great number, and afterwards dissolved, some in a
+  shorter, some in a longer time, and to be by the Conversion or
+  Revolution of the Sun in it selfe, which in a Lunar Moneth, or
+  thereabouts, finisheth its Period, caried about in a Circle, an
+  accident great of it selfe, and greater for its Consequences._
+
+As to the other particular in the next place [B] Many causes have
+moved me to write the present Tract, the subject whereof, is the
+Dispute which I held some dayes since, with some learned men of this
+City, about which, as your Highnesse knows, have followed many
+Discourses: The principall of which Causes hath been the Intimation of
+your Highnesse, having commended to me Writing, as a singular means to
+make true known from false, reall from apparent Reasons, farr better
+than by Disputing vocally, where the one or the other, or very often
+both the Disputants, through too greate heate, or exalting of the
+voyce, either are not understood, or else being transported by
+ostentation of not yeilding to one another, farr from the first
+Proposition, with the novelty, of the various Proposals, confound both
+themselves and their Auditors.
+
+    [B] The occasion inducing the Author to write this Treatise.
+
+Moreover, it seemed to me convenient to informe your Highnesse of all
+the sequell, concerning the Controversie of which I treat, as it hath
+been advertised often already by others: and because the Doctrine
+which I follow, in the discussion of the point in hand, is different
+from that of _Aristotle_; and interferes with his Principles, I have
+considered that against the Authority of that most famous Man, which
+amongst many makes all suspected that comes not from the Schooles of
+the Peripateticks, its farr better to give ones Reasons by the Pen
+than by word of mouth, and therfore I resolved to write the present
+discourse: in which yet I hope to demonstrate that it was not out of
+capritiousnesse, or for that I had not read or understood _Aristotle_,
+that I sometimes swerve from his opinion, but because severall Reasons
+perswade me to it, and the same _Aristotle_ hath tought me to fix my
+judgment on that which is grounded upon Reason, and not on the bare
+Authority of the Master[2]; and it is most certaine according to the
+sentence of _Alcinoos_, that philosophating should be free. Nor is the
+resolution of our Question in my judgment without some benefit to the
+Universall[3], forasmuch as treating whether the figure of Solids
+operates, or not, in their going, or not going to the bottome in
+Water, in occurrences of building Bridges or other Fabricks on the
+Water, which happen commonly in affairs of grand import, it may be of
+great availe to know the truth.
+
+    [2] _Aristotle_ prefers Reason to the Authority ofan Author.
+
+    [3] The benefit of this Argument.
+
+I say therfore, that being the last Summer in company with certain
+Learned men, it was said in the argumentation; That Condensation was
+the propriety of Cold[4], and there was alledged for instance, the
+example of Ice: now I at that time said, that, in my judgment, the Ice
+should be rather Water rarified than condensed[5], and my reason was,
+because Condensation begets diminution of Mass, and augmentation of
+gravity, and Rarifaction causeth greater Lightness, and augmentarion
+of Masse: and Water in freezing, encreaseth in Masse, and the Ice made
+thereby is lighter than the Water on which it swimmeth.
+
+    [4] Condensation the Propriety of Cold, according to the
+    Peripateticks.
+
+    [5] Ice rather water rarified, than condensed, and why:
+
+  _What I say, is manifest, because, the medium subtracting from the
+  whole Gravity of Sollids the weight of such another Masse of the
+  said Medium; as_ Archimedes _proves in his_ [C] First Booke De
+  Insidentibus Humido; _when ever the Masse of the said Solid
+  encreaseth by Distraction, the more shall the_ Medium _detract from
+  its entire Gravity; and lesse, when by Compression it shall be
+  condensed and reduced to a lesse Masse._
+
+    [C] In lib: 1. of Natation of Bodies Prop. 7.
+
+    [Sidenote: Figure operates not in the Natation of Sollids.]
+
+It was answered me, tha{t} that proceeded not from the greater Levity,
+but from the Figure, large and flat, which not being able to penetrate
+the Resistance of the Water, is the cause that it submergeth not. I
+replied, that any piece of Ice, of whatsoever Figure, swims upon the
+Water, a manifest signe, that its being never so flat and broad, hath
+not any part in its floating: and added, that it was a manifest proofe
+hereof to see a piece of Ice of very broad Figure being thrust to the
+botome of the Water, suddenly return to flote atoppe, which had it
+been more grave, and had its swimming proceeded from its Forme, unable
+to penetrate the Resistance of the _Medium_, that would be altogether
+impossible; I concluded therefore, that the Figure was in sort a Cause
+of the Natation or Submersion of Bodies, but the greater or lesse
+Gravity in respect of the Water: and therefore all Bodyes heavier than
+it of what Figure soever they be, indifferently go to the bottome, and
+the lighter, though of any figure, float indifferently on the top: and
+I suppose that those which hold otherwise, were induced to that
+beliefe, by seeing how that diversity of Formes or Figures, greatly
+altereth the Velosity, and Tardity of Motion; so that Bodies of Figure
+broad and thin, descend far more leasurely into the Water, than those
+of a more compacted Figure, though both made of the same Matter: by
+which some might be induced to believe that the Dilatation of the
+Figure might reduce it to such amplenesse that it should not only
+retard but wholly impede and take away the Motion, which I hold to be
+false. Upon this Conclusion, in many dayes discourse, was spoken much,
+and many things, and divers Experiments produced, of which your
+Highnesse heard, and saw some, and in this discourse shall have all
+that which hath been produced against my Assertion, and what hath been
+suggested to my thoughts on this matter, and for confirmation of my
+Conclusion: which if it shall suffice to remove that (as I esteem
+hitherto false) Opinion, I shall thinke I have not unprofitably spent
+my paynes and time. and although that come not to passe, yet ought I
+to promise another benefit to my selfe, namely, of attaining the
+knowledge of the truth, by hearing my Fallacyes confuted, and true
+demonstrations produced by those of the contrary opinion.
+
+And to proceed with the greatest plainness and perspicuity that I can
+possible, it is, I conceive, necessary, first of all to declare what
+is the true, intrinsecall, and totall Cause, of the ascending of some
+Sollid Bodyes in the Water, and therein floating; or on the contrary,
+of their sinking and so much the rather in asmuch as I cannot satisfie
+myselfe in that which _Aristotle_ hath left written on this Subject.
+
+    [Sidenote: The cause of the Natation & submersion of Solids in
+    the Water.]
+
+I say then the Cause why some Sollid Bodyes descend to the Bottom of
+Water, is the excesse of their Gravity, above the Gravity of the
+Water; and on the contrary, the excess of the Waters Gravity above the
+Gravity of those, is the Cause that others do not descend, rather that
+they rise from the Bottom, and ascend to the Surface. This was
+subtilly demonstrated by _Archimedes_ in his Book Of the NATATION of
+BODIES: Conferred afterwards by a very grave Author, but, if I erre
+not invisibly, as below for defence of him, I shall endeavour to
+prove.
+
+I, with a different Method, and by other meanes, will endeavour to
+demonstrate the same, reducing the Causes of such Effects to more
+intrinsecall and immediate Principles, in which also are discovered
+the Causes of some admirable and almost incredible Accidents, as that
+would be, that a very little quantity of Water, should be able, with
+its small weight, to raise and sustain a Solid Body, an hundred or a
+thousand times heavier than it.
+
+And because demonstrative Order so requires, I shall define certain
+Termes, and afterwards explain some Propositions, of which, as of
+things true and obvious, I may make use of to my present purpose.
+
+
+
+
+DEFINITION I.
+
+  _I then call equally Grave_ in specie, _those Matters of which equall
+    Masses weigh equally._
+
+
+As if for example, two Balls, one of Wax, and the other of some Wood
+of equall Masse, were also equall in Weight, we say, that such Wood,
+and the Wax are _in specie_ equally grave.
+
+
+
+
+DEFINITION II.
+
+  _But equally grave in Absolute Gravity, we call two Sollids,
+    weighing equally, though of Mass they be unequall._
+
+
+As for example, a Mass of Lead, and another of Wood, that weigh each
+ten pounds, I call equall in Absolute Gravity, though the Mass of the
+Wood be much greater then that of the Lead.
+
+_And, consequently, less Grave_ in specie.
+
+
+
+
+DEFINITION III.
+
+  _I call a Matter more Grave_ in specie _than another, of which a
+    Mass, equall to a Mass of the other, shall weigh more._
+
+
+And so I say, that Lead is more grave _in specie_ than Tinn, because
+if you take of them two equall Masses, that of the Lead weigheth more.
+
+
+
+
+DEFINITION IV.
+
+  _But I call that Body more grave absolutely than this, if that
+    weigh more than this, without any respect had to the Masses._
+
+
+And thus a great piece of Wood is said to weigh more than a little
+lump of Lead, though the Lead be _in specie_ more heavy than the Wood.
+And the same is to be understood of the less grave _in specie_, and
+the less grave absolutely.
+
+These Termes defined, I take from the Mechanicks two Principles: the
+first is, that
+
+
+
+
+AXIOME. I.
+
+  _Weights absolutely equall, moved with equall Velocity, are of
+    equall Force and Moment in their operations._
+
+
+
+
+_DEFINITION V._
+
+  Moment, amongst Mechanicians, signifieth that Vertue, that Force,
+    or that Efficacy, with which the Mover moves, and the Moveable
+    resists.
+
+
+  _Which Vertue dependes not only on the simple Gravity, but on the
+  Velocity of the Motion, and on the diverse Inclinations of the
+  Spaces along which the Motion is made: For a descending Weight
+  makes a greater Impetus in a Space much declining, than in one less
+  declining; and in summe, what ever is the occasion of such Vertue,
+  it ever retaines the name of Moment; nor in my Judgement, is this
+  sence new in our Idiome, for, if I mistake not, I think we often
+  say; This is a weighty businesse, but the other is of small moment:
+  and we consider lighter matters and let pass those of Moment; a
+  Metaphor, I suppose, taken from the Mechanicks._
+
+As for example, two weights equall in absolute Gravity, being put
+into a Ballance of equall Arms, they stand in _Equilibrium_, neither
+one going down, nor the other up: because the equality of the
+Distances of both, from the Centre on which the Ballance is supported,
+and about which it moves, causeth that those weights, the said
+Ballance moving, shall in the same Time move equall Spaces, that is,
+shall move with equall Velocity, so that there is no reason for which
+this Weight should descend more than that, or that more than this; and
+therefore they make an _Equilibrium_, and their Moments continue of
+semblable and equall Vertue.
+
+The second Principle is; That
+
+
+
+
+AXIOME II.
+
+  _The Moment and Force of the Gravity, is encreased by the Velocity
+    of the Motion._
+
+
+So that Weights absolutely equall, but conjoyned with Velocity
+unequall, are of Force, Moment and Vertue unequall: and the more
+potent, the more swift, according to the proportion of the Velocity of
+the one, to the Velocity of the other. Of this we have a very
+pertinent example in the Balance or Stiliard of unequall Arms, at
+which Weights absolutely equall being suspended, they do not weigh
+down, and gravitate equally, but that which is at a greater distance
+from the Centre, about which the Beam moves, descends, raising the
+other, and the Motion of this which ascends is slow, and the other
+swift: and such is the Force and Vertue, which from the Velocity of
+the Mover, is conferred on the Moveable, which receives it, that it
+can exquisitely compensate, as much more Weight added to the other
+slower Moveable: so that if of the Arms of the Balance, one were ten
+times as long as the other, whereupon in the Beames moving about the
+Centre, the end of that would go ten times as far as the end of this,
+a Weight suspended at the greater distance, may sustain and poyse
+another ten times more grave absolutely than it: and that because the
+Stiliard moving, the lesser Weight shall move ten times faster than
+the bigger. It ought alwayes therefore to be understood, that Motions
+are according to the same Inclinations, namely, that if one of the
+Moveables move perpendicularly to the Horizon, then the other makes
+its Motion by the like Perpendicular; and if the Motion of one were to
+be made Horizontally; that then the other is made along the same
+Horizontall plain: and in summe, alwayes both in like Inclinations.
+This proportion between the Gravity and Velocity is found in all
+Mechanicall Instruments: and is considered by _Aristotle_, as a
+Principle in his _Mechanicall Questions_; whereupon we also may take
+it for a true Assumption, That
+
+
+
+
+AXIOME III.
+
+  _Weights absolutely unequall, do alternately counterpoyse and
+    become of equall Moments, as oft as their Gravities, with
+    contrary proportion, answer to the Velocity of their Motions._
+
+
+That is to say, that by how much the one is less grave than the other,
+by so much is it in a constitution of moving more swiftly than that.
+
+Having prefatically explicated these things, we may begin to enquire,
+what Bodyes those are which totally submerge in Water, and go to the
+Bottom, and which those that by constraint float on the top, so that
+being thrust by violence under Water, they return to swim, with one
+part of their Mass visible above the Surface of the Water: and this we
+will do by considering the respective operation of the said Solids,
+and of Water: Which operation followes the Submersion and sinking; and
+this it is[6], That in the Submersion that the Solid maketh, being
+depressed downwards by its proper Gravity, it comes to drive away the
+water from the place where it successively subenters, and the water
+repulsed riseth and ascends above its first levell, to which Ascent on
+the other side it, as being a grave Body of its own nature, resists:
+And because the descending Solid more and more immerging, greater and
+greater quantity of Water ascends, till the whole Sollid be submerged;
+its necessary to compare the Moments of the Resistance of the water to
+Ascension, with the Moments of the pressive Gravity of the Solid: And
+if the Moments of the Resistance of the water, shall equalize the
+Moments of the Solid, before its totall Immersion[7]; in this case
+doubtless there shall be made an _Equilibrium_, nor shall the Body
+sink any farther. But if the Moment of the Solid, shall alwayes exceed
+the Moments wherewith the repulsed water successively makes
+Resistance[8], that Solid shall not only wholly submerge under water, but
+shall descend to the Bottom. But if, lastly, in the instant of totall
+Submersion, the equality shall be made between the Moments of the
+prement Solid, and the resisting Water[9]; then shall rest, ensue, and
+the said Solid shall be able to rest indifferently, in whatsoever part
+of the water. By this time is manifest the necessity of comparing the
+Gravity of the water, and of the Solid[10]; and this comparison might at
+first sight seem sufficient to conclude and determine which are the
+Solids that float a-top, and which those that sink to the Bottom in
+the water, asserting that those shall float which are lesse grave _in
+specie_ than the water, and those submerge, which are _in specie_ more
+grave. For it seems in appearance, that the Sollid in sinking
+continually, raiseth so much Water in Mass, as answers to the parts of
+its own Bulk submerged: whereupon it is impossible, that a Solid less
+grave _in specie_, than water, should wholly sink, as being unable to
+raise a weight greater than its own, and such would a Mass of water
+equall to its own Mass be. And likewise it seems necessary, that the
+graver Solids do go to the Bottom, as being of a Force more than
+sufficient for the raising a Masse of water, equall to its own, though
+inferiour in weight. Nevertheless the business succeeds otherwise: and
+though the Conclusions are true, yet are the Causes thus assigned
+deficient, nor is it true, that the Solid in submerging, raiseth and
+repulseth Masses of Water, equall to the parts of it self submerged;
+but the Water repulsed, is alwayes less than the parts of the Solid
+submerged[11]: and so much the more by how much the Vessell in which the
+Water is contained is narrower: in such manner that it hinders not,
+but that a Solid may submerge all under Water, without raising so much
+Water in Mass, as would equall the tenth or twentieth part of its own
+Bulk: like as on the contrary, a very small quantity of Water, may
+raise a very great Solid Mass[12], though such Solid should weigh
+absolutely a hundred times as much, or more, than the said Water, if
+so be that the Matter of that same Solid be _in specie_ less grave
+than the Water. And thus a great Beam, as suppose of a 1000 weight,
+may be raised and born afloat by Water, which weighs not 50: and this
+happens when the Moment of the Water is compensated by the Velocity of
+its Motion.
+
+    [6] How the submersion of Solids in the Water, is effected.
+
+    [7] What Solids shall float on the Water.
+
+    [8] What Solids shall sinke to the botome.
+
+    [9] What Solids shall rest in all places of the Water.
+
+    [10] The Gravitie of the Water and Solid must be compared in all
+    Problems, of Natation of Bodies.
+
+    [11] The water repelled is ever less than the parts of the Sollid
+    submerged.
+
+    [12] _A_ small quantity of water, may float a very great Solid
+    Mass.
+
+But because such things, propounded thus in abstract, are somewhat
+difficult to be comprehended, it would be good to demonstrate them by
+particular examples; and for facility of demonstration, we will
+suppose the Vessels in which we are to put the Water, and place the
+Solids, to be inviron'd and included with sides erected perpendicular
+to the Plane of the Horizon, and the Solid that is to be put into such
+vessell to be either a streight Cylinder, or else an upright Prisme.
+
+_The which proposed and declared, I proceed to demonstrate the truth
+of what hath been hinted, forming the ensuing Theoreme._
+
+
+
+
+_THEOREME I._
+
+    [Sidenote: The Proportion of the water raised to the Solid
+    submerged.]
+
+  The Mass of the Water which ascends in the submerging of a Solid,
+    Prisme or Cylinder, or that abaseth in taking it out, is less
+    than the Mass of the said Solid, so depressed or advanced: and
+    hath to it the same proportion, that the Surface of the Water
+    circumfusing the Solid, hath to the same circumfused Surface,
+    together with the Base of the Solid.
+
+
+_Let the Vessell be A B C D, and in it the Water raised up to the
+Levell E F G, before the Solid Prisme H I K be therein immerged; but
+after that it is depressed under Water, let the Water be raised as
+high as the Levell L M, the Solid H I K shall then be all under Water,
+and the Mass of the elevated Water shall be L G, which is less than
+the Masse of the Solid depressed, namely of H I K, being equall to the
+only part E I K, which is contained under the first Levell E F G.
+Which is manifest, because if the Solid H I K be taken out, the Water
+I G shall return into the place occupied by the Mass E I K, where it
+was continuate before the submersion of the Prisme. And the Mass L G
+being equall to the Mass E K: adde thereto the Mass E N, and it shall
+be the whole Mass E M, composed of the parts of the Prisme E N, and of
+the Water N F, equall to the whole Solid H I K: And, therefore, the
+Mass L G shall have the same proportion to E M, as to the Mass H I K:
+But the Mass L G hath the same proportion to the Mass E M, as the
+Surface L M hath to the Surface M H: Therefore it is manifest, that
+the Mass of Water repulsed L G, is in proportion to the Mass of the
+Solid submerged H I K; as the Surface L M, namely, that of the Water
+ambient about the Sollid, to the whole Surface H M, compounded of the
+said ambient water, and the Base of the Prisme H N. But if we suppose
+the first Levell of the Water the according to the Surface H M, and
+the Prisme allready submerged H I K; and after to be taken out and
+raised to E A O, and the Water to be faln from the first Levell H L M
+as low as E F G; It is manifest, that the Prisme E A O being the same
+with H I K, its superiour part H O, shall be equall to the inferiour E
+I K: and remove the common part E N, and, consequently, the Mass of
+the Water L G is equall to the Mass H O; and, therefore, less than the
+Solid, which is without the Water, namely, the whole Prisme E A O, to
+which likewise, the said Mass of Water abated L G, hath the same
+proportion, that the Surface of the Waters circumfused L M hath to the
+same circumfused Surface, together with the Base of the Prisme A O:
+which hath the same demonstration with the former case above._
+
+[Illustration]
+
+_And from hence is inferred, that the Mass of the Water, that riseth
+in the immersion of the Solid, or that ebbeth in elevating it, is not
+equall to all the Mass of the Solid, which is submerged or elevated,
+but to that part only, which in the immersion is under the first
+Levell of the Water, and in the elevation remaines above the first
+Levell: Which is that which was to be demonstrated. We will now pursue
+the things that remain._
+
+And first we will demonstrate that,
+
+
+
+
+THEOREME II.
+
+    [Sidenote: The proportion of the water abated, to the Solid
+    raised.]
+
+  _When in one of the above said Vessels, of what ever breadth,
+    whether wide or narrow, there is placed such a Prisme or
+    Cylinder, inviron'd with Water, if we elevate that Solid
+    perpendicularly, the Water circumfused shall abate, and the
+    Abatement of the Water, shall have the same proportion to the
+    Elevation of the Prisme, as one of the Bases of the Prisme, hath
+    to the Surface of the Water Circumfused._
+
+
+[Illustration]
+
+Imagine in the Vessell, as is aforesaid, the Prisme A C D B to be
+placed, and in the rest of the Space the Water to be diffused as far
+as the Levell E A: and raising the Solid, let it be transferred to G
+M, and let the Water be abased from E A to N O: I say, that the
+descent of the Water, measured by the Line A O, hath the same
+proportion to the rise of the Prisme, measured by the Line G A, as the
+Base of the Solid G H hath to the Surface of the Water N O. The which
+is manifest: because the Mass of the Solid G A B H, raised above the
+first Levell E A B, is equall to the Mass of Water that is abased E N
+O A. Therefore, E N O A and G A B H are two equall Prismes; for of
+equall Prismes, the Bases answer contrarily to their heights:
+Therefore, as the Altitude A O is to the Altitude A G, so is the
+Superficies or Base G H to the Surface of the Water N O. If therefore,
+for example, a Pillar were erected in a waste Pond full of Water, or
+else in a Well, capable of little more then the Mass of the said
+Pillar, in elevating the said Pillar, and taking it out of the Water,
+according as it riseth, the Water that invirons it will gradually
+abate, and the abasement of the Water at the instant of lifting out
+the Pillar, shall have the same proportion, that the thickness of the
+Pillar hath to the excess of the breadth of the said Pond or Well,
+above the thickness of the said Pillar: so that if the breadth of the
+Well were an eighth part larger than the thickness of the Pillar, and
+the breadth of the Pond twenty five times as great as the said
+thickness, in the Pillars ascending one foot, the water in the Well
+shall descend seven foot, and that in the Pond only 1/25 of a foot.
+
+    [Sidenote: Why a Solid less grave _in specie_ than water, stayeth
+    not under water, in very small depths:]
+
+This Demonstrated, it will not be difficult to show the true cause,
+how it comes to pass, that,
+
+
+
+
+THEOREME III.
+
+  _A Prisme or regular Cylinder, of a substance specifically less
+    grave than Water, if it should be totally submerged in Water,
+    stayes not underneath, but riseth, though the Water circumfused
+    be very little, and in absolute Gravity, never so much inferiour
+    to the Gravity of the said Prisme._
+
+
+Let then the Prisme A E F B, be put into the Vessell C D F B, the same
+being less grave _in specie_ than the Water: and let the Water infused
+rise to the height of the Prisme: I say, that the Prisme left at
+liberty, it shall rise, being born up by the Water circumfused C D E
+A. For the Water C E being specifically more grave than the Solid A F,
+the absolute weight of the water C E, shall have greater proportion to
+the absolute weight of the Prisme A F, than the Mass C E hath to the
+Mass A F (in regard the Mass hath the same proportion to the Mass,
+that the weight absolute hath to the weight absolute, in case the
+Masses are of the same Gravity _in specie_.) But the Mass C E is to
+the Mass A F, as the Surface of the water A C, is to the Superficies,
+or Base of the Prisme A B; which is the same proportion as the ascent
+of the Prisme when it riseth, hath to the descent of the Water
+circumfused C E.
+
+[Illustration]
+
+Therefore, the absolute Gravity of the water C E, hath greater
+proportion to the absolute Gravity of the Prisme A F; than the Ascent
+of the Prisme A F, hath to the descent of the said water C E. The
+Moment, therefore, compounded of the absolute Gravity of the water C
+E, and of the Velocity of its descent, whilst it forceably repulseth
+and raiseth the Solid A F, is greater than the Moment compounded of
+the absolute Gravity of the Prisme A F, and of the Tardity of its
+ascent, with which Moment it contrasts and resists the repulse and
+violence done it by the Moment of the water: Therefore, the Prisme
+shall be raised.
+
+    [Sidenote: The Proportion according to which the Submersion &
+    Natation of Solids is made.]
+
+It followes, now, that we proceed forward to demonstrate more
+particularly, how much such Solids shall be inferiour in Gravity to
+the water elevated; namely, what part of them shall rest submerged,
+and what shall be visible above the Surface of the water: but first it
+is necessary to demonstrate the subsequent Lemma.
+
+
+
+
+LEMMA I.
+
+    [Sidenote: The absolute Gravity of Solids, are in a proportion
+    compounded of their Specifick Gravities, and of their Masses.]
+
+  _The absolute Gravities of Solids, have a proportion compounded of
+    the proportions of their specificall Gravities, and of their
+    Masses._
+
+
+[Illustration]
+
+Let A and B be two Solids. I say, that the Absolute Gravity of A,
+hath to the Absolute Gravity of B, a proportion compounded of the
+proportions of the specificall Gravity of A, to the Specificall
+Gravity of B, and of the Mass A to the Mass B. Let the Line D have the
+same proportion to E, that the specifick Gravity of A, hath to the
+specifick Gravity of B; and let E be to F, as the Mass A to the Mass
+B: It is manifest, that the proportion of D to F, is compounded of the
+proportions D and E; and E and F. It is requisite, therefore, to
+demonstrate, that as D is to F, so the absolute Gravity of A, is to
+the absolute Gravity of B. Take the Solid C, equall in Mass to the
+Solid A, and of the same Gravity _in specie_ with the Solid B.
+Because, therefore, A and C are equall in Mass, the absolute Gravity
+of A, shall have to the absolute Gravity of C, the same proportion, as
+the specificall Gravity of A, hath to the specificall Gravity of C, or
+of B, which is the same _in specie_; that is, as D is to E. And,
+because, C and B are of the same Gravity _in specie_, it shall be,
+that as the absolute weight of C, is to the absolute weight of B, so
+the Mass C, or the Mass A, is to the Mass B; that is, as the Line E to
+the Line F. As therefore, the absolute Gravity of A, is to the
+absolute Gravity of C, so is the Line D to the Line E: and, as the
+absolute Gravity of C, is to the absolute Gravity of B, so is the Line
+E to the Line F: Therefore, by Equality of proportion, the absolute
+Gravity of A, is to the absolute Gravity of B, as the Line D to the
+Line F: which was to be demonstrated. I proceed now to demonstrate,
+how that,
+
+
+
+
+THEOREME IV.
+
+    [Sidenote: The proportion of water requisite to make a Solid
+    swim:]
+
+  _If a Solid, Cylinder, or Prisme, lesse grave specifically than the
+    Water, being put into a Vessel, as above, of whatsoever
+    greatnesse, and the Water, be afterwards infused, the Solid shall
+    rest in the bottom, unraised, till the Water arrive to that part
+    of the Altitude, of the said Prisme, to which its whole Altitude
+    hath the same proportion, that the Specificall Gravity of the
+    Water, hath to the Specificall Gravity of the said Solid: but
+    infusing more Water, the Solid shall ascend._
+
+
+[Illustration]
+
+Let the Vessell be M L G N of any bigness, and let there be placed in
+it the Solid Prisme D F G E, less grave _in specie_ than the water;
+and look what proportion the Specificall Gravity of the water, hath to
+that of the Prisme, such let the Altitude D F, have to the Altitude F
+B. I say, that infusing water to the Altitude F B, the Solid D G shall
+not float, but shall stand in _Equilibrium_, so, that that every
+little quantity of water, that is infused, shall raise it. Let the
+water, therefore, be infused to the Levell A B C; and; because the
+Specifick Gravity of the Solid D G, is to the Specifick Gravity of the
+water, as the altitude B F is to the altitude F D; that is, as the
+Mass B G to the Mass G D; as the proportion of the Mass B G is to the
+Mass G D, as the proportion of the Mass G D is to the Mass A F, they
+compose the Proportion of the Mass B G to the Mass A F. Therefore, the
+Mass B G is to the Mass A F, in a proportion compounded of the
+proportions of the Specifick Gravity of the Solid G D, to the
+Specifick Gravity of the water, and of the Mass G D to the Mass A F:
+But the same proportions of the Specifick Gravity of G D, to the
+Specifick Gravity of the water, and of the Mass G D to the Mass A F,
+do also by the precedent _Lemma_, compound the proportion of the
+absolute Gravity of the Solid D G, to the absolute Gravity of the Mass
+of the water A F: Therefore, as the Mass B G is to the Mass A F, so is
+the Absolute Gravity of the Solid D G, to the Absolute Gravity of the
+Mass of the water A F. But as the Mass B G is to the Mass A F; so is
+the Base of the Prisme D E, to the Surface of the water A B; and so is
+the descent of the water A B, to the Elevation of the Prisme D G;
+Therefore, the descent of the water is to the elevation of the Prisme,
+as the absolute Gravity of the Prisme, is to the absolute Gravity of
+the water: Therefore, the Moment resulting from the absolute Gravity
+of the water A F, and the Velocity of the Motion of declination, with
+which Moment it forceth the Prisme D G, to rise and ascend, is equall
+to the Moment that results from the absolute Gravity of the Prisme D
+G, and from the Velocity of the Motion, wherewith being raised, it
+would ascend: with which Moment it resists its being raised: because,
+therefore, such Moments are equall, there shall be an _Equilibrium_
+between the water and the Solid. And, it is manifest, that putting a
+little more water unto the other A F, it will increase the Gravity and
+Moment, whereupon the Prisme D G, shall be overcome, and elevated till
+that the only part B F remaines submerged. Which is that that was to
+be demonstrated.
+
+
+COROLLARY I.
+
+    [Sidenote: _H_ow far Solids less grave _in specie_ than water, do
+    submerge.]
+
+  _By what hath been demonstrated, it is manifest, that Solids less
+    grave_ in specie _than the water, submerge only so far, that as
+    much water in Mass, as is the part of the Solid submerged, doth
+    weigh absolutely as much as the whole Solid._
+
+For, it being supposed, that the Specificall Gravity of the water, is
+to the Specificall Gravity of the Prisme D G, as the Altitude D F, is
+to the Altitude F B; that is, as the Solid D G is to the Solid B G; we
+might easily demonstrate, that as much water in Mass as is equall to
+the Solid B G, doth weigh absolutely as much as the whole Solid D G;
+For, by the _Lemma_ foregoing, the Absolute Gravity of a Mass of
+water, equall to the Mass B G, hath to the Absolute Gravity of the
+Prisme D G, a proportion compounded of the proportions, of the Mass B
+G to the Mass G D, and of the Specifick Gravit{y} of the water, to the
+Specifick Gravity of the Prisme: But the Gravity _in specie_ of the
+water, to the Gravity _in specie_ of the Prisme, is supposed to be as
+the Mass G D to the Mass G B. Therefore, the Absolute Gravity of a
+Mass of water, equall to the Mass B G, is to the Absolute Gravity of
+the Solid D G, in a proportion compounded of the proportions, of the
+Mass B G to the Mass G D, and of the Mass D G to the Mass G B; which
+is a proportion of equalitie. The Absolute Gravity, therefore, of a
+Mass of Water equall to the part of the Mass of the Prisme B G, is
+equall to the Absolute Gravity of the whole Solid D G.
+
+
+COROLLARY II.
+
+    [Sidenote: _A_ Rule to equilibrate Solids in the water.]
+
+  _It followes, moreover, that a Solid less grave than the water,
+    being put into a Vessell of any imaginable greatness, and water
+    being circumfused about it to such a height, that as much water
+    in Mass, as is the part of the Solid submerged, do weigh
+    absolutely as much as the whole Solid; it shall by that water be
+    justly sustained, be the circumfused Water in quantity greater or
+    lesser._
+
+[Illustration]
+
+For, if the Cylinder or Prisme M, less grave than the water, _v. gra._
+in Subsequiteriall proportion, shall be put into the capacious Vessell
+A B C D, and the water raised about it, to three quarters of its
+height, namely, to its Levell A D: it shall be sustained and exactly
+poysed in _Equilibrium_. The same will happen; if the Vessell E N S F
+were very small, so, that between the Vessell and the Solid M, there
+were but a very narrow space, and only capable of so much water, as
+the hundredth part of the Mass M, by which it should be likewise
+raised and erected, as before it had been elevated to three fourths of
+the height of the Solid: which to many at the first sight, may seem a
+notable Paradox, and beget a conceit, that the Demonstration of these
+effects, were sophisticall and fallacious: but, for those who so
+repute it, the Experiment is a means that may fully satisfie them. But
+he that shall but comprehend of what Importance Velocity of Motion is,
+and how it exactly compensates the defect and want of Gravity, will
+cease to wonder, in considering that at the elevation of the Solid M,
+the great Mass of water A B C D abateth very little, but the little
+Mass of water E N S F decreaseth very much, and in an instant, as the
+Solid M before did rise, howbeit for a very short space: Whereupon the
+Moment, compounded of the small Absolute Gravity of the water E N S F,
+and of its great Velocity in ebbing, equalizeth the Force and and
+Moment, that results from the composition of the immense Gravity of
+the water A B C D, with its great slownesse of ebbing; since that in
+the Elevation of the Sollid M, the abasement of the lesser water E S,
+is performed just so much more swiftly than the great Mass of water A
+C, as this is more in Mass than that which we thus demonstrate.
+
+    [Sidenote: _T_he proportion according to which water riseth and
+    falls in different Vessels at the Immersion and Elevation of
+    Solids.]
+
+In the rising of the Solid M, its elevation hath the same proportion
+to the circumfused water E N S F, that the Surface of the said water,
+hath to the Superficies or Base of the said Solid M; which Base hath
+the same proportion to the Surface of the water A D, that the
+abasement or ebbing of the water A C, hath to the rise or elevation of
+the said Solid M. Therefore, by Perturbation of proportion, in the
+ascent of the said Solid M, the abasement of the water A B C D, to the
+abasement of the water E N S F, hath the same proportion, that the
+Surface of the water E F, hath to the Surface of the water A D; that
+is, that the whole Mass of the water E N S F, hath to the whole Mass A
+B C D, being equally high: It is manifest, therefore, that in the
+expulsion and elevation of the Solid M, the water E N S F shall exceed
+in Velocity of _M_otion the water A B C D, asmuch as it on the other
+side is exceeded by that in quantity: whereupon their Moments in such
+operations, are mutually equall.
+
+[Illustration]
+
+  _And, for ampler confirmation, and clearer explication of this, let
+  us consider the present Figure, (which if I be not deceived, may
+  serve to detect the errors of some Practick Mechanitians who upon a
+  false foundation some times attempt impossible enterprizes,) in
+  which, unto the large Vessell E I D F, the narrow Funnell or Pipe I
+  C A B is continued, and suppose water infused into them, unto the
+  Levell L G H, which water shall rest in this position, not without
+  admiration in some, who cannot conceive how it can be, that the
+  heavie charge of the great Mass of water G D, pressing downwards,
+  should not elevate and repulse the little quantity of the other,
+  contained in the Funnell or Pipe C L, by which the descent of it is
+  resisted and hindered: But such wonder shall cease, if we begin to
+  suppose the water G D to be abased only to Q D, and shall
+  afterwards consider, what the water C L hath done, which to give
+  place to the other, which is descended from the Levell G H, to the
+  Levell Q O, shall of necessity have ascended in the same time, from
+  the Levell L unto A B. And the ascent L B, shall be so much greater
+  than the descent G Q, by how much the breadth of the Vessell G D,
+  is greater than that of the Funnell I C; which, in summe, is as
+  much as the water G D, is more than the water L C: but in regard
+  that the Moment of the Velocity of the Motion, in one Moveable,
+  compensates that of the Gravity of another what wonder is it, if
+  the swift ascent of the lesser Water C L, shall resist the slow
+  descent of the greater G D?_
+
+The same, therefore, happens in this operation, as in rhe Stilliard,
+in which a weight of two pounds counterpoyseth an other of 200,
+asoften as that shall move in the same time, a space 100 times greater
+than this: which falleth out when one Arme of the Beam is an hundred
+times as long as the other. Let the erroneous opinion of those
+therefore cease, who hold that a Ship is better, and easier born up in
+a great abundance of water, then in a lesser quantity[13], (_this was
+believed by_ Aristotle _in his Problems, Sect. 23, Probl. 2._) it being
+on the contrary true, that its possible, that a Ship may as well float
+in ten Tun of water, as in an Ocean.
+
+    [13] A ship flotes as well in ten Tun of Water as in an Ocean.
+
+    [Sidenote: A Solid specifiaclly graver than the water, cannot be
+    born up by any quantity of it.]
+
+But following our matter, I say, that by what hath been hitherto
+demonstrated, we may understand how, that
+
+
+COROLLARY III.
+
+  _One of the above named Solids, when more grave_ in specie _than the
+    water, can never be sustained, by any whatever quantity of it._
+
+For having seen how that the Moment wherewith such a Solid, as grave
+_in specie_ as the water, contrasts with the Moment of any Mass of
+water whatsoever, is able to retain it, even to its totall Submersion,
+without its ever ascending; it remaineth, manifest, that the water is
+far less able to raise it up, when it exceeds the same _in specie_:
+so, that though you infuse water till its totall Submersion, it shall
+still stay at the Bottome, and with such Gravity, and Resistance to
+Elevation, as is the excess of its Absolute Gravity, above the
+Absolute Gravity of a Mass equall to it, made of water, or of a Matter
+_in specie_ equally grave with the water: and, though you should
+moreover adde never so much water above the Levell of that which
+equalizeth the Altitude of the Solid, it shall not, for all that,
+encrease the Pression, or Gravitation, of the parts circumfused about
+the said Solid, by which greater pression, it might come to be
+repulsed; because, the Resistance is not made, but only by those parts
+of the water, which at the Motion of the said Solid do also move, and
+these are those only, which are comprehended by the two Superficies
+equidistant to the Horizon, and their parallels, that comprehend the
+Altitude of the Solid immerged in the water.
+
+I conceive, I have by this time sufficiently declared and opened the
+way to the contemplation of the true, intrinsecall and proper Causes
+of diverse Motions, and of the Rest of many Solid Bodies in diverse
+_Mediums_, and particularly in the water, shewing how all in effect,
+depend on the mutuall excesses of the Gravity of the Moveables and of
+the _Mediums_: and, that which did highly import, removing the
+Objection, which peradventure would have begotten much doubting, and
+scruple in some, about the verity of my Conclusion, namely, how that
+notwithstanding, that the excess of the Gravity of the water, above
+the Gravity of the Solid, demitted into it, be the cause of its
+floating and rising from the Bottom to the Surface, yet a quantity of
+water, that weighs not ten pounds, can raise a Solid that weighs above
+100 pounds: in that we have demonstrated, That it sufficeth, that such
+difference be found between the Specificall Gravities of the _Mediums_
+and Moveables, let the particular and absolute Gravities be what they
+will: insomuch, that a Solid, provided that it be Specifically less
+grave than the water, although its absolute weight were 1000 pounds,
+yet may it be born up and elevated by ten pounds of water, and less:
+and on the contrary, another Solid, so that it be Specifically more
+grave than the water, though in absolute Gravity it were not above a
+pound, yet all the water in the Sea, cannot raise it from the Bottom,
+or float it. This sufficeth me, for my present occasion, to have, by
+the above declared Examples, discovered and demonstrated, without
+extending such matters farther, and, as I might have done, into a long
+Treatise: yea, but that there was a necessity of resolving the above
+proposed doubt, I should have contented my self with that only, which
+is demonstrated by _Archimedes_, in his first _Book De Insidentibus
+humido_[14]: where in generall termes he infers and confirms the same
+Conclusions, namely, that Solids (_a_) less grave than water, swim or
+float upon it, the (_b_) more grave go to the Bottom, and the (_c_)
+equally grave rest indifferently in all places, yea, though they
+should be wholly under water.
+
+    [14] _Of Natation_ (a) _Lib. 1, Prop. 4._ (b) _Id. Lib. 1. Prop.
+    3._ (c) _Id. Lib. 1. Prop. 3._
+
+    [Sidenote: The Authors defence of _Archimedes_ his Doctrine,
+    against the oppositions of _Buonamico_.]
+
+But, because that this Doctrine of Archimedes, perused, transcribed
+and examined by _Signor Francesco Buonamico_, in his _fifth Book of
+Motion, Chap. 29_, and afterwards by him confuted, might by the
+Authority of so renowned, and famous a Philosopher, be rendered
+dubious, and suspected of falsity; I have judged it necessary to
+defend it, if I am able so to do, and to clear _Archimedes_, from
+those censures, with which he appeareth to be charged. _Buonamico_
+rejecteth the Doctrine of _Archimedes_, first[15], as not consentaneous
+with the Opinion of _Aristotle_, adding, that it was a strange thing
+to him, that the Water should exceed the Earth in Gravity[16], seeing on
+the contrary, that the Gravity of water, increaseth, by means of the
+participation of Earth. And he subjoyns presently after[17], that he was
+not satisfied with the Reasons of _Archimedes_, as not being able with
+that Doctrine, to assign the cause whence it comes, that a Boat and a
+Vessell, which otherwise, floats above the water, doth sink to the
+Bottom, if once it be filled with water; that by reason of the
+equality of Gravity, between the water within it, and the other water
+without, it should stay a top; but yet, nevertheless, we see it to go
+to the Bottom.
+
+    [15] His first Objection against the Doctrine of _Archimedes_.
+
+    [16] His Second Objection.
+
+    [17] His third Objection.
+
+He farther addes[18], that _Aristotle_ had clearly confuted the Ancients,
+who said, that light Bodies moved upwards[19], driven by the impulse of
+the more grave Ambient: which if it were so, it should seem of
+necessity to follow, that all naturall Bodies are by nature heavy, and
+none light: For that the same would befall the Fire and Air, if put in
+the Bottom of the water. And, howbeit, _Aristotle_ grants a Pulsion in
+the Elements, by which the Earth is reduced into a Sphericall Figure,
+yet nevertheless, in his judgement; it is not such that it can remove
+grave Bodies from their naturall places, but rather, that it send them
+toward the Centre, to which (as he somewhat obscurely continues to
+say,) the water principally moves, if it in the interim meet not with
+something that resists it, and, by its Gravity, thrusts it out of its
+place: in which case, if it cannot directly, yet at least as well as
+it can, it tends to the Centre: but it happens, that light Bodies by
+such Impulsion, do all ascend upward: but this properly they have by
+nature, as also, that other of swimming. He concludes, lastly[20], that he
+concurs with _Archimedes_ in his Conclusions; but not in the Causes,
+which he would referre to the facile and difficult Separation of the
+_Medium_, and to the predominance of the Elements, so that when the
+Moveable superates the power of the _Medium_; as for example, Lead
+doth the Continuity of water, it shall move thorow it, else not.
+
+    [18] His fourth Objection.
+
+    [19] The _A_ncients denyed _A_bsolute Levity.
+
+    [20] The causes of Natation & Submersion, according to the
+    Peripateticks.
+
+This is all that I have been able to collect, as produced against
+_Archimedes_ by _Signor Buonamico_: who hath not well observed the
+Principles and Suppositions of _Archimedes_; which yet must be false,
+if the Doctrine be false, which depends upon them; but is contented to
+alledge therein some Inconveniences, and some Repugnances to the
+Doctrine and Opinion of _Aristotle_. In answer to which Objections, I
+say, first[21], That the being of _Archimedes_ Doctrine, simply different
+from the Doctrine of _Aristotle_, ought not to move any to suspect it,
+there being no cause, why the Authority of this should be preferred to
+the Authority of the other: but, because, where the decrees of Nature
+are indifferently exposed to the intellectuall eyes of each, the
+Authority of the one and the other, loseth all a{u}thenticalness of
+Perswasion, the absolute power residing in Reason; therefore I pass to
+that which he alledgeth in the second place[22], as an absurd consequent
+of the Doctrine of _Archimedes_, namely, That water should be more
+grave than Earth. But I really find not, that ever _Archimedes_ said
+such a thing, or that it can be rationally deduced from his
+Conclusions: and if that were manifest unto me, I verily believe, I
+should renounce his Doctrine, as most erroneous. Perhaps this
+Deduction of _Buonamico_, is founded upon that which he citeth of the
+Vessel, which swims as long as its voyd of water, but once full it
+sinks to the Bottom, and understanding it of a Vessel of Earth, he
+infers against _Archimedes_ thus: Thou sayst that the Solids which
+swim, are less grave than water: this Vessell swimmeth: therefore,
+this Vessell is lesse grave than water. If this be the Illation. I
+easily answer, granting that this Vessell is lesse grave than water,
+and denying the other consequence, namely, that Earth is less Grave
+than Water. The Vessel that swims occupieth in the water, not only a
+place equall to the Mass of the Earth, of which it is formed; but
+equall to the Earth and to the Air together, contained in its
+concavity. And, if such a Mass compounded of Earth and Air, shall be
+less grave than such another quantity of water, it shall swim, and
+shall accord with the Doctrine of _Archimedes_; but if, again,
+removing the Air, the Vessell shall be filled with water, so that the
+Solid put in the water, be nothing but Earth, nor occupieth other
+place, than that which is only possest by Earth, it shall then go to
+the Bottom, by reason that the Earth is heavier than the water: and
+this corresponds well with the meaning of _Archimedes_. See the same
+effect illustrated, with such another Experiment, In pressing a Viall
+Glass to the Bottom of the water, when it is full of Air, it will meet
+with great resistance, because it is not the Glass alone, that is
+pressed under water, but together with the Glass a great Mass of Air,
+and such, that if you should take as much water, as the Mass of the
+Glass, and of the Air contained in it, you would have a weight much
+greater than that of the Viall, and of its Air: and, therefore, it
+will not submerge without great violence: but if we demit only the
+Glass into the water, which shall be when you shall fill the Glass
+with water, then shall the Glass descend to the Bottom; as superiour
+in Gravity to the water.
+
+    [21] The Authors answer to the first Objection.
+
+    [22] The Authors answer to the second Objection.
+
+Returning, therefore, to our first purpose; I say, that Earth is more
+grave than water, and that therefore, a Solid of Earth goeth to the
+bottom of it; but one may possibly make a composition of Earth and
+Air, which shall be less grave than a like Mass of Water; and this
+shall swim: and yet both this and the other experiment shall very well
+accord with the Doctrine of _Archimedes_. But because that in my
+judgment it hath nothing of difficulty in it, I will not positively
+affirme that _Signor Buonamico_, would by such a discourse object unto
+_Archimedes_ the absurdity of inferring by his doctrine, that Earth
+was less grave than Water, though I know not how to conceive what
+other accident he could have induced thence.
+
+Perhaps such a Probleme (in my judgement false) was read by _Signor
+Buonamico_ in some other Author, by whom peradventure it was
+attributed as a singular propertie, of some particular Water, and so
+comes now to be used with a double errour in confutation of
+_Archimedes_, since he saith no such thing, nor by him that did say it
+was it meant of the common Element of Water.
+
+    [Sidenote: The Authors answer to the third Objection.]
+
+The third difficulty in the doctrine of _Archimedes_ was, that he
+could not render a reason whence it arose, that a piece of Wood, and a
+Vessell of Wood, which otherwise floats, goeth to the bottom, if
+filled with Water. _Signor Buonamico_ hath supposed that a Vessell of
+Wood, and of Wood that by nature swims, as before is said, goes to the
+bottom, if it be filled with water; of which he in the following
+Chapter, which is the 30 of the fifth Book copiously discourseth: but
+I (speaking alwayes without diminution of his singular Learning) dare
+in defence of _Archimedes_ deny this experiment, being certain that a
+piece of Wood which by its nature sinks not in Water, shall not sinke
+though it be turned and converted into the forme of any Vessell
+whatsoever, and then filled with Water: and he that would readily see
+the Experiment in some other tractable Matter, and that is easily
+reduced into several Figures, may take pure Wax, and making it first
+into a Ball or other solid Figure, let him adde to it so much Lead as
+shall just carry it to the bottome, so that being a graine less it
+could not be able to sinke it, and making it afterwards into the forme
+of a Dish, and filling it with Water, he shall finde that without the
+said Lead it shall not sinke, and that with the Lead it shall descend
+with much slowness: & in short he shall satisfie himself, that the
+Water included makes no alteration. I say not all this while, but that
+its possible of Wood to make Barkes, which being filled with water,
+sinke; but that proceeds not through its Gravity, encreased by the
+Water, but rather from the Nailes and other Iron Workes, so that it no
+longer hath a Body less grave than Water, but one mixt of Iron and
+Wood, more grave than a like Masse of Water. Therefore let _Signor
+Buonamico_ desist from desiring a reason of an effect, that is not in
+nature: yea if the sinking of the Woodden Vessell when its full of
+Water, may call in question the Doctrine of _Archimedes_, which he
+would not have you to follow, is on the contrary consonant and
+agreeable to the Doctrine of the Peripateticks, since it aptly
+assignes a reason why such a Vessell must, when its full of Water,
+descend to the bottom; converting the Argument the other way, we may
+with safety say that the Doctrine of _Archimedes_ is true, since it
+aptly agreeth with true experiments, and question the other, whose
+Deductions are fastened upon erroneouss Conclusions. As for the other
+point hinted in this same Instance, where it seemes that _Benonamico_
+understands the same not only of a piece of wood, shaped in the forme
+of a Vessell, but also of massie Wood, which filled, _scilicet_, as I
+believe, he would say, soaked and steeped in Water, goes finally to
+the bottom that happens in some porose Woods, which, while their
+Porosity is replenished with Air, or other Matter less grave than
+Water, are Masses specificially less grave than the said Water, like
+as is that Viall of Glass whilest it is full of Air: but when, such
+light Matter departing, there succeedeth Water into the same
+Porosities and Cavities, there results a compound of Water and Glass
+more grave than a like Mass of Water: but the excess of its Gravity
+consists in the Matter of the Glass, and not in the Water, which
+cannot be graver than it self: so that which remaines of the Wood, the
+Air of its Cavities departing, if it shall be more grave _in specie_
+than Water, fil but its Porosities with Water, and you shall have a
+Compost of Water and of Wood more grave than Water, but not by vertue
+of the Water received into and imbibed by the Porosities, but of that
+Matter of the Wood which remains when the Air is departed: and being
+such it shall, according to the Doctrine of _Archimedes_, goe to the
+bottom, like as before, according to the same Doctrine it did swim.
+
+    [Sidenote: The Authors answer to the fourth Objection.]
+
+As to that finally which presents itself in the fourth place,
+namely, that the _Ancients_ have been heretofore confuted by
+_Aristotle_, who denying Positive and Absolute Levity, and truely
+esteeming all Bodies to be grave, said, that that which moved upward
+was driven by the circumambient Air, and therefore that also the
+Doctrine of _Archimedes_, as an adherent to such an Opinion was
+convicted and confuted: I answer first, that _Signor Buonamico_ in my
+judgement hath imposed upon _Archimedes_, and deduced from his words
+more than ever he intended by them, or may from his Propositions be
+collected, in regard that _Archimedes_ neither denies, nor admitteth
+Positive Levity, nor doth he so much as mention it: so that much less
+ought _Buonamico_ to inferre, that he hath denyed that it might be the
+Cause and Principle of the Ascension of Fire, and other Light Bodies[23]:
+having but only demonstrated, that Solid Bodies more grave than Water
+descend in it, according to the excess of their Gravity above the
+Gravity of that, he demonstrates likewise, how the less grave ascend
+in the same Water[24], accordng to its excess of Gravity, above the
+Gravity of them. So that the most that can be gathered from the
+Demonstration of _Archimedes_ is, that like as the excess of the
+Gravity of the Moveable above the Gravity of the Water, is the Cause
+that it descends therein, so the excess of the Gravity of the water
+above that of the Moveable, is a sufficient Cause why it descends not,
+but rather betakes it self to swim: not enquiring whether of moving
+upwards there is, or is not any other Cause contrary to Gravity: nor
+doth _Archimedes_ discourse less properly than if one should say: If
+the South Winde shall assault the Barke with greater _Impetus_ than is
+the violence with which the Streame of the River carries it towards
+the South, the motion of it shall be towards the North: but if the
+_Impetus_ of the Water shall overcome that of the Winde, its motion
+shall be towards the South. The discourse is excellent and would be
+unworthily contradicted by such as should oppose it, saying: Thou
+mis-alledgest as Cause of the motion of the Bark towards the South,
+the _Impetus_ of the Stream of the Water above that of the South
+Winde; mis-alledgest I say, for it is the Force of the North Winde
+opposite to the South, that is able to drive the Bark towards the
+South. Such an Objection would be superfluous, because he which
+alledgeth for Cause of the Motion the Stream of the Water, denies not
+but that the Winde opposite to the South may do the same, but only
+affirmeth that the force of the Water prevailing over the South Wind,
+the Bark shall move towards the South: and saith no more than is true.
+And just thus when _Archimedes_ saith, that the Gravity of the Water
+prevailing over that by which the moveable descends to the Bottom,
+such moveable shall be raised from the Bottom to the Surface alledgeth
+a very true Cause of such an Accident, nor doth he affirm or deny that
+there is, or is not, a vertue contrary to Gravity, called by some
+Levity, that hath also a power of moving some Matters upwards. Let
+therefore the Weapons of _Signor Buonamico_ be directed against
+_Plato_[25], and other _Ancients_, who totally denying _Levity_, and
+taking all Bodies to be grave, say that the Motion upwards is made,
+not from an intrinsecal Principle of the Moveable, but only by the
+Impulse of the _Medium_; and let _Archimedes_ and his Doctrine escape
+him, since he hath given him no Cause of quarelling with him. But if
+this Apologie, produced in defence of _Archimedes_, should seem to
+some insufficient to free him from the Objections and Arguments,
+produced by _Aristotle_ against _Plato_, and the other _Ancients_, as if
+they did also fight against _Archimedes_, alledging the Impulse of the
+Water as the Cause of the swimming of some Bodies less grave than it[26],
+I would not question, but that I should be able to maintaine the
+Doctrine of _Plato_ and those others to be most true, who absolutely
+deny Levity, and affirm no other Intrinsecal Principle of Motion to be
+in Elementary Bodies save only that towards the Centre of the Earth[27],
+nor no other Cause of moving upwards, speaking of that which hath the
+resemblance of natural Motion, but only the repulse of the _Medium_,
+fluid, and exceeding the Gravity of the Moveable[28]: and as to the
+Reasons of _Aristotle_ on the contrary, I believe that I could be able
+fully to answer them, and I would assay to do it, if it were
+absolutely necessary to the present Matter, or were it not too long a
+Digression for this short Treatise. I will only say, that if there
+were in some of our Ellementary Bodies an Intrinsecall Principle and
+Naturall Inclination to shun the Centre of the Earth, and to move
+towards the Concave of the Moon, such Bodies, without doubt, would
+more swiftly ascend through those _Mediums_ that least oppose the
+Velocity of the Moveable, and these are the more tenuous and subtle;
+as is, for example, the Air in comparison of the Water, we daily
+proving that we can with farre more expeditious Velocity move a Hand
+or a Board to and again in one than in the other[29]: nevertheless, we
+never could finde any Body, that did not ascend much more swiftly in
+the water than in the Air. Yea of Bodies which we see continually to
+ascend in the Water, there is none that having arrived to the confines
+of the Air, do not wholly lose their Motion[30]; even the Air it self,
+which rising with great Celerity through the Water, being once come to
+its Region it loseth all
+
+    [23] Of Natation, Lib. 1. Prop. 7.
+
+    [24] Of Natation, Lib. 1. Prop. 4.
+
+    [25] _Plato_ denyeth Positive Levity.
+
+    [26] The Authors defence of the doctrine of _Plato_ and the
+    _Ancients_, who absolutely deny Levity:
+
+    [27] According to _Plato_ there is no Principle of the Motion, of
+    descent in Naturall Bodies, save that to the Centre.
+
+    [28] No cause of the motion of Ascent, save the Impulse of the
+    _Medium_, exceeding the Moveable in Gravitie.
+
+    [29] Bodies ascend much swifter in the Water, than in the Air.
+
+    [30] All Bodies ascending through Water, lose their Motion,
+    comming to the confines of the Air.
+
+    [Sidenote: The lighter Bodies ascend more swiftly through Water.]
+
+And, howbeit, Experience shewes, that the Bodies, successively less
+grave, do most expeditiously ascend in water, it cannot be doubted,
+but that the Ignean Exhalations do ascend more swiftly through the
+water, than doth the Air: which Air is seen by Experience to ascend
+more swiftly through the Water, than the Fiery Exhalations through the
+Air[31]: Therefore, we must of necessity conclude, that the said
+Exhalations do much more expeditiously ascend through the Water, than
+through the Air; and that, consequently, they are moved by the Impulse
+of the Ambient _Medium_, and not by an intrinsick Principle that is in
+them, of avoiding the Centre of the Earth; to which other grave Bodies
+tend.
+
+    [31] Fiery Exhalations ascend thorow the Water more swiftly than
+    doth the Air; & the Air ascends more swiftly thorow the Water,
+    than Fire thorow the Air.
+
+    [Sidenote: _T_he Authors confutation of the Peripateticks Causes
+    of Natation & Submersion.]
+
+To that which for a finall conclusion, _Signor Buonamico_ produceth
+of going about to reduce the descending or not descending, to the
+easie and uneasie Division of the _Medium_, and to the predominancy of
+the Elements: I answer, as to the first part, that that cannot in any
+manner be admitted as a Cause, being that in none of the Fluid
+_Mediums_, as the Air, the Water, and other Liquids, there is any
+Resistance against Division[32], but all by every the least Force, are
+divided and penetrated, as I will anon demonstrate: so, that of such
+Resistance of Division there can be no Act, since it self is not in
+being. As to the other part, I say, that the predominancy of the
+Elements in Moveables[33], is to be considered, as far as to the excesse
+or defect of Gravity, in relation to the _Medium_: for in that Action,
+the Elements operate not, but only, so far as they are grave or light:
+therefore, to say that the Wood of the Firre sinks not, because Air
+predominateth in it, is no more than to say, because it is less grave
+than the Water. Yea, even the immediate Cause, is its being less grave
+than the Water[34]: and it being under the predominancy of the Air, is the
+Cause of its less Gravity: Therefore, he that alledgeth the
+predominancy of the Element for a Cause, brings the Cause of the
+Cause, and not the neerest and immediate Cause. Now, who knows not
+that the true Cause is the immediate, and not the mediate[35]? Moreover,
+he that alledgeth Gravity, brings a Cause most perspicuous to Sence[36]:
+The cause we may very easily assertain our selves; whether Ebony, for
+example, and Firre, be more or less grave than water: but whether
+Earth or Air predominates in them, who shall make that manifest?
+Certainly, no Experiment can better do it than to observe whether they
+swim or sink. So, that he who knows, not whether such a Solid swims,
+unless when he knows that Air predominates in it, knows not whether it
+swim, unless he sees it swim, for then he knows that it swims, when he
+knows that it is Air that predominates, but knows not that Air hath
+the predominance, unless he sees it swim: therefore, he knows not if
+it swims, till such time as he hath seen it swim.
+
+    [32] Water & other fluids void of Resistance against Division.
+
+    [33] _T_he predominancy of Elements in Moveables to be considered
+    only in relation to their excess or defect of Gravity in reference
+    to the _Medium_.
+
+    [34] _T_he immediate Cause of Natation is that the Moveable is
+    less grave than the Water.
+
+    [35] _T_he Peripateticks alledge for the reason of Natation the
+    Cause of the Cause.
+
+    [36] Gravity a Cause most perspicuous to sence.
+
+Let us not then despise those Hints, though very dark, which Reason,
+after some contemplation, offereth to our Intelligence, and lets be
+content to be taught by _Archimedes_, that then any Body shall
+submerge in water[37], when it shall be specifically more grave than it,
+and that if it shall be less grave[38], it shall of necessity swim, and
+that it will rest indifferently in any place under water, if its
+Gravity be perfectly like to that of the water.
+
+    [37] Lib 1. of Natation Prop. 7
+
+    [38] Id. Lib. 1. Prop. 4.
+
+These things explained and proved[39], I come to consider that which
+offers it self, touching what the Diversity of figure given unto the
+said Moveable hath to do with these Motions and Rests; and proceed to
+affirme, that,
+
+    [39] Id. Lib 1. Prop. 3.
+
+
+
+
+THEOREME V.
+
+    [Sidenote: Diversity of Figure no Cause of its absolute Natation
+    or Submersion.]
+
+  _The diversity of Figures given to this or that Solid, cannot any
+    way be a Cause of its absolute Sinking or Swimming._
+
+
+So that if a Solid being formed, for example, into a Sphericall
+Figure, doth sink or swim in the water, I say, that being formed into
+any other Figure, the same figure in the same water, shall sink or
+swim: nor can such its Motion by the Expansion or by other mutation of
+Figure, be impeded or taken away.
+
+    [Sidenote: The Expansion of Figure, retards the Velocity of the
+    ascent or descent of the Moveable in the water; but doth not
+    deprive it of all Motion.]
+
+The Expansion of the Figure may indeed retard its Velocity, aswell of
+ascent as descent, and more and more according as the said Figure is
+reduced to a greater breadth and thinness: but that it may be reduced
+to such a form as that that same matter be wholly hindred from moving
+in the same water, that I hold to be impossible. In this I have met
+with great contradictors, who producing some Experiments, and in
+perticular a thin Board of Ebony, and a Ball of the same Wood, and
+shewing how the Ball in Water descended to the bottom, and the Board
+being put lightly upon the Water submerged not, but rested; have held,
+and with the Authority of _Aristotle_, confirmed themselves in their
+Opinions, that the Cause of that Rest was the breadth of the Figure,
+u{n}able by its small weight to pierce and penetrate the Resistance of
+the Waters Crassitude, which Resistance is readily overcome by the
+other Sphericall Figure.
+
+This is the Principal point in the present Question, in which I
+perswade my self to be on the right side.
+
+Therefore, beginning to investigate with the examination of exquisite
+Experiments that really the Figure doth not a jot alter the descent or
+Ascent of the same Solids, and having already demonstrated that the
+greater or less Gravity of the Solid in relation to the Gravity of the
+_Medium_ is the cause of Descent or Ascent: when ever we would make
+proof of that, which about this Effect the diversity of Figure
+worketh, its necessary to make the Experiment with Matter wherein
+variety of Gravities hath no place. For making use of Matters which
+may be different in their Specifical Gravities, and meeting with
+varieties of effects of Ascending and Descending, we shall alwayes be
+left unsatisfied whether that diversity derive it self really from the
+sole Figure, or else from the divers Gravity also. We may remedy this
+by takeing one only Matter, that is tractable and easily reduceable
+into every sort of Figure. Moreover, it will be an excellent expedient
+to take a kinde of Matter, exactly alike in Gravity unto the Water:
+for that Matter, as far as pertaines to the Gravity, is indifferent
+either to Ascend or Descend; so that we may presently observe any the
+least difference that derives it self from the diversity of Figure.
+
+    [Sidenote: An Experiment in Wax, that proveth Figure to have no
+    Operation in Natation & Submersion.]
+
+Now to do this, Wax is most apt, which, besides its incapacity of
+receiveing any sensible alteration from its imbibing of Water, is
+ductile or pliant, and the same piece is easily reduceable into all
+Figures: and being _in Specie_ a very inconsiderable matter inferiour
+in Gravity to the Water, by mixing therewith a little of the fileings
+of Lead it is reduced to a Gravity exactly equall to that of the
+Water.
+
+This Matter prepared, and, for example, a Ball being made thereof as
+bigge as an Orange or biger, and that made so grave as to sink to the
+bottom, but so lightly, that takeing thence one only Grain of Lead, it
+returns to the top, and being added, it submergeth to the bottom, let
+the same Wax afterwards be made into a very broad and thin Flake or
+Cake; and then, returning to make the same Experiment, you shall see
+that it being put to the bottom, it shall, with the Grain of Lead rest
+below, and that Grain deducted, it shall ascend to the very Surface,
+and added again it shall dive to the bottom. And this same effect
+shall happen alwaies in all sort of Figures, as wel regular as
+irregular: nor shall you ever finde any that will swim without the
+removall of the Grain of Lead, or sinke to the bottom unless it be
+added: and, in short, about the going or not going to the Bottom, you
+shall discover no diversity, although, indeed, you shall about the
+quick and slow descent: for the more expatiated and distended Figures
+move more slowly aswel in the diveing to the bottom as in the rising
+to the top; and the other more contracted and compact Figures, more
+speedily. Now I know not what may be expected from the diversity of
+Figures, if the most contrary to one another operate not so much as
+doth a very small Grain of Lead, added or removed.
+
+Me thinkes I hear some of the Adversaries to raise a doubt upon my
+produced Experiment[40]. And first that they offer to my consideration,
+that the Figure, as a Figure simply, and disjunct from the Matter
+workes not any effect, but requires to be conjoyned with the Matter;
+and, furthermore, not with every Matter, but with those only,
+wherewith it may be able to execute the desired operation. Like as we
+see it verified by Experience, that the Acute and sharp Angle is more
+apt to cut, than the Obtuse; yet alwaies provided, that both the one
+and the other, be joyned with a Matter apt to cut, as for example,
+with Steel. Therefore, a Knife with a fine and sharp edge, cuts Bread
+or Wood with much ease, which it will not do, if the edge be blunt and
+thick: but he that will instead of Steel, take Wax, and mould it into
+a Knife, undoubtedly shall never know the effects of sharp and blunt
+edges: because neither of them will cut, the Wax being unable by
+reason of its flexibility, to overcome the hardness of the Wood and
+Bread. And, therefore, applying the like discourse to our purpose,
+they say, that the difference of Figure will shew different effects,
+touching Natation and Submersion, but not conjoyned with any kind of
+Matter, but only with those Matters which, by their Gravity, are apt
+to resist the Velocity of the water, whence he that would elect for
+the Matter, Cork or other light wood, unable, through its Levity, to
+superate the Crassitude of the water, and of that Matter should forme
+Solids of divers Figures, would in vain seek to find out what
+operation Figure hath in Natation or Submersion; because all would
+swim, and that not through any property of this or that Figure, but
+through the debility of the Matter, wanting so much Gravity, as is
+requisite to superate and overcome the Density and Crassitude of the
+water.
+
+    [40] An objection against the Experiment in Water.
+
+Its needfull, therefore, if wee would see the effect wrought by the
+Diversity of Figure, first to make choice of a Matter of its nature
+apt to penetrate the Crassitude of the water. And, for this effect[41],
+they have made choice of such a Matter, as fit, that being readily
+reduced into Sphericall Figure, goes to the Bottom; and it is Ebony,
+of which they afterwards making a small Board or Splinter, as thin as
+a Lath, have illustrated how that this, put upon the Surface of the
+water, rests there without descending to the Bottom: and making, on
+the otherside, of the same wood a Ball, no less than a hazell Nut,
+they shew, that this swims not, but descendes. From which Experiment,
+they think they may frankly conclude, that the Breadth of the Figure
+in the flat Lath or Board, is the cause of its not descending to the
+Bottom, for as much as a Ball of the same Matter, not different from
+the Board in any thing but in Figure, submergeth in the same water to
+the Bottom. The discourse and the Experiment hath really so much of
+probability and likelyhood of truth in it, that it would be no wonder,
+if many perswaded by a certain cursory observation, should yield
+credit to it; nevertheless, I think I am able to discover, how that it
+is not free from falacy.
+
+    [41] An Experiment in Ebany, brought to disprove the Experiment
+    in Wax.
+
+Beginning, therefore, to examine one by one, all the particulars that
+have been produced, I say, that Figures, as simple Figures, not only
+operate not in naturall things, but neither are they ever seperated
+from the Corporeall substance[42]: nor have I ever alledged them stript of
+sensible Matter, like as also I freely admit, that in our endeavouring
+to examine the Diversity of Accidents, dependant upon the variety of
+Figures, it is necessary to apply them to Matters, which obstruct not
+the various operations of those various Figures: and I admit and
+grant, that I should do very ill; if I would experiment the influence
+of Acutenesse of edge with a Knife of Wax, applying it to cut an Oak,
+because there is no Acuteness in Wax able to cut that very hard wood.
+But yet such an Experiment of this Knife, would not be besides the
+purpose, to cut curded Milk, or other very yielding Matter: yea, in
+such like Matters, the Wax is more commodious than Steel; for finding
+the diversity depending upon Angles, more or less Acute, for that Milk
+is indifferently cut with a Raisor, and with a Knife, that hath a
+blunt edge. It needs, therefore, that regard be had, not only to the
+hardness, solidity or Gravity of Bodies, which under divers figures,
+are to divide and penetrate some Matters, but it forceth also, that
+regard be had, on the other side, to the Resistance of the Matters, to
+be divided and penetrated. But since I have in making the Experiment
+concerning our Contest; chosen a Matter which penetrates the
+Resistance of the water; and in all figures descendes to the Bottome,
+the Adversaries can charge me with no defect; yea, I have propounded
+so much a more excellent Method than they, in as much as I have
+removed all other Causes, of descending or not descending to the
+Bottom, and retained the only sole and pure variety of Figures,
+demonstrating that the same Figures all descende with the only
+alteration of a Grain in weight: which Grain being removed, they
+return to float and swim; it is not true, therefore, (resuming the
+Example by them introduced) that I have gon{e} about to experiment the
+efficacy of Acuteness, in cutting with Matters unable to cut, but with
+Matters proportioned to our occasion, since they are subjected to no
+other variety, then that alone which depends on the Figure more or
+less acute.
+
+    [42] Figure is unseperable from Corporeall Substance.
+
+    [Sidenote: The answer to the Objection against the Experiment of
+    the Wax.]
+
+But let us proceed a little farther, and observe, how that indeed the
+Consideration, which, they say, ought to be had about the Election of
+the Matter, to the end, that it may be proportionate for the making of
+our experiment, is needlessly introduced, declaring by the example of
+Cutting, that like as Acuteness is inefficient to cut, unless when it
+is in a Matter hard and apt to superate the Resistance of the wood or
+other Matter, which we intend to cut; so the aptitude of descending or
+not descending in water, ought and can only be known in those Matters,
+that are able to overcome the Renitence, and superate the Crassitude
+of the water. Unto which, I say, that to make distinction and
+election, more of this than of that Matter, on which to impress the
+Figures for cutting or penetrating this or that Body, as the solidity
+or obdurateness of the said Bodies shall be greater or less, is very
+necessary: but withall I subjoyn, that such distinction, election and
+caution would be superfluous and unprofitable, if the Body to be cut
+or penetrated, should have no Resistance, or should not at all
+withstand the Cutting or Penitration: and if the Knife were to be used
+in cutting a Mist or Smoak, one of Paper would be equally serviceable
+with one of _Damascus_ Steel: and so by reason the water hath not any
+Resistance against the Penitration of any Solid Body, all choice of
+Matter is superfluous and needless, and the Election which I said
+above to have been well made of a Matter reciprocall in Gravity to
+water, was not because it was necessary, for the overcoming of the
+crassitude of the water, but its Gravity, with which only it resists
+the sinking of Solid Bodies: and for what concerneth the Resistance of
+the crassitude, if we narrowly consider it, we shall find that all
+Solid Bodies, as well those that sink, as those that swim, are
+indifferently accomodated and apt to bring us to the knowledge of the
+truth in question. Nor will I be frighted out of the belief of these
+Conclusions, by the Experiments which may be produced against me, of
+many severall Woods, Corks, Galls, and, moreover, of subtle slates and
+plates of all sorts of Stone and Mettall, apt by means of their
+Naturall Gravity, to move towards the Centre of the Earth, the which,
+nevertheless, being impotent, either through the Figure (as the
+Adversaries thinke) or through Levity, to break and penetrate the
+Continuity of the parts of the water, and to distract its union, do
+continue to swimm without submerging in the least: nor on the other
+side, shall the Authority of _Aristotle_ move me, who in more than one
+place, affirmeth the contrary to this, which Experience shews me.
+
+    [Sidenote: No Solid of such Levity, nor of such Figure, but that
+    it doth penetrate the Crassitude of the Water.]
+
+    [Sidenote: Bodies of all Figures, laid upon the water, do
+    penetrate its Crassitude, and in what proportion.]
+
+I return, therefore, to assert, that there is not any Solid of such
+Levity, nor of such Figure, that being put upon the water, doth not
+divide and penetrate its Crassitude: yea if any with a more
+perspicatious eye, shall return to observe more exactly the thin
+Boards of Wood, he shall see them to be with part of their thickness
+under water, and not only with their inferiour Superficies, to kisse
+the Superiour of the water, as they of necessity must have believed,
+who have said, that such Boards submerge not, as not being able to
+divide the Tenacity of the parts of the water: and, moreover, he shall
+see, that subtle shivers of Ebony, Stone or Metall, when they float,
+have not only broak the Continuity of the water, but are with all
+their thickness, under the Surface of it; and more and more, according
+as the Matters are more grave: so that a thin Plate of Lead, shall be
+lower than the Surface of the circumfused water, by at least twelve
+times the thickness of the Plate, and Gold shall dive below the Levell
+of the water, almost twenty times the thickness of the Plate, as I
+shall anon declare.
+
+But let us proceed to evince, that the water yields and suffers it
+self to be penetrated by every the lightest Body; and therewithall
+demonstrate, how, even by Matters that submerge not, we may come to
+know that Figure operates nothing about the going or not going to the
+Bottom, seeing that the water suffers it self to be penetrated equally
+by every Figure.
+
+    [Sidenote: The Experiment of a Cone, demitted with its Base, and
+    after with its Point downwards.]
+
+Make a Cone, or a Piramis of Cypress, of Firre, or of other Wood of
+like Gravity, or of pure Wax, and let its height be somewhat great,
+namely a handfull, or more, and put it into the water with the Base
+downwards: first, you shall see that it will penetrate the water, nor
+shall it be at all impeded by the largeness of the Base, nor yet shall
+it sink all under water, but the part towards the point shall lye
+above it: by which shall be manifest, first, that that Solid forbeares
+not to sink out of an inability to divide the Continuity of the water,
+having already divided it with its broad part, that in the opinion of
+the Adversaries is the less apt to make the division. The Piramid
+being thus fixed, note what part of it shall be submerged, and revert
+it afterwards with the point downwards, and you shall see that it
+shall not dive into the water more than before, but if you observe how
+far it shall sink, every person expert in Geometry, may measure, that
+those parts that remain out of the water, both in the one and in the
+other Experiment are equall to an hair: whence he may manifestly
+conclude, that the acute Figure which seemed most apt to part and
+penetrate the water, doth not part or penetrate it more than the large
+and spacious.
+
+And he that would have a more easie Experiment, let him take two
+Cylinders of the same Matter, one long and small, and the other short,
+but very broad, and let him put them in the water, not distended, but
+erect and endways: he shall see, if he diligently measure the parts of
+the one and of the other, that in each of them the part submerged,
+retains exactly the same proportion to that out of the water, and that
+no greater part is submerged of that long and small one, than of the
+other more spacious and broad: howbeit, this rests upon a very large,
+and that upon a very little Superficies of water: therefore the
+diversity of Figure, occasioneth neither facility, nor difficulty, in
+parting and penetrating the Continuity of the water, and,
+consequently, cannot be the Cause of the Natation or Submersion. He
+may likewise discover the non operating of variety of Figures, in
+arising from the Bottom of the water, towards the Surface, by taking
+Wax, and tempering it with a competent quantity of the filings of
+Lead, so that it may become a considerable matter graver than the
+water: then let him make it into a Ball, and thrust it unto the Bottom
+of the water; and fasten to it as much Cork, or other light matter, as
+just serveth to raise it, and draw it towards the Surface: for
+afterwards changing the same Wax into a thin Cake, or into any other
+Figure, that same Cork shall raise it in the same manner to a hair.
+
+This silenceth not my Antagonists, but they say, that all the
+discourse hitherto made by me little importeth to them, and that it
+serves their turn, that they have demonstrated in one only particular,
+and in what matter, and under what Figure pleaseth them, namely, in a
+Board and in a Ball of Ebony, that this put in the water, descends to
+the Bottom, and that stays atop to swim: and the Matter being the
+same, and the two Bodies differing in nothing but in Figure, they
+affirm, that they have with all perspicuity demonstrated and sensibly
+manifested what they undertook; and lastly, that they have obtained
+their intent. Nevertheless, I believe, and thinke, I can demonstrate,
+that that same Experiment proveth nothing against my Conclusion.
+
+    [Sidenote: In Experiments of Natation, the Solid is to be put
+    into, not upon the water.]
+
+And first, it is false, that the Ball descends, and the Board not: for
+the Board shall also descend, if you do to both the Figures, as the
+words of our Question requireth; that is, if you put them both into
+the water.
+
+    [Sidenote: The Question of Natation stated.]
+
+  _The words were these. That the Antagonists having an opinion, that
+  the Figure would alter the Solid Bodies, in relation to the
+  descending or not descending, ascending or not ascending in the
+  same_ Medium, _as_ v. gr. _in the same water, in such sort, that, for
+  Example, a Solid that being of a Sphericall Figure, shall descend
+  to the Bottom, being reduced into some other Figure, shall not
+  descend: I holding the contrary, do affirm, that a Corporeall Solid
+  Body, which reduced into a Sphericall Figure, or any other, shall
+  go to the Bottom, shall do the like under whatsoever other Figure,
+  {&}c._
+
+    [Sidenote: Place defined according to Aristotle.]
+
+But to be in the water, implies to be placed in the water, and by
+_Aristotles_ own Definition of place, to be placed, importeth to be
+invironed by the Superficies of the Ambient Body, therefore, then
+shall the two Figures be in the water, when the Superficies of the
+water, shall imbrace and inviron them: but when the Adversaries shew
+the Board of Ebony not descending to the Bottom, they put it not into
+the water, but upon the water, where being by a certain impediment (as
+by and by we will shew) retained, it is invironed, part by water, and
+part by air, which thing is contrary to our agreement, that was, that
+the Bodies should be in the water, and not part in water, and part in
+air.
+
+  _The which is again made manifest, by the questions being put as
+  well about the things which go to the Bottom, as those which arise
+  from the Bottom to swimme, and who sees not that things placed in
+  the Bottom, must have water about them._
+
+    [Sidenote: The confutation of the Experiment in the Ebany.]
+
+It is now to be noted, that the Board of Ebany and the Ball, put into
+the water, both sink, but the Ball more swiftly, and the Board more
+slowly; and slower and slower, according as it shall be more broad and
+thin, and of this Tardity the breadth of the Figure is the true Cause:
+But these broad Boards that slowly descend, are the same, that being
+put lightly upon the water, do swimm: Therefore, if that were true
+which the Adversaries affirm, the same numerical Figure, would in the
+same numericall water, cause one while Rest, and another while Tardity
+of Motion, which is impossible: for every perticular Figure which
+descends to the Bottom[43], hath of necessity its own determinate Tardity
+and slowness, proper and naturall unto it, according to which it
+moveth, so that every other Tardity, greater or lesser is improper to
+its nature: if, therefore, a Board, as suppose of a foot square,
+descendeth naturally with six degrees of Tardity, it is impossible,
+that it should descend with ten or twenty, unless some new impediment
+do arrest it. Much less can it, by reason of the same Figure rest, and
+wholly cease to move; but it is necessary, that when ever it resteth,
+there do some greater impediment intervene than the breadth of the
+Figure. Therefore, it must be somewhat else, and not the Figure, that
+stayeth the Board of Ebany above water, of which Figure the only
+Effect is the retardment of the Motion, according to which it
+descendeth more slowly than the Ball. Let it be confessed, therefore,
+rationally discoursing, that the true and sole Cause of the Ebanys
+going to the Bottom, is the excess of its Gravity above the Gravity of
+the water: and the Cause of the greater or less Tardity, the breadth
+of this Figure, or the contractedness of that: but of its Rest, it can
+by no means be allowed, that the quallity of the Figure, is the Cause
+thereof: aswell, because, making the Tardity greater, according as the
+Figure more dilateth, there cannot be so immense a Dilatation, to
+which there may not be found a correspondent immence Tardity without
+redusing it to Nullity of Motion; as, because the Figures produced by
+the Antagonists for effecters of Rest, are the self same that do also
+go to the Bottom.
+
+    [43] Every perticular Figure hath its own peculiar Tardity.
+
+I will not omit another reason, founded also upon Experience, and if
+I deceive not my self, manifestly concluding, how that the
+Introduction of the breadth or amplitude of Figure, and the Resistance
+of the water against penetration, have nothing to do in the Effect of
+descending, or ascending, or resting in the water. [D]Take a piece of
+wood or other Matter, of which a Ball ascends from the Bottom of the
+water to the Surface, more slowly than a Ball of Ebony of the same
+bignesse, so that it is manifest, that the Ball of Ebony more readily
+divideth the water in descending, than the other in ascending; as for
+Example, let the Wood be Walnut-tree. Then take a Board of
+Walnut-tree, like and equall to that of Ebony of the Antagonists,
+which swims; and if it be true, that this floats above water, by
+reason of the Figure, unable through its breadth, to pierce the
+Crassitude of the same, the other of Wallnut-tree, without all
+question, being thrust unto the Bottom, will stay there, as less apt,
+through the same impediment of Figure, to divide the said Resistance
+of the water. But if we shall find, and by experience see, that not
+only the thin Board, but every other Figure of the same Wallnut-tree
+will return to float, as undoubtedly we shall, then I must desier my
+opposers to forbear to attribute the floating of the Ebony, unto the
+Figure of the Board, in regard that the Resistance of the water is the
+same, as well to the ascent, as to the descent, and the force of the
+Wallnut-trees ascension, is lesse than the Ebonys force in going to
+the Bottom.
+
+    [D] The Figure & Resistance of the Medium against Division, have
+    nothing to do with the Effect of Natation or Submersion, by an
+    Experiment in Wallnut tree.
+
+    [Sidenote: An Experiment in Gold, to prove the non-operating of
+    Figure in Natation and Submersion.]
+
+Nay, I will say more, that if we shall consider Gold in comparison of
+water, we shall find, that it exceeds it in Gravity almost twenty
+times, so that the Force and Impetus, wherewith a Ball of Gold goes to
+the Bottom, is very great. On the contrary, there want not matters, as
+Virgins Wax, and some Woods, which are not above a fiftieth part less
+grave than water, whereupon their Ascension therein is very slow, and
+a thousand times weaker than the _Impetus_ of the Golds descent: yet
+notwithstanding, a plate of Gold swims without descending to the
+Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin
+Board of Wood, which put in the Bottom of the Water, shall rest there
+without ascending. Now if the Figure can obstruct the Penetration, and
+impede the descent of Gold, that hath so great an _Impetus_, how can
+it choose but suffice to resist the same Penetration of the other
+matter in ascending, when as it hath scarce a thousandth part of the
+_Impetus_ that the Gold hath in descending? Its therefore, necessary,
+that that which suspends the thin Plate of Gold, or Board of Ebony,
+upon the water, be some thing that is wanting to the other Cakes and
+Boards of Matters less grave than the water; since that being put to
+the Bottom, and left at liberty, they rise up to the Surface, without
+any obstruction: But they want not for flatness and breadth of Figure:
+Therefore, the spaciousnesse of the Figure, is not that which makes
+the Gold and Ebony to swim.
+
+And, because, that the excess of their Gravity above the Gravity of
+the water, is questionless the Cause of the sinking of the flat piece
+of Ebony, and the thin Plate of Gold, when they go to the Bottom,
+therefore, of necessity, when they float, the Cause of their staying
+above water, proceeds from Levity, which in that case, by some
+Accident, peradventure not hitherto observed, cometh to meet with the
+said Board, rendering it no longer as it was before, whilst it did
+sink more ponderous than the water, but less.
+
+Now, let us return to take the thin Plate of Gold, or of Silver, or
+the thin Board of Ebony, and let us lay it lightly upon the water, so
+that it stay there without sinking, and diligently observe its effect.
+And first, see how false the assertion of _Aristotle_, and our
+oponents is, to wit, that it stayeth above water, through its
+unability to pierce and penetrate the Resistance of the waters
+Crassitude: for it will manifestly appear, not only that the said
+Plates have penetrated the water, but also that they are a
+considerable matter lower than the Surface of the same, the which
+continueth eminent, and maketh as it were a Rampert on all sides,
+round about the said Plates, the profundity of which they stay
+swimming: and, according as the said Plates shall be more grave than
+the water, two, four, ten or twenty times, it is necessary, that their
+Superficies do stay below the universall Surface of the water, so much
+more, than the thickness of those Plates, as we shal more distinctly
+shew anon. In the mean space, for the more easie understanding of what
+I say, observe with me a little the present Scheme: in which let us
+suppose the Surface of the water to be distended, according to the
+Lines F L D B, upon which if one shall put a board of matter
+specifically more grave than water, but so lightly that it submerge
+not, it shall not rest any thing above, but shall enter with its whole
+thickness into the water: and, moreover, shall sink also, as we see by
+the Board A I, O I, whose breadth is wholly sunk into the water, the
+little Ramperts of water L A and D O incompassing it, whose
+Superficies is notably higher than the Superficies of the Board. See
+now whether it be true, that the said Board goes not to the Bottom, as
+being of Figure unapt to penetrate the Crassitude of the water.
+
+[Illustration]
+
+    [Sidenote: Why solids having penitrated the Water, do not proceed
+    to a totall Submersion.]
+
+But, if it hath already penetrated, and overcome the Continuity of
+the water, & is of its own nature more grave than the said water, why
+doth it not proceed in its sinking, but stop and suspend its self
+within that little dimple or cavitie, which with its ponderosity it
+hath made in the water? I answer; because that in submerging it self,
+so far as till its Superficies come to the Levell with that of the
+water, it loseth a part of its Gravity, and loseth the rest of it as
+it submergeth & descends beneath the Surface of the water, which
+maketh Ramperts and Banks round about it, and it sustaines this loss
+by means of its drawing after it, and carrying along with it, the Air
+that is above it, and by Contact adherent to it, which Air succeeds to
+fill the Cavity that is invironed by the Ramperts of water; so that
+that which in this case descends and is placed in the water, is not
+only the Board of Ebony or Plate of Iron, but a composition of Ebony
+and Air, from which resulteth a Solid no longer superiour in Gravity
+to the water, as was the simple Ebony, or the simple Gold. And, if we
+exactly consider, what, and how great the Solid is, that in this
+Experiment enters into the water, and contrasts with the Gravity of
+the same, it will be found to be all that which we find to be beneath
+the Surface of the water, the which is an aggregate and Compound of a
+Board of Ebony, and of almost the like quantity of Air, or a Mass
+compounded of a Plate of Lead, and ten or twelve times as much Air.
+But, Gentlemen, you that are my Antagonists in our Question, we
+require the Identity of Matter, and the alteration only of the Figure;
+therefore, you must remove that Air, which being conjoyned with the
+Board, makes it become another Body less grave than the Water, and put
+only the Ebony into the Water, and you shall certainly see the Board
+descend to the Bottom; and, if that do not happen, you have got the
+day. And to seperate the Air from the Ebony[44], there needs no more but
+only to bath the Superficies of the said Board with the same Water:
+for the Water being thus interposed between the Board and the Air, the
+other circumfused Water shall run together without any impediment, and
+shall receive into it the sole and bare Ebony, as it was to do.
+
+    [44] How to seperate the Air from Solids in demitting them into
+    the water.
+
+But, me thinks I hear some of the Adversaries cunningly opposing this,
+and telling me, that they will not yield, by any means, that their
+Board be wetted, because the weight added thereto by the Water, by
+making it heavier than it was before, draws it to the Bottom, and that
+the addition of new weight is contrary to our agreement, which was,
+that the Matter be the same.
+
+To this, I answer, first; that treating of the operation of Figure
+in Bodies put into the Water, none can suppose them to be put into the
+Water without being wet; nor do I desire more to be done to the Board,
+then I will give you leave to do to the Ball. Moreover, it is untrue,
+that the Board sinks by vertue of the new Weight added to it by the
+Water, in the single and slight bathing of it: for I will put ten or
+twenty drops of Water upon the same Board, whilst it is sustained upon
+the water; which drops, because not conjoyned with the other Water
+circumfused, shall not so encrease the weight of it, as to make it
+sink: but if the Board being taken out, and all the water wiped off
+that was added thereto, I should bath all its Superficies with one
+only very small drop, and put it again upon the water, without doubt
+it shall sink, the other Water running to cover it, not being retained
+by the superiour Air; which Air by the interposition of the thin vail
+of water, that takes away its Contiguity unto the Ebony, shall without
+Renitence be seperated, nor doth it in the least oppose the succession
+of the other Water: but rather, to speak better, it shall descend
+freely; because it shall be all invironed and covered with water, as
+soon as its superiour Superficies, before vailed with water, doth
+arrive to the Levell of the universall Surface of the said water. To
+say, in the next place, that water can encrease the weight of things
+that are demitted into it, is most false; for water hath no Gravity in
+water[45], since it descends not: yea, if we would well consider what any
+immense Mass of water doth put upon a grave Body; that is placed in
+it, we shall find experimentally, that it, on the contrary, will
+rather in a great part deminish the weight of it[46], and that we may be
+able to lift an huge Stone from the Bottom of the water, which the
+water being removed, we are not able to stir. Nor let them tell me by
+way of reply, that although the superposed water augment not the
+Gravity of things that are in it, yet it increaseth the ponderosity of
+those that swim, and are part in the water and part in the Air, as is
+seen, for Example, in a Brass Ketle[47], which whilst it is empty of
+water, and replenished only with Air shall swim, but pouring of Water
+therein, it shall become so grave, that it shall sink to the Bottom,
+and that by reason of the new weight added thereto. To this I will
+return answer, as above, that the Gravity of the Water, contained in
+the Vessel is not that which sinks it to the Bottom, but the proper
+Gravity of the Brass, superiour to the Specificall Gravity of the
+Water: for if the Vessel were less grave than water, the Ocean would
+not suffice to submerge it[48]. And, give me leave to repeat it again, as
+the fundamentall and principall point in this Case, that the Air
+contained in this Vessel before the infusion of the Water, was that
+which kept it a-float[49], since that there was made of it, and of the
+Brass, a Composition less grave than an equall quantity of Water: and
+the place that the Vessel occupyeth in the Water whilst it floats, is
+not equall to the Brass alone, but to the Brass and to the Air
+together, which filleth that part of the Vessel that is below the
+Levell of the water: Moreover, when the Water is infused, the Air is
+removed, and there is a composition made of Brass and of water, more
+grave _in specie_ than the simple water, but not by vertue of the
+water infused, as having greater Specifick Gravity than the other
+water, but through the proper Gravity of the Brass, and through the
+alienation of the Air. Now, as he that should say that Brass, that by
+its nature goes to the Bottom, being formed into the Figure of a
+Ketle[50], acquireth from that Figure a vertue of lying in the Water
+without sinking, would say that which is false; because that Brass
+fashioned into any whatever Figure, goeth always to the Bottom,
+provided, that that which is put into the water be simple Brass; and
+it is not the Figure of the Vessel that makes the Brass to float, but
+it is because that that is not purely Brass which is put into the
+water, but an aggregate of Brass and of Air: so is it neither more nor
+less false, that a thin Plate of Brass or of Ebony, swims by vertue of
+its dilated & broad Figure: for the truth is, that it bares up without
+submerging, because that that which is put in the water, is not pure
+Brass or simple Ebony, but an aggregate of Brass and Air, or of Ebony
+and Air. And, this is not contrary unto my Conclusion, the which,
+(having many a time seen Vessels of Mettall, and thin pieces of
+diverse grave Matters float, by vertue of the Air conjoyned with them)
+did affirm, That Figure was not the Cause of the Natation or
+Submersion of such Solids as were placed in the water. Nay more, I
+cannot omit, but must tell my Antagonists, that this new conceit of
+denying that the Superficies of the Board should be bathed, may beget
+in a third person an opinion of a poverty of Arguments of defence on
+their part, since that such bathing was never insisted upon by them in
+the beginning of our Dispute, and was not questioned in the least,
+being that the Originall of the discourse arose upon the swiming of
+Flakes of Ice, wherein it would be simplicity to require that their
+Superficies might bedry: besides, that whether these pieces of Ice be
+wet or dry they alwayes swim, and as the Adversaries say, by reason of
+the Figure.
+
+    [45] Water hath no Gravity in Water.
+
+    [46] Water deminisheth the Gravity of Solids immerged therein.
+
+    [47] The Experiment of a brass Ketle swiming when empty, & sinking
+    when full, alledged to prove that water gravitates in water,
+    answered.
+
+    [48] An Ocean sufficeth not to sink a Vessel specifically less
+    grave than water.
+
+    [49] Air, the Cause of the Natation of empty Vessels of Matters
+    graver _in specie_ than the water.
+
+    [50] Neither Figure, nor the breadth of Figure, is the Cause of
+    Natation.
+
+Some peradventure, by way of defence, may say, that wetting the Board
+of Ebony, and that in the superiour Superficies, it would, though of
+it self unable to pierce and penetrate the water, be born downwards,
+if not by the weight of the additionall water, at least by that desire
+and propension that the superiour parts of the water have to re-unite
+and rejoyn themselves: by the Motion of which parts, the said Board
+cometh in a certain manner, to be depressed downwards.
+
+    [Sidenote: The Bathed Solid descends not out of any affectation
+    of union in the upper parts of the water.]
+
+This weak Refuge will be removed, if we do but consider, that the
+repugnancy of the inferiour parts of the water, is as great against
+Dis-union, as the Inclination of its superiour parts is to union: nor
+can the uper unite themselves without depressing the board, nor can it
+descend without disuniting the parts of the nether Water: so that it
+doth follow, by necessary consequence, that for those respects, it
+shall not descend. Moreover, the same that may be said of the upper
+parts of the water, may with equall reason be said of the nether,
+namely, that desiring to unite, they shall force the said Board
+upwards.
+
+Happily, some of these Gentlemen that dissent from me, will wonder,
+that I affirm, that the contiguous superiour Air is able to sustain
+that Plate of Brass or of Silver, that stayeth above water; as if I
+would in a certain sence allow the Air[51], a kind of Magnetick vertue of
+sustaining the grave Bodies, with which it is contiguous. To satisfie
+all I may, to all doubts, I have been considering how by some other
+sensible Experiment I might demonstrate, how truly that little
+contiguous and superiour Air sustaines those Solids, which being by
+nature apt to descend to the Bottom, being placed lightly on the water
+submerge not, unless they be first thorowly bathed; and have found,
+that one of these Bodies having descended to the Bottom, by
+conveighing to it (without touching it in the least) a little Air,
+which conjoyneth with the top of the same, it becometh sufficient, not
+only, as before to sustain it, but also to raise it, and to carry it
+back to the top, where it stays and abideth in the same manner, till
+such time, as the assistance of the conjoyned Air is taken away. And
+to this effect, I have taken a Ball of Wax, and made it with a little
+Lead, so grave, that it leasurely descends to the Bottom, making with
+all its Superficies very smooth and pollite: and this being put gently
+into the water, almost wholly submergeth, there remaining vissible
+only a little of the very top[52], the which so long as it is conjoyned
+with the Air, shall retain the Ball a-top, but the Contiguity of the
+Air taken away by wetting it, it shall descend to the Bottom and there
+remain. Now to make it by vertue of the Air, that before sustained it
+to return again to the top, and stay there, thrust into the water a
+Glass reversed with the mouth downwards, the which shall carry with it
+the Air it contains, and move this towards the Ball, abasing it till
+such time that you see, by the transparency of the Glass, that the
+contained Air do arrive to the summity of the _B_all[53]: then gently
+withdraw the Glass upwards, and you shall see the _B_all to rise, and
+afterwards stay on the top of the water[54], if you carefully part the
+Glass and the water without overmuch commoving and disturbing it.
+There is, therefore, a certain affinity between the Air and other
+Bodies, which holds them unied, so, that they seperate not without a
+kind of violence. The same likewise is seen in the water[55]; for if we
+shall wholly submerge some Body in it, so that it be thorowly bathed,
+in the drawing of it afterwards gently out again, we shall see the
+water follow it, and rise notably above its Surface, before it
+seperates from it. Solid Bodies, also[56], if they be equall and alike in
+Superficies, so, that they make an exact Contact without the
+interposition of the least Air, that may part them in the seperation
+and yield untill that the ambient _Medium_ succeeds to replenish the
+place, do hold very firmly conjoyned, and are not to be seperated
+without great force but, because, the Air, Water, and other Liquids,
+very expeditiously shape themselves to contact with any Solid
+_B_odies, so that their Superficies do exquisitely adopt themselves to
+that of the Solids, without any thing remaining between them,
+therefore, the effect of this Conjunction and Adherence is more
+manifestly and frequently observed in them, than in hard and
+inflexible Bodies, whose Superficies do very rarely conjoyn with
+exactness of Contact[57]. This is therefore that Magnetick vertue, which
+with firm Connection conjoyneth all Bodies, that do touch without the
+interposition of flexible fluids; and, who knows, but that that a
+Contact, when it is very exact, may be a sufficient Cause of the Union
+and Continuity of the parts of a naturall _B_ody?
+
+    [51] _A_ Magnetisme in the _A_ir, by which it bears up those
+    Solids in the water, that are contiguous with it.
+
+    [52] The Effect of the Airs Contiguity in the Natation of Solids.
+
+    [53] The force of Contact.
+
+    [54] _A_n Affectation of Conjunction betwixt Solids and the Air
+    contiguous to them.
+
+    [55] The like affectation of Conjunction betwixt Solids & the
+    water.
+
+    [56] Also the like affectation and Conjunction betwixt Solids
+    themselves.
+
+    [57] Contact may be the Cause of the Continuity of Naturall
+    Bodies.
+
+Now, pursuing my purpose, I say; that it needs not, that we have
+recourse to the Tenacity, that the parts of the water have amongst
+themselves, by which they resist and oppose Division, Distraction, and
+Seperation, because there is no such Coherence and Resistance of
+Division for if there were, it would be no less in the internall parts
+than in those nearer the superiour or externall Surface, so that the
+same Board, finding alwayes the same Resistance and Renitence, would
+no less stop in the middle of the water than about the Surface, which
+is false. Moreover, what Resistance can we place in the Continuity of
+the water, if we see that it is impossible to find any Body of
+whatsoever Matter, Figure or Magnitude, which being put into the
+water, shall be obstructed and impeded by the Tenacity of the parts of
+the water to one another, so, but that it is moved upwards or
+downwards, according as the Cause of their Motion transports it? And,
+what greater proof of it can we desier, than that which we daily see
+in Muddy waters, which being put into Vessels to be drunk, and being,
+after some hours setling[58], still, as we say, thick in the end, after
+four or six dayes they are wholly setled, and become pure and clear?
+Nor can their Resistance of Penetration stay those impalpable and
+insensible Atomes of Sand, which by reason of their exceeding small
+force, spend six dayes in descending the space of half a yard.
+
+    [58] The settlement of _M_uddy Water, proveth that that Element
+    hath no aversion to Division.
+
+  _Nor let them say, that the seeing of such small Bodies, consume
+  six dayes in descending so little a way, is a sufficient Argument
+  of the Waters Resistance of Division; because that is no resisting
+  of Division, but a retarding of Motion; and it would be simplicity
+  to say, that a thing opposeth Division[59], and that in the same
+  instant, it permits it self to be divided: nor doth the Retardation
+  of Motion at all favour the Adversaries cause, for that they are to
+  instance in a thing that wholly prohibiteth Motion, and procureth
+  Rest; it is necessary, therefore, to find out Bodies that stay in
+  the water, if one would shew its repugnancy to Division, and not
+  such as move in it, howbeit but slowly._
+
+    [59] Water cannot oppose division, and at the same time permit it
+    self to be divided.
+
+What then is this Crassitude of the water, with which it resisteth
+Division? What, I beseech you, should it be, if we (as we have said
+above) with all diligence attempting the reduction of a Matter into so
+like a Gravity with the water, that forming it into a dilated Plate it
+rests suspended as we have said, between the two waters, it be
+impossible to effect it, though we bring them to such an
+Equiponderance, that as much Lead as the fourth part of a Grain of
+Musterd-seed, added to the same expanded Plate, that in Air [_i. e.
+out of the water_] shall weigh four or six pounds, sinketh it to the
+Bottom, and being substracted, it ascends to the Surface of the water?
+I cannot see, (if what I say be true, as it is most certain) what
+minute vertue and force we can possibly find or imagine, to which the
+Resistance of the water against Division and Penetration is not
+inferiour; whereupon, we must of necessity conclude that it is
+nothing: because, if it were of any sensible power, some large Plate
+might be found or compounded of a Matter alike in Gravity to the
+water, which not only would stay between the two waters; but,
+moreover, should not be able to descend or ascend without notable
+force. We may likewise collect the same from an other Experiment[60],
+shewing that the Water gives way also in the same manner to
+transversall Division; for if in a setled and standing water we should
+place any great Mass that goeth not to the bottom, drawing it with a
+single Womans Hair, we might carry it from place to place without any
+opposition, and this whatever Figure it hath, though that it possess a
+great space of water, as for instance, a great Beam would do moved
+side-ways. Perhaps some might oppose me and say, that if the
+Resistance of water against Division, as I affirm, were nothing; Ships
+should not need such a force of Oars and Sayles for the moving of them
+from place to place in a tranquile Sea, or standing Lake. To him that
+should make such an objection, I would reply[61], that the water
+contrasteth not against, nor simply resisteth Division, but a sudden
+Division, and with so much greater Renitence, by how much greater the
+Velocity is: and the Cause of this Resistance depends not on
+Crassitude, or any other thing that absolutely opposeth Division, but
+because that the parts of the water divided, in giving way to that
+Solid that is moved in it, are themselves also necessitated locally to
+move, some to the one side, and some to the other, and some downwards:
+and this must no less be done by the waves before the Ship, or other
+Body swimming through the water, than by the posteriour and
+subsequent; because, the Ship proceeding forwards, to make it self a
+way to receive its Bulk, it is requisite, that with the Prow it
+repulse the adjacent parts of the water, as well on one hand as on the
+other, and that it move them as much transversly, as is the half of
+the breadth of the Hull: and the like removall must those waves make,
+that succeeding the Poump do run from the remoter parts of the Ship
+towards those of the middle, successively to replenish the places,
+which the Ship in advancing forwards, goeth, leaving vacant. Now,
+because, all Motitions are made in Time[62], and the longer in greater
+time: and it being moreover true, that those Bodies that in a certain
+time are moved by a certain power such a certain space, shall not be
+moved the same space, and in a shorter Time, unless by a greater
+Power: therefore, the broader Ships move slower than the narrower,
+being put on by an equall Force: and the same Vessel requires so much
+greater force of Wind, or Oars, the faster it is to move.
+
+    [60] An hair will draw a great Mass thorow the Water; which
+    proveth, that it hath no Resistance against transversall
+    Division.
+
+    [61] How ships are moved in the water.
+
+    [62] Bodies moved a certain space in a certain Time, by a
+    certain power, cannot be moved the same space and in a shorter
+    time, but by a greater power.
+
+  _But yet for all this, any great Mass swimming in a standing Lake,
+  may be moved by any petit force; only it is true, that a lesser
+  force more slowly moves it: but if the waters Resistance of
+  Division, were in any manner sensible, it would follow, that the
+  said Mass, should, notwithstanding the percussion of some sensible
+  force, continue immoveable, which is not so[63]. Yea, I will say
+  farther, that should we retire our selves into the more internall
+  contemplation of the Nature of water and other Fluids, perhaps we
+  should discover the Constitution of their parts to be such, that
+  they not only do not oppose Division, but that they have not any
+  thing in them to be divided: so that the Resistance that is
+  observed in moving through the water[64], is like to that which we meet
+  with in passing through a great Throng of People, wherein we find
+  impediment, and not by any difficulty in the Division, for that
+  none of those persons are divided whereof the Croud is composed,
+  but only in moving of those persons side-ways which were before
+  divided and disjoyned: and thus we find Resistance in thrusting a
+  Stick into an heap of Sand, not because any part of the Sand is to
+  be cut in pieces, but only to be moved and raised[65]. Two manners of
+  Penetration, therefore, offer themselves to us, one in Bodies,
+  whose parts were continuall, and here Division seemeth necessary,
+  the other in the aggregates of parts not continuall, but contiguous
+  only[66], and here there is no necessity of dividing but of moving
+  only. Now, I am not well resolved, whether water and other Fluids
+  may be esteemed to be of parts continuall or contiguous only[67]; yet I
+  find my self indeed inclined to think that they are rather
+  contiguous (if there be in Nature no other manner of aggregating,
+  than by the union, or by the touching of the extreams:) and I am
+  induced thereto by the great difference that I see between the
+  Conjunction of the parts of an hard or Solid Body[68], and the
+  Conjunction of the same parts when the same Body shall be made
+  Liquid and Fluid: for if, for example, I take a Mass of Silver or
+  other Solid and hard Mettall, I shall in dividing it into two
+  parts, find not only the resistance that is found in the moving of
+  it only[69], but an other incomparably greater, dependent on that
+  vertue, whatever it be, which holds the parts united: and so if we
+  would divide again those two parts into other two, and successively
+  into others and others, we should still find a like Resistance, but
+  ever less by how much smaller the parts to be divided shall be; but
+  if, lastly, employing most subtile and acute Instruments, such as
+  are the most tenuous parts of the Fire, we shall resolve it
+  (perhaps) into its last and least Particles, there shall not be
+  left in them any longer either Resistance of Division, or so much
+  as a capacity of being farther divided, especially by Instruments
+  more grosse than the acuities of Fire: and what Knife or Rasor put
+  into well melted Silver can we finde, that will divide a thing
+  which surpasseth the separating power of Fire? Certainly none:
+  because either the whole shall be reduced to the most minute and
+  ultimate Divisions, or if there remain parts capable still of other
+  Subdidivisions, they cannot receive them, but only from acuter
+  Divisors than Fire; but a Stick or Rod of Iron, moved in the melted
+  Metall, is not such a one. Of a like Constitution and Consistence,
+  I account the parts of Water[70], and other Liquids to be, namely,
+  incapable of Division by reason of their Ienuity; or if not
+  absolutely indivisible, yet at least not to be divided by a Board,
+  or other Solid Body, palpable unto the hand, the Sector being
+  alwayes required to be more sharp than the Solid to be cut. Solid
+  Bodies, therefore, do only move, and not divide the Water[71], when put
+  into it; whose parts being before divided to the extreamest
+  minuity, and therefore capable of being moved, either many of them
+  at once, or few, or very few, they soon give place to every small
+  Corpuscle, that descends in the same: for that, it being little and
+  light, descending in the Air, and arriving to the Surface of the
+  Water, it meets with Particles of Water more small, and of less
+  Resistance against Motion and Extrusion, than is its own prement
+  and extrusive force; whereupon it submergeth, and moveth such a
+  portion of them, as is proportionate to its Power. There is not,
+  therefore, any Resistance in Water against Division, nay, there is
+  not in it any divisible parts. I adde; moreover, that in case yet
+  there should be any small Resistance found (which is absolutely
+  false)[72] haply in attempting with an Hair to move a very great natant
+  Machine, or in essaying by the addition of one small Grain of Lead
+  to sink, or by removall of it to raise a very broad Plate of
+  Matter, equall in Gravity with Water, (which likewise will not
+  happen, in case we proceed with dexterity) we may observe that that
+  Resistance is a very different thing from that which the
+  Adversaries produce for the Cause of the Natation of the Plate of
+  Lead or Board of Ebony, for that one may make a Board of Ebony,
+  which being put upon the Water swimmeth, and cannot be submerged,
+  no not by the addition of an hundred Grains of Lead put upon the
+  same, and afterwards being bathed, not only sinks, though the said
+  Lead be taken away, but though moreover a quantity of Cork, or of
+  some other light Body fastened to it, sufficeth not to hinder it
+  from sinking unto the bottome: so that you see, that although it
+  were granted that there is a certain small Resistance of Division
+  found in the substance of the Water, yet this hath nothing to do
+  with that Cause which supports the Board above the Water, with a
+  Resistance an hundred times greater than that which men can find in
+  the parts of the Water: nor let them tell me, that only the Surface
+  of the Water hath such Resistance[73], and not the internall parts, or
+  that such Resistance is found greatest in the beginning of the
+  Submersion, as it also seems that in the beginning, Motion meets
+  with greater opposition, than in the continuance of it; because,
+  first, I will permit, that the Water be stirred, and that the
+  superiour parts be mingled with the middle[74], and inferiour parts, or
+  that those above be wholly removed, and those in the middle only
+  made use off, and yet you shall see the effect for all that, to be
+  still the same: Moreover, that Hair which draws a Beam through the
+  Water, is likewise to divide the upperparts, and is also to begin
+  the Motion, and yet it begins it, and yet it divides it: and
+  finally, let the Board of Ebony be put in the midway, betwixt the
+  bottome and the top of the Water, and let it there for awhile be
+  suspended and setled, and afterwards let it be left at liberty, and
+  it will instantly begin its Motion, and will continue it unto the
+  bottome. Nay, more, the Board so soon as it is dimitted upon the
+  Water, hath not only begun to move and divide it, but is for a good
+  space dimerged into it._
+
+    [63] The parts of Liquids, so farre from resisting Division, that
+    they contain not any thing that may be divided.
+
+    [64] The Resistance a Solid findeth in moving through the water,
+    like to that we meet with in passing through a throng of people:
+
+    [65] Or in thrusting a Stick into an heap of Sand.
+
+    [66] Two kinds of Penetration, one in Bodies continuall, the other
+    in Bodies only contiguous.
+
+    [67] Water consists not of continuall, but only of contiguous
+    parts.
+
+    [68] _Se{e} what satisfaction he hath given, as to this point, in
+    Lib. de Motu. Dial. 2._
+
+    [69] Great difference betwixt the Conjunction of the parts of a
+    Body when Solid, and when fluid.
+
+    [70] Water consists of parts that admit of no farther division.
+
+    [71] Solids dimitted into the water, do onely move, and not divide
+    it.
+
+    [72] If there were any Resistance of Division in water, it must
+    needs be small, in that it is overcome by an Hair, a Grain of
+    Lead, or a slight bathing of the Solid.
+
+    [73] The uper parts of the Water, do no more resist Division than
+    the middle or lower parts.
+
+    [74] Waters Resistance of division, not greater in the beginning
+    of the Submersion.
+
+Let us receive it, therefore, for a true and undoubted Conclusion,
+That the Water hath not any Renitence against simple Division, and
+that it is not possible to find any Solid Body, be it of what Figure
+it will, which being put into the Water, its Motion upwards or
+downwards, according as it exceedeth, or shall be exceeded by the
+Water in Gravity (although such excesse and difference be insensible)
+shall be prohibited, and taken away, by the Crassitude of the said
+Water. When, therefore, we see the Board of Ebony, or of other Matter,
+more grave than the Water, to stay in the Confines of the Water and
+Air, without submerging, we must have recourse to some other
+Originall, for the investing the Cause of that Effect, than to the
+breadth of the Figure, unable to overcome the Renitence with which the
+Water opposeth Division, since there is no Resistance; and from that
+which is not in being, we can expect no Action. It remains most true,
+therefore, as we have said before, that this so succeds, for that that
+which in such manner put upon the water, not the same Body with that
+which is put _into_ the Water: because this which is put _into_ the
+Water, is the pure Board of Ebony, which for that it is more grave
+than the Water, sinketh, and that which is put _upon_ the Water, is a
+Composition of Ebony, and of so much Air, that both together are
+specifically less grave than the Water, and therefore they do not
+descend.
+
+I will farther confirm this which I say. Gentlemen, my Antagonists, we
+are agreed, that the excess or defect of the Gravity of the Solid,
+unto the Gravity of the Water, is the true and proper Cause of
+Natation or Submersion.
+
+    [Sidenote: Great Caution to be had in experimenting the operation
+    of Figure in Natation.]
+
+Now, if you will shew that besides the former Cause, there is another
+which is so powerfull, that it can hinder and remove the Submersion of
+those very Solids, that by their Gravity sink, and if you will say,
+that this is the breadth or ampleness of Figure, you are oblieged,
+when ever you would shew such an Experiment, first to make the
+circumstances certain, that that Solid which you put into the Water,
+be not less grave _in specie_ than it, for if you should not do so,
+any one might with reason say, that not the Figure, but the Levity was
+the cause of that Natation. But I say, that when you shall dimit a
+Board of Ebony into the Water, you do not put therein a Solid more
+grave _in specie_ than the Water, but one lighter, for besides the
+Ebony, there is in the Water a Mass of Air, united with the Ebony, and
+such, and so light, that of both there results a Composition less
+grave than the Water: See, therefore, that you remove the Air, and put
+the Ebony alone into the Water, for so you shall immerge a Solid more
+grave then the Water, and if this shall not go to the Bottom, you have
+well Philosophized and I ill.
+
+Now, since we have found the true Cause of the Natation of those
+Bodies, which otherwise, as being graver than the Water, would descend
+to the bottom, I think, that for the perfect and distinct knowledge of
+this business, it would be good to proceed in a way of discovering
+demonstratively those particular Accidents that do attend these
+effects, and,
+
+
+
+
+PROBL. I.
+
+    [Sidenote: To finde the proportion Figures ought to have to the
+    waters Gravity, that by help of the contiguous Air, they may
+    swim.]
+
+  _To finde what proportion severall Figures of different Matters
+    ought to have, unto the Gravity of the Water, that so they may be
+    able by vertue of the Contiguous Air to stay afloat._
+
+
+[Illustration]
+
+Let, therefore, for better illustration, D F N E be a Vessell,
+wherein the water is contained, and suppose a Plate or Board, whose
+thickness is comprehended between the Lines I C and O S, and let it be
+of Matter exceeding the water in Gravity, so that being put upon the
+water, it dimergeth and abaseth below the Levell of the said water,
+leaving the little Banks A I and B C, which are at the greatest height
+they can be, so that if the Plate I S should but descend any little
+space farther, the little Banks or Ramparts would no longer consist,
+but expulsing the Air A I C B, they would diffuse themselves over the
+Superficies I C, and would submerge the Plate. The height A I B C is
+therefore the greatest profundity that the little Banks of water admit
+of. Now I say, that from this, and from the proportion in Gravity,
+that the Matter of the Plate hath to the water, we may easily finde of
+what thickness, at most, we may make the said Plates, to the end, they
+may be able to bear up above water: for if the Matter of the Plate or
+Board I S were, for Example, as heavy again as the water, a Board of
+that Matter shall be, at the most of a thickness equall to the
+greatest height of the Banks, that is, as thick as A I is high: which
+we will thus demonstrate. Let the Solid I S be double in Gravity to
+the water, and let it be a regular Prisme, or Cylinder, to wit, that
+hath its two flat Superficies, superiour and inferiour, alike and
+equall, and at Right Angles with the other laterall Superficies, and
+let its thickness I O be equall to the greatest Altitude of the Banks
+of water: I say, that if it be put upon the water, it will not
+submerge: for the Altitude A I being equall to the Altitude I O, the
+Mass of the Air A B C I shall be equall to the Mass of the Solid C I O
+S: and the whole Mass A O S B double to the Mass I S; And since the
+Mass of the Air A C, neither encreaseth nor diminisheth the Gravity of
+the Mass I S, and the Solid I S was supposed double in Gravity to the
+water; Therefore as much water as the Mass submerged A O S B,
+compounded of the Air A I C B, and of the Solid I O S C, weighs just
+as much as the same submerged Mass A O S B: but when such a Mass of
+water, as is the submerged part of the Solid, weighs as much as the
+said Solid, it descends not farther, but resteth, as by (_a_)
+_Archimedes_[75], and above by us, hath been demonstrated: Therefore, I S
+shall descend no farther, but shall rest. And if the Solid I S shall
+be Sesquialter in Gravity to the water, it shall float, as long as its
+thickness be not above twice as much as the greatest Altitude of the
+Ramparts of water, that is, of A I. For I S being Sesquialter in
+Gravity to the water, and the Altitude O I, being double to I A, the
+Solid submerged A O S B, shall be also Sesquialter in Mass to the
+Solid I S. And because the Air A C, neither increaseth nor diminisheth
+the ponderosity of the Solid I S: Therefore, as much water in quantity
+as the submerged Mass A O S B, weighs as much as the said Mass
+submerged: And, therefore, that Mass shall rest. And briefly in
+generall.
+
+    [75] Of Natation Lib. 1. Prop. 3.
+
+[Illustration]
+
+
+
+
+THEOREME. VI.
+
+    [Sidenote: The proportion of the greatest thickness of Solids,
+    beyond which encreased they sink.]
+
+  _When ever the excess of the Gravity of the Solid above the Gravity
+    of the Water, shall have the same proportion to the Gravity of
+    the Water, that the Altitude of the Rampart, hath to the
+    thickness of the Solid, that Solid shall not sink, but being
+    never so little thicker it shall._
+
+
+[Illustration]
+
+Let the Solid I S be superior in Gravity to the water, and of such
+thickness, that the Altitude of the Rampart A I, be in proportion to
+the thickness of the Solid I O, as the excess of the Gravity of the
+said Solid I S, above the Gravity of a Mass of water equall to the
+Mass I S, is to the Gravity of the Mass of water equall to the Mass I
+S. I say, that the Solid I S shall not sinke, but being never so
+little thicker it shall go to the bottom: For being that as A I is to
+I O, so is the Excess of the Gravity of the Solid I S, above the
+Gravity of a Mass of water equall to the Mass I S, to the Gravity of
+the said Mass of water: Therefore, compounding, as A O is to O I, so
+shall the Gravity of the Solid I S, be to the Gravity of a Mass of
+water equall to the Mass I S: And, converting, as I O is to O A, so
+shall the Gravity of a Mass of water equall to the Mass I S, be to the
+Gravity of the Solid I S: But as I O is to O A, so is a Mass of water
+I S, to a Mass of water equall to the Mass A B S O: and so is the
+Gravity of a Mass of water I S, to the Gravity of a Mass of water A S:
+Therefore as the Gravity of a Mass of water, equall to the Mass I S,
+is to the Gravity of the Solid I S, so is the same Gravity of a Mass
+of water I S, to the Gravity of a Mass of Water A S: Therefore the
+Gravity of the Solid I S, is equall to the Gravity of a Mass of water
+equall to the Mass A S: But the Gravity of the Solid I S, is the same
+with the Gravity of the Solid A S, compounded of the Solid I S, and of
+the Air A B C I. Therefore the whole compounded Solid A O S B, weighs
+as much as the water that would be comprised in the place of the said
+Compound A O S B: And, therefore, it shall make an _Equilibrium_ and
+rest, and that same Solid I O S C shall sinke no farther. But if its
+thickness I O should be increased, it would be necessary also to
+encrease the Altitude of the Rampart A I, to maintain the due
+proportion: But by what hath been supposed, the Altitude of the
+Rampart A I, is the greatest that the Nature of the Water and Air do
+admit, without the waters repulsing the Air adherent to the
+Superficies of the Solid I C, and possessing the space A I C B:
+Therefore, a Solid of greater thickness than I O, and of the same
+Matter with the Solid I S, shall not rest without submerging, but
+shall descend to the bottome: which was to be demonstrated. In
+consequence of this that hath been demonstrated, sundry and various
+Conclusions may be gathered, by which the truth of my principall
+Proposition comes to be more and more confirmed, and the imperfection
+of all former Argumentations touching the present Question cometh to
+be discovered.
+
+_And first we gather from the things demonstrated, that,_
+
+
+
+
+THEOREME VII.
+
+    [Sidenote: The heaviest Bodies may swimme.]
+
+  _All Matters, how heavy soever, even to Gold it self, the heaviest
+    of all Bodies, known by us, may float upon the Water._
+
+
+Because its Gravity being considered to be almost twenty times greater
+than that of the water, and, moreover, the greatest Altitude that the
+Rampart of water can be extended to, without breaking the Contiguity
+of the Air, adherent to the Surface of the Solid, that is put upon the
+water being predetermined, if we should make a Plate of Gold so thin,
+that it exceeds not the nineteenth part of the Altitude of the said
+Rampart, this put lightly upon the water shall rest, without going to
+the bottom: and if Ebony shall chance to be in sesquiseptimall
+proportion more grave than the water, the greatest thickness that can
+be allowed to a Board of Ebony, so that it may be able to stay above
+water without sinking, would be seaven times more than the height of
+the Rampart Tinn, _v. gr._ eight times more grave than water, shall
+swimm as oft as the thickness of its Plate, exceeds not the 7th part
+of the Altitude of the Rampart.
+
+    [Sidenote: _He elsewhere cites this as a Proposition, therefore I
+    make it of that number._]
+
+And here I will not omit to note, as a second Corrollary dependent
+upon the things demonstrated, that,
+
+
+
+
+THEOREME VIII.
+
+    [Sidenote: Natation and Submersion, collected from the thickness,
+    excluding the length and breadth of Plates.]
+
+  _The Expansion of Figure not only is not the Cause of the Natation
+    of those grave Bodies, which otherwise do submerge, but also the
+    determining what be those Boards of Ebony, or Plates of Iron or
+    Gold that will swimme, depends not on it, rather that same
+    determination is to be collected from the only thickness of those
+    Figures of Ebony or Gold, wholly excluding the consideration of
+    length and breadth, as having no wayes any share in this Effect._
+
+
+It hath already been manifested, that the only cause of the Natation
+of the said Plates, is the reduction of them to be less grave than the
+water, by means of the connexion of that Air, which descendeth
+together with them, and possesseth place in the water; which place so
+occupyed, if before the circumfused water diffuseth it self to fill
+it, it be capable of as much water, as shall weigh equall with the
+Plate, the Plate shall remain suspended, and sinke no farther.
+
+Now let us see on which of these three dimensions of the Solid
+depends the terminating, what and how much the Mass of that ought to
+be, that so the assistance of the Air contiguous unto it, may suffice
+to render it specifically less grave than the water, whereupon it may
+rest without Submersion. It shall undoubtedly be found, that the
+length and breadth have not any thing to do in the said determination,
+but only the height, or if you will the thickness: for, if we take a
+Plate or Board, as for Example, of Ebony, whose Altitude hath unto the
+greatest possible Altitude of the Rampart, the proportion above
+declared, for which cause it swims indeed, but yet not if we never so
+little increase its thickness; I say, that retaining its thickness,
+and encreasing its Superficies to twice, four times, or ten times its
+bigness, or dminishing it by dividing it into four, or six, or twenty,
+or a hundred parts, it shall still in the same manner continue to
+float: but encreasing its thickness only a Hairs breadth, it will
+alwaies submerge, although we should multiply the Superficies a
+hundred and a hundred times. Now forasmuch as that this is a Cause,
+which being added, we adde also the Effect, and being removed, it is
+removed; and by augmenting or lessening the length or breadth in any
+manner, the effect of going, or not going to the bottom, is not added
+or removed: I conclude, that the greatness and smalness of the
+Superficies hath no influence upon the Natation or Submersion. And
+that the proportion of the Altitude of the Ramparts of Water, to the
+Altitude of the Solid, being constituted in the manner aforesaid, the
+greatness or smalness of the Superficies, makes not any variation, is
+manifest from that which hath been above demonstrated, and from this,
+that, _The Prisms and Cylinders which have the same Base, are in
+proportion to one another as their heights._ Whence Cylinders or
+Prismes[76], namely, the Board, be they great or little, so that they be
+all of equall thickness, have the same proportion to their
+Conterminall Air, which hath for Base the said Superficies of the
+Board, and for height the Ramparts of water; so that alwayes of that
+Air, and of the Board, Solids, are compounded, that in Gravity equall
+a Mass of water equall to the Mass of the Solids, compounded of Air,
+and of the Board: whereupon all the said Solids do in the same manner
+continue afloat. We will conclude in the third place, that,
+
+    [76] Prismes and Cylinders having the same Base, are to one
+    another as their heights.
+
+
+
+
+THEOREME. IX.
+
+    [Sidenote: All Figures of all Matters, float by hep of the
+    Rampart replenished with Air, and some but only touch the water.]
+
+  _All sorts of Figures of whatsoever Matter, albeit more grave than
+    the Water, do by Benefit of the said Rampart, not only float, but
+    some Figures, though of the gravest Matter, do stay wholly above
+    Water, wetting only the inferiour Surface that toucheth the
+    Water._
+
+
+And these shall be all Figures, which from the inferiour Base upwards,
+grow lesser and lesser; the which we shall exemplifie for this time in
+Piramides or Cones, of which Figures the passions are common. We will
+demonstrate therefore, that,
+
+  _It is possible to form a Piramide, of any whatsoever Matter
+  preposed, which being put with its Base upon the Water, rests not
+  only without submerging, but without wetting it more then its
+  Base._
+
+For the explication of which it is requisite, that we first
+demonstrate the subsequent Lemma, namely, that,
+
+
+
+
+LEMMA II.
+
+    [Sidenote: Solids whose Masses are in contrary proportion to
+    their Specifick Gravities are equall in absolute Gravity.]
+
+  _Solids whose Masses answer in proportion contrarily to their
+    Specificall Gravities, are equall in Absolute Gravities._
+
+
+[Illustration]
+
+Let A C and B be two Solids, and let the Mass A C be to the Mass B,
+as the Specificall Gravity of the Solid B, is to the Specificall
+Gravity of the Solid A C: I say, the Solids A C and B are equall in
+absolute weight, that is, equally grave. For if the Mass A C be equall
+to the Mass B, then, by the Assumption, the Specificall Gravity of B,
+shall be equall to the Specificall Gravity of A C, and being equall in
+Mass, and of the same Specificall Gravity they shall absolutely weigh
+one as much as another. But if their Masses shall be unequall, let the
+Mass A C be greater, and in it take the part C, equall to the Mass B.
+And, because the Masses B and C are equall; the Absolute weight of B,
+shall have the same proportion to the Absolute weight of C, that the
+Specificall Gravity of B, hath to the Specificall Gravity of C; or of
+C A, which is the same _in specie_: But look what proportion the
+Specificall Gravity of B, hath to the Specificall Gravity of C A, the
+like proportion, by the Assumption, hath the Mass C A, to the Mass B,
+that is, to the Mass C: Therefore, the absolute weight of B, to the
+absolute weight of C, is as the Mass A C to the Mass C: But as the
+Mass A C, is to the Mass C, so is the absolute weight of A C, to the
+absolute weight of C: Therefore the absolute weight of B, hath the
+same proportion to the absolute weight of C, that the absolute weight
+of A C, hath to the absolute weight of C: Therefore, the two Solids A
+C and B are equall in absolute Gravity: which was to be demonstrated.
+Having demonstrated this, I say,
+
+
+
+
+THEOREME X.
+
+    [Sidenote: There may be Cones and Piramides of any Matter, which
+    demitted into the water, rest only their Bases.]
+
+  _That it is possible of any assigned Matter, to form a Piramide or
+    Cone upon any Base, which being put upon the Water shall not
+    submerge, nor wet any more than its Base._
+
+
+[Illustration]
+
+Let the greatest possible Altitude of the Rampart be the Line D B,
+and the Diameter of the Base of the Cone to be made of any Matter
+assigned B C, at right angles to D B: And as the Specificall Gravity
+of the Matter of the Piramide or Cone to be made, is to the
+Specificall Gravity of the water, so let the Altitude of the Rampart D
+B, be to the third part of the Piramide or Cone A B C, described upon
+the Base, whose Diameter is B C: I say, that the said Cone A B C, and
+any other Cone, lower then the same, shall rest upon the Surface of
+the water B C without sinking. Draw D F parallel to B C, and suppose
+the Prisme or Cylinder E C, which shall be tripple to the Cone A B C.
+And, because the Cylinder D C hath the same proportion to the Cylinder
+C E, that the Altitude D B, hath to the Altitude B E: But the Cylinder
+C E, is to the Cone A B C, as the Altitude E B is to the third part of
+the Altitude of the Cone: Therefore, by Equality of proportion, the
+Cylinder D C is to the Cone A B C, as D B is to the third part of the
+Altitude B E: But as D B is to the third part of B E, so is the
+Specificall Gravity of the Cone A B C, to the Specificall Gravity of
+the water: Therefore, as the Mass of the Solid D C, is to the Mass of
+the Cone A _B_ C, so is the Specificall Gravity of the said Cone, to
+the Specificall Gravity of the water: Therefore, by the precedent
+Lemma, the Cone A B C weighs in absolute Gravity, as much as a Mass of
+Water equall to the Mass D C: But the water which by the imposition of
+the Cone A B C, is driven out of its place, is as much as would
+precisely lie in the place D C, and is equall in weight to the Cone
+that displaceth it: Therefore, there shall be an _Equilibrium_, and
+the Cone shall rest without farther submerging. And its manifest,
+
+
+COROLARY I.
+
+    [Sidenote: Amongst Cones of the same Base, those of least
+    Altitude shall sink the least.]
+
+  _That making upon the same Basis, a Cone of a less Altitude, it
+    shall be also less grave, and shall so much the more rest without
+    Submersion._
+
+
+COROLARY II.
+
+    [Sidenote: There may be Cones and Piramides of any Matter, which
+    demitted with the Point downwards do float atop.]
+
+  _It is manifest, also, that one may make Cones and Piramids of any
+    Matter whatsoever, more grave than the water, which being put
+    into the water, with the Apix or Point downwards, rest without
+    Submersion._
+
+Because if we reassume what hath been above demonstrated, of Prisms
+and Cylinders, and that on Bases equall to those of the said
+Cylinders, we make Cones of the same Matter, and three times as high
+as the Cylinders, they shall rest afloat, for that in Mass and Gravity
+they shall be equall to those Cylinders, and by having their Bases
+equall to those of the Cylinders, they shall leave equall Masses of
+Air included within the Ramparts. This, which for Example sake hath
+been demonstrated, in Prisms, Cylinders, Cones and Piramids, might be
+proved in all other Solid Figures, but it would require a whole Volume
+(such is the multitude and variety of their Symptoms and Accidents) to
+comprehend the particuler demonstration of them all, and of their
+severall Segments: but I will to avoid prolixity in the present
+Discourse, content my self, that by what I have declared every one of
+ordinary Capacity may comprehend, that there is not any Matter so
+grave, no not Gold it self, of which one may not form all sorts of
+Figures, which by vertue of the superiour Air adherent to them, and
+not by the Waters Resistance of Penetration, do remain afloat, so that
+they sink not. Nay, farther, I will shew, for removing that Error,
+that,
+
+
+
+
+THEOREME XI.
+
+    [Sidenote: A Piramide or Cone, demitted with the Point downwards
+    shal swim, with its Base downward shall sink.]
+
+  _A Piramide or Cone put into the Water, with the Point downward
+    shall swimme, and the same put with the Base downwards shall
+    sinke, and it shall be impossible to make it float._
+
+
+Now the quite contrary would happen, if the difficulty of Penetrating
+the water, were that which had hindred the descent, for that the said
+Cone is far apter to pierce and penetrate with its sharp Point, than
+with its broad and spacious Base.
+
+And, to demonstrate this, let the Cone be _A B C_, twice as grave as
+the water, and let its height be tripple to the height of the Rampart
+_D A E C_: I say, first, that being put lightly into the water with
+the Point downwards, it shall not descend to the bottom: for the
+Aeriall Cylinder contained betwixt the Ramparts _D A C E_, is equall
+in Mass to the Cone _A B C_; so that the whole Mass of the Solid
+compounded of the Air _D A C E_, and of the Cone _A B C_, shall be
+double to the Cone _A C B_: And, because the Cone _A B C_ is supposed
+to be of Matter double in Gravity to the water, therefore as much
+water as the whole Masse _D A B C E_, placed beneath the Levell of the
+water, weighs as much as the Cone _A B C_: and, therefore, there shall
+be an _Equilibrium_, and the Cone _A B C_ shall descend no lower. Now,
+I say farther, that the same Cone placed with the Base downwards,
+shall sink to the bottom, without any possibility of returning again,
+by any means to swimme.
+
+[Illustration]
+
+Let, therefore, the Cone be _A B D_, double in Gravity to the water,
+and let its height be tripple the height of the Rampart of water L B:
+It is already manifest, that it shall not stay wholly out of the
+water, because the Cylinder being comprehended betwixt the Ramparts _L
+B D P_, equall to the Cone _A B D_, and the Matter of the Cone, beig
+double in Gravity to the water, it is evident that the weight of the
+said Cone shall be double to the weight of the Mass of water equall to
+the Cylinder _L B D P_: Therefore it shall not rest in this state, but
+shall descend.
+
+[Illustration]
+
+
+COROLARY I.
+
+    [Sidenote: Much less shall the said Cone swim, if one immerge a
+    part thereof.]
+
+  _I say farther; that much lesse shall the said Cone stay afloat, if
+    one immerge a part thereof._
+
+Which you may see, comparing with the water as well the part that
+shall immerge as the other above water. Let us therefore of the Cone A
+B D, submergeth part N T O S, and advance the Point N S F above water.
+The Altitude of the Cone F N S, shall either be more than half the
+whole Altitude of the Cone F T O, or it shall not be more: if it shall
+be more than half, the Cone F N S shall be more than half of the
+Cylinder E N S C: for the Altitude of the Cone F N S, shall be more
+than Sesquialter of the Altitude of the Cylinder E N S C: And, because
+the Matter of the Cone is supposed to be double in Specificall Gravity
+to the water, the water which would be contained within the Rampart E
+N S C, would be less grave absolutely than the Cone F N S; so that the
+whole Cone F N S cannot be sustained by the Rampart: But the part
+immerged N T O S, by being double in Specificall Gravity to the water,
+shall tend to the bottom: Therefore, the whole _C_one F T O, as well
+in respect of the part submerged, as the part above water shall
+descend to the bottom. But if the Altitude of the Point F N S, shall
+be half the Altitude of the whole Cone F T O, the same Altitude of the
+said Cone F N S shall be Sesquialter to the Altitude E N: and,
+therefore, E N S C shall be double to the Cone F N S; and as much
+water in Mass as the _C_ylinder E N S C, would weigh as much as the
+part of the _C_one F N S. But, because the other immerged part N T O
+S, is double in Gravity to the water, a Mass of water equall to that
+compounded of the _C_ylinder E N S C, and of the Solid N T O S, shall
+weigh less than the _C_one F T O, by as much as the weight of a Mass
+of water equall to the Solid N T O S: Therefore, the _C_one sha{l}l
+also descend. Again, because the Solid N T O S, is septuple to the
+Cone F N S, to which the _C_ylinder E S is double, the proportion of
+the Solid N T O S, shall be to the _C_ylinder E N S C, as seaven to
+two: Therefore, the whole Solid compounded of the _C_ylinder E N S C,
+and of the Solid N T O S, is much less than double the Solid N T O S:
+Therefore, the single Solid N T O S, is much graver than a Mass of
+water equall to the Mass, compounded of the _C_ylinder E N S C, and of
+N T O S.
+
+
+COROLARY II.
+
+    [Sidenote: Part of the Cones towards the Cuspis removed, it shall
+    still sink.]
+
+  _From whence it followeth, that though one should remove and take
+    away the part of the Cone F N S, the sole remainder N T O S would
+    go to the bottom._
+
+
+COROLARY III.
+
+    [Sidenote: The more the Cone is immerged, the more impossible is
+    its floating.]
+
+  _And if we should more depress the Cone F T O, it would be so much
+    the more impossible that it should sustain it self afloat, the
+    part submerged N T O S still encreasing, and the Mass of Air
+    contained in the Rampart diminishing, which ever grows less, the
+    more the Cone submergeth._
+
+That Cone, therefore, that with its Base upwards, and its _Cuspis_
+downwards doth swimme, being dimitted with its Base downward must of
+necessity sinke. They have argued farre from the truth, therefore, who
+have ascribed the cause of Natation to waters resistance of Division,
+as to a passive principle, and to the breadth of the Figure, with
+which the division is to be made, as the Efficient.
+
+I come in the fourth place, to collect and conclude the reason of
+that which I have proposed to the Adversaries, namely,
+
+
+
+
+THEOREME XII.
+
+    [Sidenote: Solids of any Figure & greatnesse, that naturally
+    sink, may by help of the Air in the Rampart swimme.]
+
+  _That it is possible to fo{r}m Solid Bodies, of what Figure and
+    greatness soever, that of their own Nature goe to the Bottome;
+    But by the help of the Air contained in the Rampart, rest without
+    submerging._
+
+
+[Illustration]
+
+The truth of this Proposition is sufficiently manifest in all those
+Solid Figures, that determine in their uppermost part in a plane
+Superficies: for making such Figures of some Matter specifically as
+grave as the water, putting them into the water, so that the whole
+Mass be covered, it is manifest, that they shall rest in all places,
+provided, that such a Matter equall in weight to the water, may be
+exactly adjusted: and they shall by consequence, rest or lie even with
+the Levell of the water, without making any Rampart. If, therefore, in
+respect of the Matter, such Figures are apt to rest without
+submerging, though deprived of the help of the Rampart, it is
+manifest, that they may admit so much encrease of Gravity, (without
+encreasing their Masses) as is the weight of as much water as would be
+contained within the Rampart, that is made about their upper plane
+Surface: by the help of which being sustained, they shall rest afloat,
+but being bathed, they shall descend, having been made graver than the
+water. In Figures, therefore, that determine above in a plane, we may
+cleerly comprehend, that the Rampart added or removed, may prohibit or
+permit the descent: but in those Figures that go lessening upwards
+towards the top, some Persons may, and that not without much seeming
+Reason, doubt whether the same may be done, and especially by those
+which terminate in a very acute Point, such as are your Cones and
+small Piramids. Touching these, therefore, as more dubious than the
+rest, I will endeavour to demonstrate, that they also lie under the
+same Accident of going, or not going to the Bottom, be they of any
+whatever bigness. Let therefore the Cone be A B D, made of a matter
+specifically as grave as the water; it is manifest that being put all
+under water, it shall rest in all places (alwayes provided, that it
+shall weigh exactly as much as the water, which is almost impossible
+to effect) and that any small weight being added to it, it shall sink
+to the bottom: but if it shall descend downwards gently, I say, that
+it shall make the Rampart E S T O, and that there shall stay out of
+the water the point A S T, tripple in height to the Rampart E S: which
+is manifest, for the Matter of the Cone weighing equally with the
+water, the part submerged _S B D T_, becomes indifferent to move
+downwards or upwards; and the Cone _A S T_, being equall in Mass to
+the water that would be contained in the concave of the Rampart _E S T
+O_, shall be also equall unto it in Gravity: and, therefore, there
+shall be a perfect _Equilibrium_, and, consequently, a Rest. Now here
+ariseth a doubt, whether the Cone _A B D_ may be made heavier, in such
+sort, that when it is put wholly under water, it goes to the bottom,
+but yet not in such sort, as to take from the Rampart the vertue of
+sustaining it that it sink not, and, the reason of the doubt is this:
+that although at such time as the Cone _A B D_ is specifically as
+grave as the water, the Rampart _E S T O_ sustaines it, not only when
+the point _A S T_ is tripple in height to the Altitude of the Rampart
+_E S_, but also when a lesser part is above water; [for although in
+the Descent of the Cone the Point _A S T_ by little and little
+diminisheth, and so likewise the Rampart _E S T O_, yet the Point
+diminisheth in greater proportion than the Rampart, in that it
+diminisheth according to all the three Dimensions, but the Rampart
+according to two only, the Altitude still remaining the same; or, if
+you will, because the Cone _S {A} T_ goes diminishing, according to
+the proportion of the cubes of the Lines that do successively become
+the Diameters of the Bases of emergent Cones, and the Ramparts
+diminish according to the proportion of the Squares of the same Lines;
+whereupon the proportions of the Points are alwayes Sesquialter of the
+proportions of the Cylinders, contained within the Rampart; so that
+if, for Example, the height of the emergent Point were double, or
+equall to the height of the Rampart, in these cases, the Cylinder
+contained within the Rampart, would be much greater than the said
+Point, because it would be either sesquialter or tripple, by reason of
+which it would perhaps serve over and above to sustain the whole Cone,
+since the part submerged would no longer weigh any thing;] yet,
+nevertheless, when any Gravity is added to the whole Mass of the Cone,
+so that also the part submerged is not without some excesse of Gravity
+above the Gravity of the water, it is not manifest, whether the
+Cylinder contained within the Rampart, in the descent that the Cone
+shall make, can be reduced to such a proportion unto the emergent
+Point, and to such an excesse of Mass above the Mass of it, as to
+compensate the excesse of the Cones Specificall Gravity above the
+Gravity of the water: and the Scruple ariseth, because that howbeit in
+the descent made by the Cone, the emergent Point _A S T_ diminisheth,
+whereby there is also a diminution of the excess of the Cones Gravity
+above the Gravity of the water, yet the case stands so, that the
+Rampart doth also contract it self, and the Cylinder contained in it
+doth deminish. Nevertheless it shall be demonstrated, how that the
+Cone _A B D_ being of any supposed bignesse, and made at the first of
+a Matter exactly equall in Gravity to the Water, if there may be
+affixed to it some Weight, by means of which i{t} may descend to the
+bottom, when submerged under water, it may also by vertue of the
+Rampart stay above without sinking.
+
+[Illustration]
+
+[Illustration]
+
+Let, therefore, the Cone _A B D_ be of any supposed greatnesse, and
+alike in specificall Gravity to the water. It is manifest, that being
+put lightly into the water, it shall rest without descending; and it
+shall advance above water, the Point _A S T_, tripple in height to the
+height of the Rampart _E S_: Now, suppose the Cone _A B D_ more
+depressed, so that it advance above water, only the Point _A I R_,
+higher by half than the Point _A S T_, with the Rampart about it _C I
+R N_. And, because, the Cone _A B D_ is to the Cone _A I R_, as the
+cube of the Line _S T_ is to the cube of the Line _I R_, but the
+Cylinder _E S T O_, is to the Cylinder _C I R N_, as the Square of _S
+T_ to the Square of _I R_, the Cone _A S T_ shall be Octuple to the
+Cone _A I R_, and the Cylinder _E S T O_, quadruple to the Cylinder _C
+I R N_: But the Cone _A S T_, is equall to the Cylinder _E S T O_:
+Therefore, the Cylinder _C I R N_, shall be double to the Cone _A I
+R_: and the water which might be contained in the Rampart _C I R N_,
+would be double in Mass and in Weight to the Cone _A I R_, and,
+therefore, would be able to sustain the double of the Weight of the
+Cone _A I R_: Therefore, if to the whole Cone _A B D_, there be added
+as much Weight as the Gravity of the Cone _A I R_, that is to say, the
+eighth part of the weight of the Cone _A S T_, it also shall be
+sustained by the Rampart _C I R N_, but without that it shall go to
+the bottome: the Cone _A B D_, being, by the addition of the eighth
+part of the weight of the Cone _A S T_, made specifically more grave
+than the water. But if the Altitude of the Cone _A I R_, were two
+thirds of the Altitude of the Cone _A S T_, the Cone _A S T_ would be
+to the Cone _A I R_, as twenty seven to eight; and the Cylinder _E S T
+O_, to the Cylinder _C I R N_, as nine to four, that is, as twenty
+seven to twelve; and, therefore, the Cylinder _C I R N_, to the Cone
+_A I R_, as twelve to eight; and the excess of the Cylinder _C I R N_,
+above the Cone _A I R_, to the Cone _A S T_, as four to twenty seven:
+therefore if to the Cone _A B D_ be added so much weight as is the
+four twenty sevenths of the weight of the Cone _A S T_, which is a
+little more then its seventh part, it also shall continue to swimme,
+and the height of the emergent Point shall be double to the height of
+the Rampart. This that hath been demonstrated in Cones, exactly holds
+in Piramides, although the one or the other should be very sharp in
+their Point or Cuspis[77]: From whence we conclude, that the same Accident
+shall so much the more easily happen in all other Figures, by how much
+the less sharp the Tops shall be, in which they determine, being
+assisted by more spacious Ramparts.
+
+    [77] Natatio{n} easiest effected in Figures broad toward the top.
+
+
+
+
+THEOREME XIII.
+
+    [Sidenote: All Figures sink or swim, upon bathing or not bathing
+    of their tops.]
+
+  _All Figures, therefore, of whatever greatnesse, may go, and not
+    go, to the Bottom, according as their Sumities or Tops shall be
+    bathed or not bathed._
+
+
+And this Accident being common to all sorts of Figures, without
+exception of so much as one. Figure hath, therefore, no part in the
+production of this Effect, of sometimes sinking, and sometimes again
+not sinking, but only the being sometimes conjoyned to, and sometimes
+seperated from, the supereminent Air: which cause, in fine, who so
+shall rightly, and, as we say, with both his Eyes, consider this
+business, will find that it is reduced to, yea, that it really is the
+same with, the true, Naturall and primary cause of Natation or
+Submersion; to wit, the excess or deficiency of the Gravity of the
+water, in relation to the Gravity of that Solid Magnitude, that is
+demitted into the water. For like as a Plate of Lead, as thick as the
+back of a Knife, which being put into the water by it self alone goes
+to the bottom, if upon it you fasten a piece of Cork four fingers
+thick, doth continue afloat, for that now the Solid that is demitted
+in the water, is not, as before, more grave than the water, but less,
+so the Board of Ebony, of its own nature more grave than water; and,
+therefore, descending to the bottom, when it is demitted by it self
+alone into the water, if it shall be put upon the water, conjoyned
+with an Expanded vail of Air, that together with the Ebony doth
+descend, and that it be such, as that it doth make with it a compound
+less grave than so much water in Mass, as equalleth the Mass already
+submerged and depressed beneath the Levell of the waters Surface, it
+shall not descend any farther, but shall rest, for no other than the
+universall and most common cause, which is that Solid Magnitudes, less
+grave _in specie_ than the water, go not to the bottom.
+
+So that if one should take a Plate of Lead, as for Example, a finger
+thick, and an handfull broad every way, and should attempt to make it
+swimme, with putting it lightly on the water, he would lose his
+Labour, because that if it should be depressed an Hairs breadth beyond
+the possible Altitude of the Ramparts of water, it would dive and
+sink; but if whilst it is going downwards, one should make certain
+Banks or Ramparts about it, that should hinder the defusion of the
+water upon the said Plate, the which Banks should rise so high, as
+that they might be able to contain as much water, as should weigh
+equally with the said Plate, it would, witho{u}t all Question, descend
+no lower, but would rest, as being sustained by vertue of the Air
+contained within the aforesaid Ramparts: and, in short, there would be
+a Vessell by this means formed with the bottom of Lead. But if the
+thinness of the Lead shall be such, that a very small height of
+Rampart would suffice to contain so much Air, as might keep it afloat,
+it shall also rest without the Artificiall Banks or Ramparts, but yet
+not without the Air, because the Air by it self makes Banks sufficient
+for a small height, to resist the Superfusion of the water: so that
+that which in this case swimmes, is as it were a Vessell filled with
+Air, by vertue of which it continueth afloat.
+
+I will, in the last place, with an other Experime{n}t, attempt to
+remove all difficulties, if so be there should yet be any doubt left
+in any one, touching the opperation of this [E]Continuity of the Air,
+with the thin Plate which swims, and afterwards put an end to this
+part of my discourse.
+
+    [E] Or rather Contiguity,
+
+I suppose my self to be questioning with some of my Oponents.
+
+Whether Figure have any influence upon the encrease or diminution of
+the Resistance in any Weight against its being raised in the Air[78]; and
+I suppose, that I am to maintain the Affirmative, asserting that a
+Mass of Lead, reduced to the Figure of a Ball, shall be raised with
+less force, then if the same had been made into a thinne and broad
+Plate, because that it in this spacious Figure, hath a great quantity
+of Air to penetrate, and in that other, more compacted and contracted
+very little: and to demonstrate the truth of such my Opinion, I will
+hang in a small thred first the Ball or Bullet, and put that into the
+water, tying the thred that upholds it to one end of the Ballance that
+I hold in the Air, and to the other end I by degrees adde so much
+Weight, till that at last it brings up the Ball of Lead out of the
+water: to do which, suppose a Gravity of thirty Ounces sufficeth; I
+afterwards reduce the said Lead into a flat and thinne Plate, the
+which I likewise put into the water, suspended by three threds, which
+hold it parallel to the Surface of the water, and putting in the same
+manner, Weights to the other end, till such time as the Plate comes to
+be raised and drawn out of the water: I finde that thirty six ounces
+will not suffice to seperate it from the water, and raise it thorow
+the Air: and arguing from this Experiment, I affirm, that I have fully
+demonstrated the truth of my Proposition. Here my Oponents desires me
+to look down, shewing me a thing which I had not before observed, to
+wit, that in the Ascent of the Plate out of the water, it draws after
+it another Plate (_if I may so call it_) of water, which before it
+divides and parts from the inferiour Surface of the Plate of Lead, is
+raised above the Levell of the other water, more than the thickness of
+the back of a Knife: Then he goeth to repeat the Experiment with the
+Ball, and makes me see, that it is but a very small quantity of water,
+which cleaves to its compacted and contracted Figure: and then he
+subjoynes, that its no wonder, if in seperating the thinne and broad
+Plate from the water, we meet with much greater Resistance, than in
+seperating the Ball, since together with the Plate, we are to raise a
+great quantity of water, which occurreth not in the Ball: He telleth
+me moreover, how that our Question is, whether the Resistance of
+Elevation be greater in a dilated Plate of Lead, than in a Ball, and
+not whether more resisteth a Plate of Lead with a great quantity of
+water, or a Ball with a very little water: He sheweth me in the close,
+that the putting the Plate and the Ball first into the water, to make
+proofe thereby of their Resistance in the Air, is besides our case,
+which treats of Elivating in the Air, and of things placed in the Air,
+and not of the Resistance that is made in the Confines of the Air and
+water, and by things which are part in Air and part in water: and
+lastly, they make me feel with my hand, that when the thinne Plate is
+in the Air, and free from the weight of the water, it is raised with
+the very same Force that raiseth the Ball. Seeing, and understanding
+these things, I know not what to do, unless to grant my self
+convinced, and to thank such a Friend, for having made me to see that
+which I never till then observed: and, being advertised by this same
+Accident, to tell my Adversaries, that our Question is, whether a
+Board and a Ball of Ebony, equally go to the bottom in water, and not
+a Ball of Ebony and a Board of Ebony, joyned with another flat Body of
+Air: and, farthermore, that we speak of sinking, and not sinking to
+the bottom, in water, and not of that which happeneth in the Confines
+of the water and Air to Bodies that be part in the Air, and part in
+the water; nor much less do we treat of the greater or lesser Force
+requisite in seperating this or that Body from the Air; not omitting
+to tell them, in the last place, that the Air doth resist, and
+gravitate downwards in the water, just so much as the water (if I may
+so speak) gravitates and resists upwards in the Air, and that the same
+Force is required to sinke a Bladder under water, that is full of Air,
+as to raise it in the Air, being full of water, removing the
+consideration of the weight of that Filme or Skinne, and considering
+the water and the Air only. And it is likewise true, that the same
+Force is required to sink a Cup or such like Vessell under water,
+whilst it is full of Air, as to raise it above the Superficies of the
+water, keeping it with the mouth downwards; whilst it is full of
+water, which is constrained in the same manner to follow the Cup which
+contains it, and to rise above the other water into the Region of the
+Air, as the Air is forced to follow the same Vessell under the Surface
+of the water, till that in this c{a}se the water, surmounting the
+brimme of the Cup, breaks in, driving thence the Air, and in that
+case, the said brimme coming out of the water, and arriving to the
+Confines of the Air, the water falls down, and the Air sub-enters to
+fill the cavity of the Cup: upon which ensues, that he no less
+transgresses the Articles of the _Convention_, who produceth a Plate
+conjoyned with much Air, to see if it descend to the bottom in water,
+then he that makes proof of the Resistance against Elevation in Air
+with a Plate of Lead, joyned with a like quantity of water.
+
+    [78] An Experiment of the operation of Figures, in encreasing or
+    lessening of the Airs Resistance of Division.
+
+    [Sidenote: _Aristotles_ opinion touching the Operation of Figure
+    examined.]
+
+I have said all that I could at present think of, to maintain the
+Assertion I have undertook. It remains, that I examine that which
+_Aristotle_ hath writ of this matter towards the end of his Book De
+Caelo[79]; wherein I shall note two things: the one that it being true as
+hath been demonstrated, that Figure hath nothing to do about the
+moving or not moving it self upwards or downwards, its seemes that
+_Aristotle_ at his first falling upon this Speculation, was of the
+same opinion, as in my opinion may be collected from the examination
+of his words. 'Tis true, indeed, that in essaying afterwards to render
+a reason of such effect, as not having in my conceit hit upon the
+right, (which in the second place I will examine) it seems that he is
+brought to admit the largenesse of Figure, to be interessed in this
+operation. As to the first particuler, hear the precise words of
+_Aristotle_.
+
+    [79] _Aristot. de Caelo_ Lib. 4. Cap 6.
+
+_Figures are not the Causes of moving simply upwards or downwards, but
+of moving more slowly or swiftly[80][81], and by what means this comes to
+pass, it is not difficult to see._
+
+    [80] _Aristotle_ makes not Figure the cause of Motion absolutely,
+    but of swift or slow motion,
+
+    [81] Lib. 4. Cap. 6: Text. 42.
+
+Here first I note, that the terms being four, which fall under the
+present consideration, namely, Motion, Rest, Slowly and Swiftly: And
+_Aristotle_ naming figures as Causes of Tardity and Velocity,
+excluding them from being the Cause of absolute and simple Motion, it
+seems necessary, that he exclude them on the other side, from being
+the Cause of Rest, so that his meaning is this. Figures are not the
+Causes of moving or not moving absolutely, but of moving quickly or
+slowly: and, here, if any should say the mind of _Aristotle_ is to
+exclude Figures from being Causes of Motion, but yet not from being
+Causes of Rest, so that the sence would be to remove from Figures,
+there being the Causes of moving simply, but yet not there being
+Causes of Rest, I would demand, whether we ought with _Aristotle_ to
+understand, that all Figures universally, are, in some manner, the
+causes of Rest in those Bodies, which otherwise would move, or else
+some particular Figures only, as for Example, broad and thinne
+Figures: If all indifferently, then every Body shall rest: because
+every Body hath some Figure, which is false; but if some particular
+Figures only may be in some manner a Cause of Rest, as, for Example,
+the broad, then the others would be in some manner the Causes of
+Motion: for if from seeing some Bodies of a contracted Figure move,
+which after dilated into Plates rest, may be inferred, that the
+Amplitude of Figure hath a part in the Cause of that Rest; so from
+seeing such like Figures rest, which afterwards contracted move, it
+may with the same reason be affirmed, that the united and contracted
+Figure, hath a part in causing Motion, as the remover of that which
+impeded it: The which again is directly opposite to what _Aristotle_
+saith, namely, that Figures are not the Causes of Motion. Besides, if
+_Aristotle_ had admitted and not excluded Figures from being Causes of
+not moving in some Bodies, which moulded into another Figure would
+move, he would have impertinently propounded in a dubitative manner,
+in the words immediately following, whence it is, that the large and
+thinne Plates of Lead or Iron, rest upon the water, since the Cause
+was apparent, namely, the Amplitude of Figure. Let us conclude,
+therefore, that the meaning of _Aristotle_ in this place is to affirm,
+that Figures are not the Causes of absolutely moving or not moving,
+but only of moving swiftly or slowly: which we ought the rather to
+believe, in regard it is indeed a most true conceipt and opinion. Now
+the mind of _Aristotle_ being such, and appearing by consequence,
+rather contrary at the first sight, then favourable to the assertion
+of the Oponents, it is necessary, that their Interpretation be not
+exactly the same with that, but such, as being in part understood by
+some of them, and in part by others, was set down: and it may easily
+be indeed so, being an Interpretation consonent to the sence of the
+more famous Interpretors, which is, that the Adverbe _Simply_ or
+_Absolutely_, put in the Text, ought not to be joyned to the Verbe to
+_Move_, but with the Noun _Causes_: so that the purport of
+_Aristotles_ words, is to affirm, That Figures are not the Causes
+absolutely of moving or not moving, but yet are Causes _Secundum
+quid_, _viz._ in some sort; by which means, they are called Auxiliary
+and Concomitant Causes: and this Proposition is received and asserted
+as true by _Signor Buonamico Lib. 5. Cap. 28._ where he thus writes.
+_There are other Causes concomitant, by which some things float, and
+others sink, among which the Figures of Bodies hath the first place_,
+&c.
+
+Concerning this Proposition, I meet with many doubts and difficulties,
+for which me thinks the words of _Aristotle_ are not capable of such a
+construction and sence, and the difficulties are these.
+
+First in the order and disposure of the words of _Aristotle_, the
+particle _Simpliciter_, or if you will _absolute_, is conjoyned with
+the Verb _to move_, and seperated from the Noun _Causes_, the which is
+a great presumption in my favour, seeing that the writing and the Text
+saith, Figures are not the Cause of moving simply upwards or
+downwards, but of quicker or slower Motion: and, saith not, Figures
+are not simply the Causes of moving upwards or downwards, and when the
+words of a Text receive, transposed, a sence different from that which
+they sound, taken in the order wherein the Author disposeth them, it
+is not convenient to inverte them. And who will affirm that
+_Aristotle_ desiring to write a Proposition, would dispose the words
+in such sort, that they should import a different, nay, a contrary
+sence? contrary, I say, because understood as they are written; they
+say, that Figures are not the Causes of Motion, but inverted, they
+say, that Figures are the Causes of Motion, &c.
+
+Moreover, if the intent of _Aristotle_ had been to say, that Figures
+are not simply the Causes of moving upwards or downwards, but only
+Causes _Secundum quid_, he would not have adjoyned those words, _but
+they are Causes of the more swift or slow Motion_; yea, the subjoining
+this would have been not only superfluous but false, for that the
+whole tenour of the Proposition would import thus much. Figures are
+not the absolute Causes of moving upwards or downwards, but are the
+absolute Cause of the swift or slow Motion; which is not true: because
+the primary Causes of greater or lesser Velocity, are by _Aristotle_
+in the 4th of his _Physicks_, _Text. 71._ attributed to the greater or
+lesser Gravity of Moveables, compared among themselves, and to the
+greater or lesser Resistance of the _Medium's_, depending on their
+greater or less Crassitude: and these are inserted by _Aristotle_ as
+the primary Causes; and these two only are in that place nominated:
+and Figure comes afterwards to be considered, _Text. 74._ rather as an
+Instrumentall Cause of the force of the Gravity, the which divides
+either with the Figure, or with the _Impetus_; and, indeed, Figure by
+it self without the force of Gravity or Levity, would opperate
+nothing.
+
+I adde, that if _Aristotle_ had an opinion that Figure had been in
+some sort the Cause of moving or not moving, the inquisition which he
+makes immediately in a doubtfull manner, whence it comes, that a Plate
+of Lead flotes, would have been impertinent; for if but just before he
+had said, that Figure was in a certain sort the Cause of moving or not
+moving, he needed not to call in Question, by what Cause the Plate of
+Lead swims, and then ascribing the Cause to its Figure; and framing a
+discourse in this manner. Figure is a Cause _Secundum quid_ of not
+sinking: but, now, if it be doubted, for what Cause a thin Plate of
+Lead goes not to the bottom; it shall be answered, that that proceeds
+from its Figure: a discourse which would be indecent in a Child, much
+more in _Aristotle_; For where is the occasion of doubting? And who
+sees not, that if _Aristotle_ had held, that Figure was in some sort a
+Cause of Natation, he would without the least Hesitation have writ;
+That Figure is in a certain sort the Cause of Natation, and therefore
+the Plate of Lead in respect of its large and expatiated Figure swims;
+but if we take the proposition of _Aristotle_ as I say, and as it is
+written, and as indeed it is true, the ensuing words come in very
+oppositely, as well in the introduction of swift and slow, as in the
+question, which very pertinently offers it self, and would say thus
+much.
+
+Figures are not the Cause of moving or not moving simply upwards or
+downwards, but of moving more quickly or slowly: But if it be so, the
+Cause is doubtfull, whence it proceeds, that a Plate of Lead or of
+Iron broad and thin doth swim, &c. And the occasion of the doubt is
+obvious, because it seems at the first glance, that the Figure is the
+Cause of this Natation, since the same Lead, or a less quantity, but
+in another Figure, goes to the bottom, and we have already affirmed,
+that the Figure hath no share in this effect.
+
+Lastly, if the intent of _Aristotle_ in this place had been to say,
+that Figures, although not absolutely, are at least in some measure
+the Cause of moving or not moving: I would have it considered, that he
+names no less the Motion upwards, than the other downwards: and
+because in exemplifying it afterwards, he produceth no other
+Experiments than of a Plate of Lead, and Board of Ebony, Matters that
+of their own Nature go to the bottom, but by vertue (as our
+Adversaries say) of their Figure, rest afloat; it is fit that they
+should produce some other Experiment of those Matters, which by their
+Nature swims, but retained by their Figure rest at the bottom. But
+since this is impossible to be done, we conclude, that _Aristotle_ in
+this place, hath not attributed any action to the Figure of simply
+moving or not moving.
+
+But though he hath exquisitely Philosophiz'd, in investigating the
+solution of the doubts he proposeth, yet will I not undertake to
+maintain, rather various difficulties, that present themselves unto
+me, give me occasion of suspecting that he hath not entirely displaid
+unto us, the true Cause of the present Conclusion: which difficulties
+I will propound one by one, ready to change opinion, whenever I am
+shewed, that the Truth is different from what I say; to the confession
+whereof I am much more inclinable than to contradiction.
+
+    [Sidenote: _Aristotle_ erred in affirming a Needle dimitted long
+    wayes to sink.]
+
+_Aristotle_ having propounded the Question, whence it proceeds, that
+broad Plates of Iron or Lead, float or swim; he addeth (as it were
+strengthening the occasion of doubting) forasmuch as other things,
+less, and less grave, be they round or long, as for instance a Needle
+go to the bottom. Now I here doubt, or rather am certain that a Needle
+put lightly upon the water, rests afloat, no less than the thin Plates
+of Iron or Lead. I cannot believe, albeit it hath been told me, that
+some to defend _Aristotle_ should say, that he intends a Needle
+demitted not longwayes but endwayes, and with the Point downwards;
+nevertheless, not to leave them so much as this, though very weak
+refuge, and which in my judgement _Aristotle_ himself would refuse, I
+say it ought to be understood, that the Needle must be demitted,
+according to the Dimension named by _Aristotle_, which is the length:
+because, if any other Dimension than that which is named, might or
+ought to be taken, I would say, that even the Plates of Iron and Lead,
+sink to the bottom, if they be put into the water edgewayes and not
+flatwayes. But because _Aristotle_ saith, broad Figures go not to the
+bottom, it is to be understood, being demitted broadwayes: and,
+therefore, when he saith, long Figures as a Needle, albeit light, rest
+not afloat, it ought to be understood of them when demitted longwayes.
+
+  _Moreover, to say that_ Aristotle _is to be understood of the
+  Needle demitted with the Point downwards, is to father upon him a
+  great impertinency; for in this place he saith, that little
+  Particles of Lead or Iron, if they be round or long as a Needle, do
+  sink to the bottome; so that by his Opinion, a Particle or small
+  Grain of Iron cannot swim: and if he thus believed, what a great
+  folly would it be to subjoyn, that neither would a Needle demitted
+  endwayes swim? And what other is such a Needle, but many such like
+  Graines accumulated one upon another? It was too unworthy of such a
+  man to say, that one single Grain of Iron could not swim, and that
+  neither can it swim, though you put a hundred more upon it._
+
+Lastly, either _Aristotle_ believed, that a Needle demitted longwayes
+upon the water, would swim, or he believed that it would not swim: If
+he believed it would not swim, he might well speak as indeed he did;
+but if he believed and knew that it would float, why, together with
+the dubious Problem of the Natation of broad Figures, though of
+ponderous Matter, hath he not also introduced the Question; whence it
+proceeds, that even long and slender Figures, howbeit of Iron or Lead
+do swim? And the rather, for that the occasion of doubting seems
+greater in long and narrow Figures, than in broad and thin, as from
+_Aristotles_ not having doubted of it, is manifested.
+
+No lesser an inconvenience would they fasten upon _Aristotle_, who in
+his defence should say, that he means a Needle pretty thick, and not a
+small one; for take it for granted to be intended of a small one; and
+it shall suffice to reply, that he believed that it would swim; and I
+will again charge him with having avoided a more wonderfull and
+intricate Probleme, and introduced the more facile and less
+wonderfull.
+
+We say freely therefore, that _Aristotle_ did hold, that only the
+broad Figure did swim, but the long and slender, such as a Needle,
+not. The which nevertheless is false, as it is also false in round
+Bodies: because, as from what hath been predemonstrated, may be
+gathered, little Balls of Lead and Iron, do in like manner swim.
+
+    [Sidenote: _Aristotle_ affirmeth some Bodies volatile for their
+    Minuity, Text. 42.]
+
+He proposeth likewise another Conclusion, which likewise seems
+different from the truth, and it is, That some things, by reason of
+their littleness fly in the Air, as the small dust of the Earth, and
+the thin leaves of beaten Gold: but in my Opinion, Experience shews
+us, that that happens not only in the Air, but also in the water, in
+which do descend, even those Particles or Atomes of Earth, that
+disturbe it, whose minuity is such, that they are not deservable, save
+only when they are many hundreds together. Therefore, the dust of the
+Earth, and beaten Gold, do not any way sustain themselves in the Air,
+but descend downwards, and only fly to and again in the same, when
+strong Windes raise them, or other agitations of the Air commove them:
+and this also happens in the commotion of the water, which raiseth its
+Sand from the bottom, and makes it muddy. But _Aristotle_ cannot mean
+this impediment of the commotion, of which he makes no mention, nor
+names other than the lightness of such Minutiae or Atomes, and the
+Resistance of the Crassitudes of the Water and Air, by which we see,
+that he speakes of a calme, and not disturbed and agitated Air: but in
+that case, neither Gold nor Earth, be they never so small, are
+sustained, but speedily descend.
+
+    [Sidenote: _Democritus_ placed the Cause of Natation in certain
+    fiery Atomes.]
+
+He passeth next to confute _Democritus_[82], which, by his Testimony would
+have it, that some Fiery Atomes, which continually ascend through the
+water, do spring upwards, and sustain those grave Bodies, which are
+very broad, and that the narrow descend to the bottom, for that but a
+small quantity of those Atomes, encounter and resist them.
+
+    [82] _Aristot. De Caelo_ lib. 4. cap. 6. text. 43.
+
+I say, _Aristotle_ confutes this position[83], saying, that that should
+much more occurre in the Air, as the same _Democritus_ instances
+against himself, but after he had moved the objection, he slightly
+resolves it, with saying, that those Corpuscles which ascend in the
+Air, make not their _Impetus_ conjunctly. Here I will not say, that
+the reason alledged by _Democritus_ is true[84], but I will only say, it
+seems in my judgement, that it is not wholly confuted by _Aristotle_,
+whilst he saith, that were it true, that the calid ascending Atomes,
+should sustain Bodies grave, but very broad, it would much more be
+done in the Air, than in Water, for that haply in the Opinion of
+_Aristotle_, the said calid Atomes ascend with much greater Force and
+Velocity through the Air, than through the water. And if this be so,
+as I verily believe it is, the Objection of _Aristotle_ in my
+judgement seems to give occasion of suspecting, that he may possibly
+be deceived in more than one particular: First, because those calid
+Atomes, (whether they be Fiery Corpuscles, or whether they be
+Exhalations, or in short, whatever other matter they be, that ascends
+upwards through the Air) cannot be believed to mount faster through
+Air, than through water: but rather on the contrary, they peradventure
+move more impetuously through the water, than through the Air, as hath
+been in part demonstrated above. And here I cannot finde the reason,
+why _Aristotle_ seeing, that the descending Motion of the same
+Moveable, is more swift in Air, than in water, hath not advertised us,
+that from the contrary Motion, the contrary should necessarily follow;
+to wit, that it is more swift in the water, than in the Air: for since
+that the Moveable which descendeth, moves swifter through the Air,
+than through the water, if we should suppose its Gravity gradually to
+diminish, it would first become such, that descending swiftly through
+the Air, it would descend but slowly through the water: and then
+again, it might be such, that descending in the Air, it should ascend
+in the water: and being made yet less grave, it shall ascend swiftly
+through the water, and yet descend likewise through the Air: and in
+short, before it can begin to ascend, though but slowly through the
+Air, it shall ascend swiftly through the water: how then is it true,
+that ascending Moveables move swifter through the Air, than through
+the water?
+
+    [83] _Democritus_ confuted by _Aristotle_, text 43.
+
+    [84] _Aristotles_ confutation of _Democritus_ refuted by the
+    Author.
+
+That which hath made _Aristotle_ believe, the Motion of Ascent to be
+swifter in Air, than in water, was first, the having referred the
+Causes of slow and quick, as well in the Motion of Ascent, as of
+Descent, only to the diversity of the Figures of the Moveable, and to
+the more or less Resistance of the greater or lesser Crassitude, or
+Rarity of the _Medium_; not regarding the comparison of the Excesses
+of the Gravities of the Moveables, and of the _Mediums_: the which
+notwithstanding, is the most principal point in this affair: for if
+the augmentation and diminution of the Tardity or Velocity, should
+have only respect to the Density or Rarity of the _Medium_, every Body
+that descends in Air, would descend in water: because whatever
+difference is found between the Crassitude of the water, and that of
+the Air, may well be found between the Velocity of the same Moveable
+in the Air, and some other Velocity: and this should be its proper
+Velocity in the water, which is absolutely false. The other occasion
+is, that he did believe, that like as there is a positive and
+intrinsecall Quality, whereby Elementary Bodies have a propension of
+moving towards the Centre of the Earth, so there is another likewise
+intrinsecall[85], whereby some of those Bodies have an _Impetus_ of flying
+the Centre, and moving upwards: by Vertue of which intrinsecall
+Principle, called by him Levity, the Moveables which have that same
+Motion more easily penetrate the more subtle _Medium_, than the more
+dense: but such a Proposition appears likewise uncertain, as I have
+above hinted in part, and as with Reasons and Experiments, I could
+demonstrate, did not the present Argument importune me, or could I
+dispatch it in few words.
+
+    [85] Lib. 4. Cap. 5.
+
+The Objection therefore of _Aristotle_ against _Democritus_, whilst he
+saith, that if the Fiery ascending Atomes should sustain Bodies grave,
+but of a distended Figure, it would be more observable in the Air than
+in the water, because such Corpuscles move swifter in that, than in
+this, is not good; yea the contrary would evene, for that they ascend
+more slowly through the Air: and, besides their moving slowly, they
+ascend, not united together, as in the water, but discontinue, and, as
+we say, scatter: And, therefore, as _Democritus_ well replyes,
+resolving the instance they make not their push or _Impetus_
+conjunctly.
+
+_Aristotle_, in the second place, deceives himself, whilst he will
+have the said grave Bodies to be more easily sustained by the said
+Fiery ascending Atomes in the Air than in the Water: not observing,
+that the said Bodies are much more grave in that, than in this, and
+that such a Body weighs ten pounds in the Air, which will not in the
+water weigh 1/2 an ounce; how can it then be more easily sustained in
+the Air, than in the Water?
+
+    [Sidenote: _Democritus_ confuted by the Authour.]
+
+Let us conclude, therefore, that _Democritus_ hath in this particular
+better Philosophated than _Aristotle_. But yet will not I affirm, that
+_Democritus_ hath reason'd rightly, but I rather say, that there is a
+manifest Experiment that overthrows his Reason, and this it is, That
+if it were true, that calid ascending Atomes should uphold a Body,
+that if they did not hinder, would go to the bottom, it would follow,
+that we may find a Matter very little superiour in Gravity to the
+water, the which being reduced into a Ball, or other contracted
+Figure, should go to the bottom, as encountring but few Fiery Atomes;
+and which being distended afterwards into a dilated and thin Plate,
+should come to be thrust upwards by the impulsion of a great Multitude
+of those Corpuscles, and at last carried to the very Surface of the
+water: which wee see not to happen; Experience shewing us, that a Body
+_v. gra._ of a Sphericall Figure, which very hardly, and with very
+great leasure goeth to the bottom, will rest there, and will also
+descend thither, being reduced into whatsoever other distended Figure.
+We must needs say then, either that in the water, there are no such
+ascending Fiery Atoms, or if that such there be, that they are not
+able to raise and lift up any Plate of a Matter, that without them
+would go to the bottom: Of which two Positions, I esteem the second to
+be true, understanding it of water, constituted in its naturall
+Coldness. But if we take a Vessel of Glass, or Brass, or any other
+hard matter, full of cold water, within which is put a Solid of a flat
+or concave Figure, but that in Gravity exceeds the water so little,
+that it goes slowly to the bottom; I say, that putting some burning
+Coals under the said Vessel, as soon as the new Fiery Atomes shall
+have penetrated the substance of the Vessel, they shall without doubt,
+ascend through that of the water, and thrusting against the foresaid
+Solid, they shall drive it to the Superficies, and there detain it, as
+long as the incursions of the said Corpuscles shall last, which
+ceasing after the removall of the Fire, the Solid being abandoned by
+its supporters, shall return to the bottom.
+
+But _Democritus_ notes, that this Cause only takes place when we
+treat of raising and sustaining of Plates of Matters, but very little
+heavier than the water, or extreamly thin: but in Matters very grave,
+and of some thickness, as Plates of Lead or other Mettal, that same
+Effect wholly ceaseth: In Testimony of which, let's observe that such
+Plates, being raised by the Fiery Atomes, ascend through all the depth
+of the water, and stop at the Confines of the Air, still staying under
+water: but the Plates of the Opponents stay not, but only when they
+have their upper Superficies dry, nor is there any means to be used,
+that when they are within the water, they may not sink to the bottom.
+The cause, therefore, of the Supernatation of the things of which
+_Democritus_ speaks is one, and that of the Supernatation of the
+things of which we speak is another. But, returning to _Aristotle_[86],
+methinks that he hath more weakly confuted _Democritus_, than
+_Democritus_ himself hath done: For _Aristotle_ having propounded the
+Objection which he maketh against him, and opposed him with saying,
+that if the calid ascendent Corpuscles were those that raised the thin
+Plate, much more then would such a Solid be raised and born upwards
+through the Air, it sheweth that the desire in _Aristotle_ to detect
+_Democritus_, was predominate over the exquisiteness of Solid
+Philosophizing: which desire of his he hath discovered in other
+occasions, and that we may not digress too far from this place, in the
+Text precedent to this Chapter which we have in hand[87]; where he
+attempts to confute the same _Democritus_ for that he, not contenting
+himself with names only, had essayed more particularly to declare what
+things Gravity and Levity were; that is, the Causes of descending and
+ascending, (and had introduced Repletion and Vacuity) ascribing this
+to Fire, by which it moves upwards, and that to the Earth, by which it
+descends; afterwards attributing to the Air more of Fire, and to the
+water more of Earth. But _Aristotle_ desiring a positive Cause, even
+of ascending Motion, and not as _Plato_, or these others, a simple
+negation, or privation, such as Vacuity would be in reference to
+Repletion[88], argueth against _Democritus_ and saith: If it be true, as
+you suppose, then there shall be a great Mass of water, which shall
+have more of Fire, than a small Mass of Air, and a great Mass of Air,
+which shall have more of Earth than a little Mass of water, whereby it
+would ensue, that a great Mass of Air, should come more swiftly
+downwards, than a little quantity of water: But that is never in any
+case soever: Therefore _Democritus_ discourseth erroneously.
+
+    [86] _Aristotle_ shews his desire of finding _Democritus_ in an
+    Error, to exceed that of discovering Truth.
+
+    [87] Cap. 5. Text 41.
+
+    [88] Id. ibid.
+
+But in my opinion, the Doctrine of _Democritus_ is not by this
+allegation overthrown, but if I erre not, the manner of _Aristotle_
+deduction either concludes not, or if it do conclude any thing, it may
+with equall force be restored against himself. _Democritus_ will grant
+to _Aristotle_, that there may be a great Mass of Air taken, which
+contains more Earth, than a small quantity of water, but yet will
+deny, that such a Mass of Air, shall go faster downwards than a little
+water, and that for many reasons. First, because if the greater
+quantity of Earth, contained in the great Mass of Air, ought to cause
+a greater Velocity than a less quantity of Earth, contained in a
+little quantity of water, it would be necessary, first, that it were
+true, that a greater Mass of pure Earth, should move more swiftly than
+a less: But this is false, though _Aristotle_ in many places affirms
+it to be true: because not the greater absolute, but the greater
+specificall Gravity, is the cause of greater Velocity[89]: nor doth a Ball
+of Wood, weighing ten pounds, descend more swiftly than one weighing
+ten Ounces, and that is of the same Matter: but indeed a Bullet of
+Lead of four Ounces, descendeth more swiftly than a Ball of Wood of
+twenty Pounds: because the Lead is more _grave in specie_ than the
+Wood. Therefore, its not necessary, that a great Mass of Air, by
+reason of the much Earth contained in it, do descend more swiftly than
+a little Mass of water[90], but on the contrary, any whatsoever Mass of
+water, shall move more swiftly than any other of Air, by reason the
+participation of the terrene parts _in specie_ is greater in the
+water, than in the Air. Let us note, in the second place, how that in
+multiplying the Mass of the Air, we not only multiply that which is
+therein of terrene, but its Fire also: whence the Cause of ascending,
+no less encreaseth, by vertue of the Fire, than that of descending on
+the account of its multiplied Earth. It was requisite in increasing
+the greatness of the Air, to multiply that which it hath of terrene
+only, leaving its Fire in its first state, for then the terrene parts
+of the augmented Air, overcoming the terrene parts of the small
+quantity of water, it might with more probability have been pretended,
+that the great quantity of Air, ought to descend with a greater
+_Impetus_, than the little quantity of water.
+
+    [89] The greater Specificall, not the greater absolute Gravity,
+    is the Cause of Velocity.
+
+    [90] Any Mass of water shal move more swiftly, than any of Air,
+    and why.
+
+Therefore, the Fallacy lyes more in the Discourse of _Aristotle_, than
+in that of _Democritus_, who with severall other Reasons might oppose
+_Aristotle_, and alledge; If it be true, that the extreame Elements be
+one simply grave, and the other simply light, and that the mean
+Elements participate of the one, and of the other Nature; but the Air
+more of Levity, and the water more of Gravity, then there shall be a
+great Mass of Air, whose Gravity shall exceed the Gravity of a little
+quantity of water, and therefore such a Mass of Air shall descend more
+swiftly than that little water: But that is never seen to occurr:
+Therefore its not true, that the mean Elements do participate of the
+one, and the other quality. This argument is fallacious, no less than
+the other against _Democritus_.
+
+Lastly, _Aristotle_ having said, that if the Position of _Democritus_
+were true, it would follow, that a great Mass of Air should move more
+swiftly than a small Mass of water, and afterwards subjoyned, that
+that is never seen in any Case: methinks others may become desirous to
+know of him in what place this should evene, which he deduceth against
+_Democritus_, and what Experiment teacheth us, that it never falls out
+so. To suppose to see it in the Element of water, or in that of the
+Air is vain, because neither doth water through water, nor Air through
+Air move, nor would they ever by any whatever participation others
+assign them, of Earth or of Fire: the Earth, in that it is not a Body
+fluid, and yielding to the mobility of other Bodies, is a most
+improper place and _Medium_ for such an Experiment: _Vacuum_,
+according to the same _Aristotle_ himself, there is none, and were
+there, nothing would move in it: there remains the Region of Fire, but
+being so far distant from us, what Experiment can assure us, or hath
+assertained _Aristotle_ in such sort, that he should as of a thing
+most obvious to sence, affirm what he produceth in confutation of
+_Democritus_, to wit, that a great Mass of Air, is moved no swifter
+than a little one of water? But I will dwell no longer upon this
+matter, whereon I have spoke sufficiently: but leaving _Democritus_, I
+return to the Text of _Aristotle_, wherein he goes about to render the
+true reason, how it comes to pass, that the thin Plates of Iron or
+Lead do swim on the water; and, moreover, that Gold it self being
+beaten into thin Leaves, not only swims in water, but flyeth too and
+again in the Air. He supposeth that of Continualls[91], some are easily
+divisible, others not: and that of the easily divisible, some are more
+so, and some less: and these he affirms we should esteem the Causes.
+He addes that that is easily divisible, which is well terminated, and
+the more the more divisible, and that the Air is more so, than the
+water, and the water than the Earth. And, lastly, supposeth that in
+each kind, the lesse quantity is easlyer divided and broken than the
+greater.
+
+    [91] _De Caelo_ l. 4. c. 6. t. 44.
+
+Here I note, that the Conclusions of _Aristotle_ in generall are all
+true, but methinks, that he applyeth them to particulars, in which
+they have no place, as indeed they have in others, as for Example, Wax
+is more easily divisible than Lead, and Lead than Silver, inasmuch as
+Wax receives all the terms more easlier than Lead, and Lead than
+Silver. Its true, moreover, that a little quantity of Silver is
+easlier divided than a great Mass: and all these Propositions are
+true, because true it is, that in Silver, Lead and Wax, there is
+simply a Resistance against Division, and where there is the absolute,
+there is also the respective. But if as well in water as in Air, there
+be no Renitence against simple Division, how can we say, that the
+water is easlier divided than the Air? We know not how to extricate
+our selves from the Equivocation: whereupon I return to answer, that
+Resistance of absolute Division is one thing, and Resistance of
+Division made with such and such Velocity is another. But to produce
+Rest, and to abate the Motion, the Resistance of absolute Division is
+necessary; and the Resistance of speedy Division, causeth not Rest,
+but slowness of Motion. But that as well in the Air, as in water,
+there is no Resistance of simple Division, is manifest, for that there
+is not found any Solid Body which divides not the Air, and also the
+water: and that beaten Gold, or small dust, are not able to superate
+the Resistance of the Air, is contrary to that which Experience shews
+us, for we see Gold and Dust to go waving to and again in the Air, and
+at last to descend downwards, and to do the same in the water, if it
+be put therein, and separated from the Air. And, because, as I say,
+neither the water, nor the Air do resist simple Division, it cannot be
+said, that the water resists more than the Air. Nor let any object
+unto me, the Example of most light Bodies, as a Feather, or a little
+of the pith of Elder, or water-reed that divides the Air and not the
+water, and from this infer, that the Air is easlier divisible than the
+water; for I say unto them, that if they do well observe, they shall
+see the same Body likewise divide the Continuity of the water[92], and
+submerge in part, and in such a part, as that so much water in Mass
+would weigh as much as the whole Solid. And if they shal yet persist
+in their doubt, that such a Solid sinks not through inability to
+divide the water, I will return them this reply, that if they put it
+under water, and then let it go, they shall see it divide the water,
+and presently ascend with no less celerity, than that with which it
+divided the Air in descending: so that to say that this Solid ascends
+in the Air, but that coming to the water, it ceaseth its Motion, and
+therefore the water is more difficult to be divided, concludes
+nothing: for I, on the contrary, will propose them a piece of Wood, or
+of Wax, which riseth from the bottom of the water, and easily divides
+its Resistance, which afterwards being arrived at the Air, stayeth
+there, and hardly toucheth it; whence I may aswell say, that the water
+is more easier divided than the Air.
+
+    [92] _Archimed. De Insident. humi_ lib. 2. prop. 1.
+
+I will not on this occasion forbear to give warning of another fallacy
+of these persons, who attribute the reason of sinking or swimming to
+the greater or lesse Resistance of the Crassitude of the water against
+Division, making use of the example of an Egg, which in sweet water
+goeth to the bottom, but in salt water swims; and alledging for the
+cause thereof, the faint Resistance of fresh water against Division,
+and the strong Resistance of salt water. But if I mistake not, from
+the same Experiment, we may aswell deduce the quite contrary; namely,
+that the fresh water is more dense, and the salt more tenuous and
+subtle, since an Egg from the bottom of salt water speedily ascends to
+the top, and divides its Resistance, which it cannot do in the fresh,
+in whose bottom it stays, being unable to rise upwards. Into such like
+perplexities, do false Principles Lead men: but he that rightly
+Philosophating, shall acknowledge the excesses of the Gravities of the
+Moveables and of the Mediums, to be the Causes of those effects, will
+say, that the Egg sinks to the bottom in fresh water, for that it is
+more grave than it, and swimeth in the salt, for that its less grave
+than it: and shall without any absurdity, very solidly establish his
+Conclusions.
+
+Therefore the reason totally ceaseth, that _Aristotle_ subjoyns in the
+Text saying[93]; The things, therefore, which have great breadth remain
+above, because they comprehend much, and that which is greater, is not
+easily divided. Such discoursing ceaseth, I say, because its not true,
+that there is in water or in Air any Resistance of Division; besides
+that the Plate of Lead when it stays, hath already divided and
+penetrated the Crassitude of the water, and profounded it self ten or
+twelve times more than its own thickness: besides that such Resistance
+of Division, were it supposed to be in the water, could not rationally
+be affirmed to be more in its superiour parts than in the middle, and
+lower: but if there were any difference, the inferiour should be the
+more dense, so that the Plate would be no less unable to penetrate the
+lower, than the superiour parts of the water; nevertheless we see that
+no sooner do we wet the superiour Superficies of the Board or thin
+Piece of Wood, but it precipitatly, and without any retension,
+descends to the bottom.
+
+    [93] Text 45.
+
+I believe not after all this, that any (thinking perhaps thereby to
+defend _Aristotle_) will say, that it being true, that the much water
+resists more than the little, the said Board being put lower
+descendeth, because there remaineth a less Mass of water to be divided
+by it: because if after the having seen the same Board swim in four
+Inches of water, and also after that in the same to sink, he shall try
+the same Experiment upon a profundity of ten or twenty fathom water,
+he shall see the very self same effect. And here I will take occasion
+to remember, for the removall of an Error that is too common; That
+that Ship or other whatsoever Body, that on the depth of an hundred or
+a thousand fathom, swims with submerging only six fathom of its own
+height, [_or in the Sea dialect, that draws six fathom water_] shall
+swim in the same manner in water, that hath but six fathom and half an
+Inch of depth[94]. Nor do I on the other side, think that it can be said,
+that the superiour parts of the water are the more dense, although a
+most grave Authour hath esteemed the superiour water in the Sea to be
+so, grounding his opinion upon its being more salt, than that at the
+bottom: but I doubt the Experiment, whether hitherto in taking the
+water from the bottom, the Observatour did not light upon some spring
+of fresh water there spouting up: but we plainly see on the contrary,
+the fresh Waters of Rivers to dilate themselves for some miles beyond
+their place of meeting with the salt water of the Sea, without
+descending in it, or mixing with it, unless by the intervention of
+some commotion or turbulency of the Windes.
+
+    [94] A Ship that in 100 Fathome water draweth 6 Fathome, shall
+    float in 6 Fathome and 1/2 an Inch of depth.
+
+But returning to _Aristotle_, I say, that the breadth of Figure hath
+nothing to do in this business more or less, because the said Plate of
+Lead, or other Matter, cut into long Slices, swim neither more nor
+less[95]; and the same shall the Slices do, being cut anew into little
+pieces, because its not the breadth but the thickness that operates in
+this business. I say farther, that in case it were really true, that
+the Renitence to Division were the proper Cause of swimming[96], the
+Figures more narrow and short, would much better swim than the more
+spacious and broad, so that augmenting the breadth of the Figure, the
+facility of supernatation will be deminished, and decreasing, that
+this will encrease.
+
+    [95] Thickness not breadth of Figure to be respected in Natation.
+
+    [96] Were Renitence the cause of Natation, breadth of Figure would
+    hinder the swiming of Bodies.
+
+And for declaration of what I say, consider that when a thin Plate of
+Lead descends, dividing the water, the Division and discontinuation is
+made between the parts of the water, invironing the perimeter or
+Circumference of the said Plate, and according to the bigness greater
+or lesser of that circuit, it hath to divide a greater or lesser
+quantity of water, so that if the circuit, suppose of a Board, be ten
+Feet in sinking it flatways, it is to make the seperation and
+division, and to so speak, an incission upon ten Feet of water; and
+likewise a lesser Board that is four Feet in Perimeter, must make an
+incession of four Feet. This granted, he that hath any knowledge in
+Geometry, will comprehend, not only that a Board sawed in many long
+thin pieces, will much better float than when it was entire, but that
+all Figures, the more short and narrow they be, shall so much the
+better swim. Let the Board A B C D be, for Example, eight Palmes long,
+and five broad, its circuit shall be twenty six Palmes; and so many
+must the incession be, which it shall make in the water to descend
+therein: but if we do saw ir, as suppose into eight little pieces,
+according to the Lines E F, G H, {&}c. making seven Segments, we must
+adde to the twenty six Palmes of the circuit of the whole Board,
+seventy others; whereupon the eight little pieces so cut and
+seperated, have to cut ninty six Palmes of water. And, if moreover, we
+cut each of the said pieces into five parts, reducing them into
+Squares, to the circuit of ninty six Palmes, with four cuts of eight
+Palmes apiece; we shall adde also sixty four Palmes, whereupon the
+said Squares to descend in the water, must divide one hundred and
+sixty Palmes of water, but the Resistance is much greater than that of
+twenty six; therefore to the lesser Superficies, we shall reduce them,
+so much the more easily will they float: and the same will happen in
+all other Figures, whose Superficies are simular amongst themselves,
+but different in bigness: because the said Superficies, being either
+deminished or encreased, always diminish or encrease their Perimeters
+in subduple proportion; to wit, the Resistance that they find in
+penetrating the water; therefore the little pieces gradually swim,
+with more and more facility as their breadth is lessened.
+
+[Illustration]
+
+  _This is manifest; for keeping still the same height of the Solid,
+  with the same proportion as the Base encreaseth or deminisheth,
+  doth the said Solid also encrease or diminish; whereupon the Solid
+  more diminishing than the Circuit, the Cause of Submersion more
+  diminisheth than the Cause of Natation: And on the contrary, the
+  Solid more encreasing than the Circuit, the Cause of Submersion
+  encreaseth more, that of Natation less._
+
+And this may all be deduced out of the Doctrine of _Aristotle_ against
+his own Doctrine.
+
+Lastly, to that which we read in the latter part of the Text[97], that is
+to say, that we must compare the Gravity of the Moveable with the
+Resistance of the Medium against Division, because if the force of the
+Gravity exceed the Resistance of the _Medium_, the Moveable will
+descend, if not it will float. I need not make any other answer, but
+that which hath been already delivered; namely, that its not the
+Resistance of absolute Division, (which neither is in Water nor Air)
+but the Gravity of the _Medium_ that must be compared with the Gravity
+of the Moveables; and if that of the _Medium_ be greater, the Moveable
+shall not descend, nor so much as make a totall Submersion, but a
+partiall only; because in the place which it would occupy in the
+water, there must not remain a Body that weighs less than a like
+quantity of water: but if the Moveable be more grave, it shall descend
+to the bottom, and possess a place where it is more conformable for it
+to remain, than another Body that is less grave. And this is the only
+true proper and absolute Cause of Natation and Submersion, so that
+nothing else hath part therein: and the Board of the Adversaries
+swimmeth, when it is conjoyned with as much Air, as, together with it,
+doth form a Body less grave than so much water as would fill the place
+that the said Compound occupyes in the water; but when they shall
+demit the simple Ebony into the water, according to the Tenour of our
+Question, it shall alwayes go to the bottom, though it were as thin as
+a Paper.
+
+    [97] Lib. 4. c. 6. Text 45.
+
+[Decoration]
+
+FINIS.
+
+[Decoration]
+
+       *       *       *       *       *
+
+  [Detailed Transcriber's Notes
+
+  The text has been made to match the original text as much as
+  possible including variation in spelling, punctuation, italics etc.
+  The following, details apparent printer's errors as well as changes
+  or additions to aid readability of text.
+
+  Page 1, missing full stop after abbreviation gr. '0 gr 54 min.'.
+
+  Page 3, sidenote, missing space between words 'the Authority ofan
+  Author.'.
+
+  Page 3, printer's error, augmentarion for augmentation 'and
+  augmentarion of Masse'.
+
+  Page 4, missing letter t 'tha{t} that proceeded not'.
+
+  Page 4, printer's error or inconsistent punctuation, 'my paynes and
+  time. and although'.
+
+  Page 6, inconsistent punctuation, full stop after axiome where as
+  there are none after those following 'AXIOME. I.'.
+
+  Page 9, missing full stop added to end of paragraph 'or else an
+  upright Prisme.'.
+
+  Page 11, printer's error, missing letter C in illustration, 'the
+  Prisme A C D B to be placed'.
+
+  Page 15, printer's error or archaic lettering, final y looking like
+  a 7 in original text'and of the Specifick Gravit{y}'.
+
+  Page 16, printer's error, letter N for T in text to refer to
+  illustration, 'if the Vessell E N S F'.
+
+  Page 16, printer's error, duplicate word in text 'equalizeth the
+  Force and and Moment,'.
+
+  Page 17, printer's error, rhe for the 'as in rhe Stilliard,'.
+
+  Page 17, missing space between words 'asoften as that'.
+
+  Page 18, sidenote, printer's error, specifiaclly for specifically
+  'A Solid specifiaclly graver'.
+
+  Page 20, potential printer's error, properly for property, 'but
+  this properly they have'.
+
+  Page 20, printer's error, n for u 'loseth all a{u}thenticalness'.
+
+  Page 22, printer's error or variation in spelling, Benonamico for
+  Buonamico 'it seemes that Benonamico'.
+
+  Page 23, printer's error, missing i 'accordng to its excess'.
+
+  Page 24, missing line at the end of page in original text 'its
+  Region it loseth all'.
+
+  Page 26, missing letter n 'u{n}able by its small weight'.
+
+  Page 29, missing letter e 'that I have gon{e} about'.
+
+  Page 32, unclear symbol in original text 'other Figure, {&}c.'.
+
+  Page 37, potential printer's error, comma in unusual position
+  'whatever Figure, goeth always'.
+
+  Page 38, missing space between words 'Superficies might bedry:'.
+
+  Page 39, missing letter t, unied for united 'which holds them unied'.
+
+  Page 41, printer's error, Motitions for Motions 'all Motitions are
+  made'.
+
+  Page 42, sidenote, possible missing letter e, 'Se{e} what satisfaction'.
+
+  Page 43, printer's error, Subdidivisions for Subdivisions, 'other
+  Subdidivisions,'.
+
+  Page 49, missing letter i, dminishing for diminishing 'or dminishing
+  it by dividing'.
+
+  Page 50, sidenote, printer's error, missing letter l, hep for help
+  'float by hep of'.
+
+  Page 53, printer's error, missing letter n, beig for being 'beig
+  double in Gravity'.
+
+  Page 54, printer's error, missing letter l, 'sha{l}l also descend.'.
+
+  Page 55, printer's error, missing letter r, 'to fo{r}m Solid Bodies'.
+
+  Page 56, printer's error, missing letter A, 'Cone S {A} T'.
+
+  Page 57, printer's error, missing letter t, 'of which i{t} may
+  descend'.
+
+  Page 58, sidenote, printer's error, inverted n, 'Natatio{n} easiest
+  effected'.
+
+  Page 59, missing letter u, 'witho{u}t all Question,'.
+
+  Page 59, printer's error, inverted n, 'with an other Experime{n}t'.
+
+  Page 59, potential printer's error, sidenote ends with comma, 'Or
+  rather Contiguity,'.
+
+  Page 61, missing letter a, 'that in this c{a}se the water,'.
+
+  Page 74, printer's error, ir for it, 'but if we do saw ir,'.
+
+  Page 75, unclear symbol in original text '{&}c. making seven
+  Segments'.
+  ]
+
+
+
+
+
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