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diff --git a/old/56312-0.txt b/old/56312-0.txt deleted file mode 100644 index 14c4da5..0000000 --- a/old/56312-0.txt +++ /dev/null @@ -1,7098 +0,0 @@ -The Project Gutenberg EBook of Rules and Examples of Perspective proper -for Painters and Architects, etc., by Andrea Pozzo - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world 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. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: Rules and Examples of Perspective proper for Painters and Architects, etc. - In English and Latin: Containing a most easie and - expeditious method to delineate in perspective all designs - relating to architecture - -Author: Andrea Pozzo - -Illustrator: John Sturt - -Translator: John James - -Release Date: January 5, 2018 [EBook #56312] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK RULES, EXAMPLES OF PERSPECTIVE *** - - - - -Produced by Chris Curnow and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - - - - -Transcriber’s Note: - -This text uses some Unicode characters that are not supported by all -fonts and may not display correctly, for example ꝫ. - -Superscripted text is indicated ^{like this}, italicised text _like -this_, upright text within italic passages ~like this~. - -Most ‘figure’ illustrations have been moved from their position in the -original book: each figure is placed by the passage that describes it, -for ease of reference. - -A list of changes made to the original text (to correct suspected -printing errors) is given at the end. - - - - - Rules and Examples of - PERSPECTIVE - _PROPER FOR_ - Painters and Architects, etc. - - In English and Latin; - - _Containing a most easie and expeditious Method to_ - _DELINEATE in PERSPECTIVE_ - All DESIGNS relating to ARCHITECTURE, - _AFTER A NEW MANNER_, - Wholly free from the Confusion of Occult Lines: - - _BY THAT GREAT MASTER THEREOF_, - ANDREA POZZO, _Soc. Jes._ - - _Engraven in 105 ample folio Plates, and adorn’d with 200 - Initial Letters to the Explanatory Discourses: - ~Printed from Copper-Plates~ on y^{e} best Paper_ - - By John Sturt. - - Done into English from the Original Printed at Rome 1693 in - Lat. and Ital. - _By M^{r} John James of Greenwich._ - - [Illustration] - - LONDON: - PRINTED by Benj. Motte, MDCCVII. - _Sold by John Sturt in Golden-Lion-Court in_ - Aldersgate-Street. - - - - - PERSPECTIVA - PICTORUM - _ET_ - ARCHITECTORUM, - - _ANDREÆ PUTEI, - E SOCIETATE JESU._ - - In quâ docetur Modus expeditissimus Delineandi - Opticè omnia quę pertinent ad Architecturam. - - [Illustration] - - LONDINI: - Juxta Exemplar ROMÆ excusum, MDCXCIII. - _Ex Sculpturâ Joannis Sturt, et ejusd. Curâ adornata_: - TYPIS Benj. Motte, MDCCVII. - - - - -[Illustration] - - - - -[Illustration] - - - - -TO - -Her most Sacred Majesty, - -QUEEN ANNE. - - -_May it please your Majesty!_ - -_The Condescension of the late Emperor of ~Germany~ to patronize this -~WORK~ in the ~Original~, could not have incited me to the Presumption -of laying the ~Translation~ at Your Royal Feet; had not the ~Art~ of -~PERSPECTIVE~, of which it treats, been so nearly ally’d to the Noble -Arts of ~PAINTING~ and ~ARCHITECTURE~. The ~First~ of these Your Majesty -has been pleas’d to honour, as well in expressing a Satisfaction with the -Performances, as in extending Your Royal Munificence to that great Master -thereof, Signor ~Verrio~._ - -_AND although Affairs of higher Consequence have hitherto deferr’d Your -Majesty’s Commands for Raising ~WHITE-HALL~ from its Ruins; yet has not -~Architecture~ been without Encouragement, under ~Your Majesty’s~ Most -Auspicious Reign: Witness the great Dispatch lately given to those Noble -Fabricks of S. ~PAUL’s~, ~Greenwich~-Hospital, and ~Blenheim~._ - -_THESE seem to presage, that a Time is coming, when, through the -Blessing of Peace, and the Happy Influence of Your Majesty’s Government; -~WHITE-HALL~ shall become a Structure worthy its Great ~Restorer~, and -its Name as much Celebrated among ~Palaces~, as Your Royal Vertues -are Illustrious among ~Princes~: When Your Majesty’s Subjects shall -exert themselves as much to their Country’s Honour, in the ~Arts~ of -~Design~, and ~Civil Architecture~; as they have already done in the ~Art -Military~, and ~Personal Valour~._ - -_PRELIMINARY to such Happy Season, I presume this ~Art of Perspective -made Practicable~, may not be improper; being One of the most Useful, -though hitherto the most Obscure and Confus’d, of all the Lineary Arts. -I therefore, with all Submission, beg Leave to supplicate Your Majesty’s -Pardon for this Address, and Your Gracious Protection of this Specimen -of ~English~ Graving; to which if ~Your Majesty~ vouchsafe ~Your~ Royal -~PATRONAGE~, it will effectually animate the future Endeavours of,_ - - May it please Your Majesty! - - _Your Most Obedient Subject_, - - J. STURT. - - - - -PREFACE TO THIS TRANSLATION. - - -NOTWITHSTANDING the _Art_ of PERSPECTIVE must be acknowledg’d so -highly and indispensably requisite in the Practice of _Painting_, -_Architecture_, and _Sculpture_; that in the First of these especially, -nothing commendable can be perform’d without its Assistance: Yet such -have been the Difficulties and Obscurities met with in the first -Attempts, and so great the Perplexity and Confusion of Lines in the -Practice thereof; that the best Instructions, hitherto made _English_, -have invited very few to such a Prosecution of this Study, as might -render their Performances of this kind, truly valuable. - -’TIS something unaccountable, that, among so many learned Persons as have -handled this Subject, _Priests_, _Architects_, and _Painters_; very few, -if any of them, have given Directions proper for shunning that Disorder -and Confusion of Lines, which, in most Instances, must necessarily -attend the Execution of their Rules: In all or most of which, the whole -Space for the Performance is confin’d between the Lines of the Plan and -Horizon; which, where the Scale is small, and the Height of the Eye not -very much advanc’d, renders the Work exceedingly confus’d; and where -those Lines are coincident, (which frequently happens) the Method becomes -utterly impracticable. - -THIS Author’s great Experience in the Practice of _Perspective_, having -furnish’d him with excellent RULES for Shortning the Work, and Obviating -the foremention’d Difficulties; he has here very generously imparted -them, and especially the latter, in the Tenth and Eleventh Figures. -And tho’ on Perusal of the first three or four Plates, this Method may -possibly seem the same that some others have before made use of; yet -whoever shall diligently observe and copy the Rules and Examples of the -succeeding Figures, must necessarily acknowledge the great Advantage this -has in a Perspective-Plan and Upright, clear and distinct; whence the -finish’d Piece is deduc’d, without the least Incumbrance of the Work. -The Explanations of the Rules here given, are short and instructive; -and the Architectonical Designs produc’d to exemplify them, Noble and -Magnificent. - -THE Manner of Designing, where the Perspective is drawn on several -Ranges of Frames one behind the other, and such Scenes of Theaters whose -Grooves lie oblique to the middle Line, is also here laid down: And by -our Author’s Method, _Horizontal Perspective_, or that of Ceilings, is -render’d less difficult than the _Vertical_, or that against an upright -Wall. Upon the whole, nothing seems wanting that may make a Work of this -nature complete; unless what concerns Designs which are either Circular, -or abound with many Columns: For the Performance whereof, the Author, as -he promises in the Sixty-fifth Figure, has, in a SECOND Volume, given -a Rule more proper for the purpose; which also may possibly be made -_English_ in due time, if this Part meet with Encouragement. - -WHAT the Author once intended should make a Part of that Second Volume, -he afterwards inserted in the Ninety-third and following Figures of -this Book: In the last of which, particular Notice should be taken of -his Conclusion; _That if_ Painters _would not run into inextricable -Errors, they ought as strictly to observe the Rules of_ Perspective, _in -designing the Figures of Men and Animals; as they do in painting Columns, -Cornices, or other Parts of Architecture_. - -THAT none therefore be discourag’d in their first Attempts, through the -Brevity or Silence of our Author; (who, writing in a Country where the -Principles of this Art are more generally known than with Us, had no -need to insist so long on some things, as might be thought necessary to -_Beginners_) we shall endeavour to speak as plainly as we can to a point -or two, most liable to be misunderstood, or to prove a Stumbling-Block at -the Entrance; and then add a Word of Advice to such as shall attempt the -putting these Rules in Execution. - -THE Author, in both his Explanations of the first Plate, has given some -Account of what he would have his Reader understand, by _Designing in -Perspective_; and a right Conception of this point being of great Use to -facilitate the Work, we thought it not improper, to describe something -more particularly, what is meant by the Art _Perspective_: but shall at -present speak only of That, which, whether Vertical or Horizontal, is -receiv’d on a Flat and Even Superficies; This being of much the more -general Use, and, when rightly understood, renders the Difficulties of -the Circular or Irregular Surfaces, easy and familiar. - -PERSPECTIVE is the Art of Delineating, on a flat Superficies, as a -Wall, Ceiling, Canvas, Paper, or the like, the Appearances of Objects, -as seen from One determinate Point: For tho’ in Works of great Length, -Two, Three, or more Points of Sight are sometimes made use of; yet such -may more properly be said to be Several Views conjoin’d, than One Piece -of Perspective: Of which see the Author’s Opinion, at the End of this -Treatise. - -IN Perspective, the Eye of the Beholder is esteem’d a Point, from whence -Rays are suppos’d to proceed to every Angle of the Object. The Wall or -Canvas to be painted (which we shall here call the _Section_) is imagin’d -to intervene at right Angles to the Axis of the said Rays, and, by -dissecting them, to receive the Appearance of the Object, in greater or -less Proportion, as the Section is more or less remote from the Point of -Sight. Our Author’s Rule is, That the Distance of the Eye ought to be -equal to the greatest Extent of the Object, whether in Length or Height: -As, to view a Building that is a hundred Foot long, and fifty high; he -would have the Distance a hundred Foot: To view a Tower sixty Foot wide, -and a hundred and fifty Foot high; the Distance should be a hundred and -fifty Foot. This Distance is not strictly to be understood of the Space -between the Eye and the Object, but of the Space between that and the -Section, the Plan of which our Author calls the Line of the Plan, or -Ground-line; for it’s often requisite, that the Section be plac’d at some -Distance before the Object, on account of Projectures of Cornices, and -other Parts of the Work that advance, as in the Eighth Figure. - -THE Place of the Eye, with respect to its Height above the Ground, -ought to be such, as is most natural and agreeable to the Object. Thus -in _Architecture_, the Basements and inferior Parts of a Building are -improper to be set above the Eye, and their Cornices and Entablatures -have but an ill Effect when below it. _General_ Perspectives indeed -require the Sight to be taken at a Birds View; and on other Occasions -the Place of the Eye may be vary’d: but the best and most general Rule -is, not to exceed five or six Foot Height above the Ground. The Height -of the Eye above the Ground, thro’ which a Line is drawn, call’d the -_horizontal_ Line, is set on by the same Scale of Proportion, as the -Design bears to the real Work; and the Point of Sight so plac’d therein, -as may render the Object most agreeable. From the Point of Sight, either -on one or both sides in the horizontal Line, you are to set, by the same -Scale, the Distance you stand from the Section. And by means of these -Points of Sight and Distance, and the Measures of the Parts brought on -the Lines of the Plan and Elevation of the Section, by the same Scale; -all the Examples of this Volume are reduc’d into Perspective; as is -manifest on Inspection of the Figures. - -WHAT we would add, by way of Advice, is, - -I. THAT you very carefully observe, what the Author understands by -_Breadth_, _Length_, and _Height_, in his Explanation of the Fifth Plate, -before you proceed to practise on any Figure; otherwise you’ll certainly -misunderstand him; especially in the Third Figure. - -II. THAT the Rules of the Tenth and Eleventh Figures be particularly -regarded, for avoiding Confusion in the Plans and Uprights. - -III. THAT from the Disposition of the Perspective-Plans and Uprights, -with respect to the finish’d Pieces in the Twelfth and many following -Figures, you would observe, with what Dispatch the said Pieces may, -without the Help of Compasses, be delineated by your Drawing-Square; -_viz._ the Perpendiculars from the Perspective-Plan, and the level Lines -from the Perspective-Upright, or Section. - -IV. THAT you would accustom yourself in Works that have many Lines, to -make the Perspective-Plans and Uprights for each Part distinct, so as to -prevent all Danger of Confusion. Thus you may have one Plan and Upright -for the Basement of a Building; and when that is drawn on your finish’d -Piece, remove them, and place those of the Body of the House; and when -that’s complete, do so by the _Attick_, &c. always observing so to place -the Plan below, and the Upright on one side of your neat Draught, that -your Drawing-Square may command each of them; which will mightily shorten -your Work. - -V. THAT the Author’s Advice of taking the Figures in Course, be strictly -follow’d in the Practice; which will be a great means to render the Whole -easy and pleasant. - -THIS is the Sum of what we thought most proper to advertise you; and -have only this farther to request, That if any Mistakes may have escap’d -the Press undiscover’d, as we well hope there are few or none, you will -favourably correct and pardon them. - - - - -MONITA ad TYRONES. - - -_Concinnitatem ac symmetriam opticæ delineationes ædificiorum habere -nequeunt, nisi utramque mutuentur ab Architectura. Proinde necesse -est, ut in istius graphide ac intelligentia te aliquandiu exerceas, -donec uniuscujusque elevationis vestigium formare didiceris, ex eoque -eruere sectionem totius longitudinis, ut in Opere toto videre est, -præsertim figuris sexagesimaoctava & septuagesima. Siquidem ex vestigio -& ex sectione derivatur in opticas imagines congrua rerum singularum -profunditas._ - -_Subjiciam his consilium summi momenti; videlicet, egregiè intelligas -oportet figuram secundam, priusquam progrediaris ad tertiam, idemque -de cæteris dictum velim; nam singulas eo disposuimus ordine, ut quæ -præcedit, necessaria sit ad percipiendas eas quæ sequuntur. Si aliqua -sint in explicatione, quæ initio non intelligas, ipsum schema sæpius -diligenter inspicies; ac vicissim si aliqua desint in schematibus, ex -declarationibus ea supplebis. Lapsus verò quos deprehenderis, facilè pro -tua benignitate, mihi, ut spero, condonabis._ - - - - -ADVICE to BEGINNERS. - - -The Perspective of Structures here treated of, can have no Grace or -Proportion, without the Help of Architecture. ’Tis therefore absolutely -necessary, that you employ yourself for some time in Drawing, and the -Study of that Art; till you can readily describe the Plan of any Upright, -and from thence project the Section or Profile, as is shewn through the -whole Course of this Work; and more particularly, in the Sixty-eighth and -Seventieth Figures: Forasmuch as the proper Depth of each Part of the -Perspective, is determin’d by the Plan and Profile thereof. - -I shall add this one thing more, which is indeed of the last Importance; -to wit, that you endeavour to understand the Second Figure throughly, -before you proceed to the Third; and so of the rest: they being dispos’d -in such Order, that the Knowledge of the preceding Figure is always -necessary to a right Understanding of that which follows. If you meet -with any thing which at first seems difficult in the Description, a -diligent Inspection of the Figure may relieve you: And on the other -hand, if you find not in the Figure every thing you desire, you may have -Recourse to the Explanation. What Errours you discover in the Work, I -hope you’ll generously overlook and pardon. - - - - -AD - -Lectorem Perspectivæ studiosum. - - -_Ars Perspectiva, oculum, licet sagacissimum inter sensus nostros -exteriores, mirabili cum voluptate decipit; eademque necessaria est iis, -quibus in pingendo, tum singulis figuris positionem ac deformationem -suam congruè tribuere, tum colores & umbras, magis vel minus intendere -aut remittere, prout oportet, curæ est. Ad id autem sensim sine sensu -illi perveniunt, qui solo studio Graphidis non contenti, singulis -Architecturæ Ordinibus exactè deformandis assueverint. Nihilominus, -inter multos qui opus hujusmodi magno impetu aggressi hucusque fuerunt, -paucos numeramus, qui animum ipso statim initio non desponderint, ob -magistrorum librorumque penuriam, ordinatè ac perspicuè docentium opticas -projectiones, à principiis hujus artis, usque ad omnimodam perfectionis -consummationem. Quum autem sentiam, longâ multorum annorum exercitatione, -me non minimam facilitatem in hac disciplina mihi parasse: censeo -Studiosorum voluntati me satisfacturum, eorumque profectui consulturum, -si methodos expeditissimas in lucem proferam, ad singulorum Architecturæ -Ordinum opticas delineationes perficiendas, adhibitâ communi regulâ, ex -qua omnia linearum occultarum offendicula sustulimus. Deinde, si tempus -& vires ad aliud Opus conscribendum Bonitas Divina dederit, projectiones -quascunque absolvemus regulâ qua in præsentia uti soleo, ac multò -facilior & universalior est regula communi & vulgata, quamvis hæc sit -fundamentum alterius. Itaque, Lector studiose, constanti animo negotium -tuum suscipe; ac lineas omnes tuarum operationum, ad verum oculi punctum -ducere, ad gloriam scilicet DEI O.M. tecum omninò decerne. Sic votis -honestissimis, ut auguror tibi ac spondeo, feliciter potieris._ - - - - -TO - -The Lovers of Perspective. - - -The Art of PERSPECTIVE does, with wonderful Pleasure, deceive the Eye, -the most subtle of all our outward Senses; and is very necessary to be -known of all, who in Painting would give a due Place and Proportion to -their Figures, and more or less Strength requisite to the Lights and -Shades of the Picture. This might be insensibly attain’d, if Persons, not -content with the Study of Drawing only, would accustom themselves exactly -to delineate the several Orders of Architecture. Nevertheless, among -many who have hitherto vigorously undertaken this Work, there have been -but very few, who have not been in a manner quite discourag’d, through -want of Masters and Books to teach them clearly and methodically the -Rules of Perspective-Projections, from the first Principles of the Art, -to the entire Perfection thereof. Wherefore, apprehending that by long -and constant Practice in Works of this kind, I had acquir’d a Method -to facilitate the same; I judg’d it might be for the Satisfaction and -Advantage of the Studious, to publish the shortest way for designing in -Perspective the several Orders of Architecture, by a common and easy -Rule, free from the Incumbrances of occult Lines. But if it please God -to give me Life and Health to compose another Book, I shall therein shew -the Method of putting Works into Perspective by the Rule I make use of at -present, which is more easy and general than the common way, though this -be the Foundation of the other. Therefore, Reader, my Advice is, that -you chearfully begin your Work, with a Resolution to draw all the Lines -thereof to that true point, the Glory of GOD; and I durst predict, and -promise you good Success in so honourable an Undertaking. - - - - -THE - -Approbation of this Edition. - -At the Request of the Engraver, We have perus’d this Volume of -PERSPECTIVE; and judge it a WORK that deserves Encouragement, and very -proper for Instruction in that ART. - - _Chr. Wren_, - _J. Vanbrugh_, - _N. Hawksmoor_. - -[Illustration] - - - - -POZZO’s - -ARCHITECTURE IN PERSPECTIVE. - - - - -[Illustration: FIG. I.] - - - - -FIGURA PRIMA. - -Explicatio linearum Plani & Horizontis, ac Punctorum Oculi & Distantiæ. - - -_Ut principia Perspectivæ faciliùs intelligas, pono tibi ob oculos -Templum, in cujus interiori facie, præter cætera, pingendum sit aliquid -ad Perspectivam pertinens. Templi hujus vestigium geometricum est ~A~, -elevatio geometrica in longum est ~B~, in latum est ~C~. In ~A~ est locus -Hominis aspicientis lineam ~DE~, cui paries pingendus incumbit. In ~B~ -idem Homo ex eâdem distantiâ intuetur lineam ~FG~, quæ refert elevationem -parietis. In figura ~C~ supponimus Hominem consistere è regione ipsius -parietis: easdemque proportiones mensuratum translatas esse ex vero -pariete in figuram ~C~, quæ ipsum in parvo repræsentat._ - -_Prima ergo linea ~HI~ dicitur linea terræ vel plani, ex quâ incipit, -eidemque incumbit ædificium. Secunda linea ~NON~ priori parallela, -dicitur horizontalis, in quâ ponitur ~O~ punctum oculi, & ~N~ punctum -distantiæ. Duo autem puncta distantiæ à nobis posita sunt, ut unum -adhibeas ex quâ parte volueris; nam ad figuras opticè contrahendas -sufficit unum punctum distantiæ: nec fieri potest ulla optica delineatio, -quin primo loco designentur duæ parallelæ, una plani seu terræ, altera -horizontis, notando in lineâ horizontis, punctum oculi, seu opticum, -& punctum distantiæ. Porrò unam eandemque rem triplici Schemate -repræsentare oportuit, ut videas, locum ex quo aspicienda est figura ~C~ -esse punctum ~N~ unius ex rectis ~NO~, quam concipere debemus veluti -normaliter infixam in ~O~; ac distantiam inter ~O~ & ~N~ eandem esse -debere cum distantiâ inter ~A~ & ~DE~, inter ~B~ & ~GF~._ - -_In picturis multum spatii occupantibus, punctum oculi poni solet -in medio lineæ horizontalis: atque ubi altitudo picturæ sit major -latitudine, distantia ~NO~ fiet æqualis altitudini. Si latitudo picturæ -sit major altitudine, distantia ~NO~ fiet æqualis latitudini; ita -enim unico intuitu totum picturæ spatium comprehendi poterit. Porrò -quamvis eadem distantia diverso modo adhibeatur in vestigio ~A~, & in -elevationibus ~B~ & ~C~; nihilominus sectiones visualium cum pariete -vestigii ~A~, & elevationis ~B~, omninò conspirant cum sectionibus -visualium figuræ ~C~._ - -_Jam si velimus ut spectatori in ~A~ & ~B~ paries depictus videatur -distare à lineis ~DE~ & ~GF~, quanta est longitudo quadrati ~P~, cujus -elevatio est ~Q~; ex punctis ~A~ & ~B~ fiant visuales ad puncta extrema -quadrati, notando sectiones visualium cum pariete ~DE~ & ~GF~, qui ab -aliis vocatur velum, vitrum diaphanum, sectio, tela, vel tabula. Invenies -autem, lineas ~RS~ ac ~TV~ esse æquales, ac similiter lineas ~XZ~ & ~YK~; -& sic de aliis._ - - - - -The First Figure. - -_Explication of the Lines of the Plan and Horizon, and of the Points of -the Eye and of the Distance._ - - -That you may the better understand the Principles of Perspective, here -is presented to your View a Temple, on the inner Wall of which, amongst -other things, one would paint something in Perspective. The Geometrical -Plan of this Church is A, the Geometrical Elevation, or Upright, -lengthwise is B, breadthwise is C. In A is the Place from whence a Man -beholds the Line DE, which is the Plan of the Wall that is to be painted: -In B the same Man, from the same Distance, looks upon the Line FG, that -represents the Elevation of the Wall. In Fig. C, the Man is supposed to -stand opposite to the said Wall; and this Figure contains, in Little, the -very same Proportions of Measures transferr’d from the real Wall. - -The first Line therefore HI is call’d the Ground-line, or Line of the -Plan, at which the Edifice begins, and on which it stands. The second -Line NON, parallel to the former, is call’d the Horizontal Line, wherein -is plac’d O the Point of the Eye, and N the Point of the Distance. Two -Points of Distance are here laid down, that you may make use of which you -please; for that on one Side only is sufficient for the fore-short’ning -Figures in Perspective: Neither can any Optick Delineation, or -Perspective, be described, without first making two Parallels; one of the -Plan, or Ground-line, the other of the Horizon; marking, in the Line of -the Horizon, the Point of the Eye, or Sight, and the Point of Distance. -It was thought besides expedient to put one and the same Thing into three -Schemes or Designs, to let you see, that the Place, from which the Figure -C is to be look’d upon, is the Point N, one of the right Lines NO, which -must be conceived as fixt at right Angles into O; the Distance ON being -the same as that between A and DE in the Plan, or between B and GF in the -Upright. - -In Pictures taking up a great deal of Room, the Point of Sight ought to -be made in the middle of the Horizontal Line; and where the Height of -the Picture happens to be greater than the Breadth, the Distance NO -must be made equal to the Height. If the Breadth of the Picture exceed -the Height, the Distance NO must be made equal to the Breadth: For so -will the Extent of the Picture be the better comprehended, or receiv’d, -at one View. And altho’ the same Distance may seem to be used in a -different manner in the Plan A, and in the Elevation B, from what it is -in C; nevertheless the Sections of the visual Rays, with the Wall of the -Plan A, and of the Elevation B, have a perfect Correspondence with the -Sections of those of the Figure C. - -Now, if to the Spectator in A and B, we would have the farthest Part of -the Work seem to recede from the Lines DE and GF, as much as the Square -P does, whose Elevation is Q; draw from the Points A and B, the visual -Rays to the extreme Points of the Square P and Q; noting the Sections -they make with the Walls DE and GF; which by some is call’d the Veil, -Transparent Medium, Section, Cloth, or Table: and you’ll find RS equal to -TV, XZ equal to YK; and so of the rest. - - - - -[Illustration: FIG. II.] - - - - -FIGURA Secunda. - -Modus delineandi opticè Quadratum. - - -_Ante descriptionem opticam quadrati ~A~, quod fingimus delineatum esse in -papyro separatâ, ducendæ sunt duæ lineæ parallelæ; altera plani, altera -horizontis, ut jam docuimus; notando in linea horizontis punctum oculi -~O~, & punctum distantiæ ~E~. Tum translatâ in lineam plani latitudine -ac longitudine ipsius quadrati ~A~, ita ut linea ~CB~ sit æqualis -latitudini, & ~DC~ sit æqualis longitudini. Ex punctis ~B~ & ~C~ fiunt -visuales ~BO~, ~CO~ ad punctum oculi; ex puncto ~D~ fit recta ~DE~ ad -punctum distantiæ. Demum ubi visualem ~CO~ secat recta ~DE~, fit ~GF~ -parallela ad ~CB~; habesque quadratum opticè contractum._ - -_Compendium temporis & laboris facies, præsertim in schematibus quæ -abundant lineis, si chartulam in medio complicaveris, eademque utaris, ut -latitudinem ac longitudinem quadrati transferas in lineam plani._ - - - - -The Second Figure. - -_Manner of delineating a ~Square~ in Perspective._ - - -Before the _Square_ A, which is supposed to be drawn on a separate Paper, -can be laid down in Perspective, two parallel Lines must be drawn; one of -the Plan, the other of the Horizon, as is already intimated; noting in -the Horizontal Line the Point of Sight O, and the Point of Distance E. -Then, when the Length and Breadth of the Square A shall be transferr’d -into the Line of the Plan, so that the Line CB be equal to the Breadth, -and DC be equal to the Length, let the visual Lines BO, CO be drawn from -the Points B and C to the Point of Sight O, and the right Line DE from -the Point D to the Point of Distance. Lastly, where the Line DE cuts the -Visual CO, make GF parallel to CB: and you have the _Square_ Optically -contracted, or fore-shorten’d in Perspective. - -To spare Time and Pains, especially in Figures that abound in Lines, fold -your Paper in the middle, and make use of it to transfer the Breadth and -Length of the Square, into the Line of the Plan. - - - - -[Illustration: FIG. III.] - - - - -FIGURA TERTIA. - -Optica delineatio rectanguli, alterâ parte longioris. - - -_Latitudo ~BC~ rectanguli ~A~ ponatur in linea plani, adhibito circino, -vel chartulâ complicatâ; & ex punctis ~B~ & ~C~ fiant visuales ad ~O~, -punctum perspectivæ. Tum papyro ex altera parte iterum complicatâ, -notetur longitudo ~CD~ rectanguli; ducendo tum rectam ~DE~ ad punctum -distantiæ, tum rectam ~FG~ parallelam ad ~BC~, quæ complebit opticam -delineationem rectanguli._ - -_Altera figura ostendit complicationem cruciformem papyri, quæ adhiberi -potest in delineandis rectangulis, seu latitudo eorum sit major -longitudine, aut vice versâ; seu latitudo & longitudo sint æquales._ - - - - -The Third Figure. - -_The Delineation of an Oblong ~Square~ in ~Perspective~._ - - -Let the Breadth BC of the Square A, be plac’d in the Line of the Plan, -by the Compass, or a folded Paper, and from the Points B and C, make the -Visuals to the Point of Sight O. Then fold your Paper cross-wise, and -mark CD the Length of the Square, drawing the Line DE to the Point of -Distance, and the Line FG parallel to BC, which will complete the Optick -Delineation of the oblong Square. - -The other Figure shews the Folding of the Paper cross-wise, which is of -ready use in delineating Squares, whose Breadth exceeds their Length, or -_vice versâ_; or whose Length and Breadth are equal. - - - - -[Illustration: FIG. IV.] - - - - -FIGURA QUARTA. - -Optica descriptio quadrati duplicis. - - -_Iam incipies frui compendio papyri complicatæ. Nam eam admovendo lineæ -plani, nullo negotio notare poteris puncta ~1~, ~2~, ~3~, ~4~, ~5~, ~6~, -linearum visualium, quæ ducentur ad ~O~ punctum perspectivæ. Exinde -complicatâ rursum chartulâ in crucem ad ~P~, notabuntur hæc puncta; ~7~, -coincidens cum puncto ~6~, nisi quadratum distet à linea plani; ~8~, ~9~, -~10~. Ductis autem rectis ex ~8~, ~9~, ~10~, ad punctum ~E~, ubi secant -visualem ~6~, ~7~, ~O~ fient parallelæ, eritque completa delineatio._ - -_In medio quadrati ~B~, aliud quadratum facilè describetur, ducendo -diagonales seu diametros ab angulo ad angulum, ut in figura._ - - - - -The Fourth Figure. - -_The Optical Delineation of a double Square._ - - -Here you’ll find the Advantage of your folded Paper; for, applying it -to the Line of the Plan, you readily mark the Points 1, 2, 3, 4, 5, 6, -of the visual Lines, which must be drawn to the Point of Sight O. Then -folding the Paper cross-wise, as in P, you mark the Points 7, 8, 9, -10, placing the Point 7 on that of 6, unless you would have the Square -removed within the Line of the Plan. Then from 8, 9, 10, drawing Lines -to the Point of Distance E; where they intersect the Line 6, 7, O, draw -Parallels to the Line of the Plan; and your Work is done. - -Within the Square B, you may easily inscribe another Square, by help of -the Diagonals; as may be seen in the Figure. - - - - -[Illustration: FIG. V.] - - - - -FIGURA QUINTA. - -Vestigia quadratorum, cum elevationibus. - - -_Suppositis iis quæ jam diximus de Contractione optica Quadratorum, -notandum est, vestigium primi Quadrati distare à linea plani spatio ~BA~ -opticè contracto; quia linea ~BD~ habet à visuali ~AO~, distantiam ~BA~. -Eodem modo Quadratum secundum distat à linea plani spatio ~EA~, & sic -deinceps._ - -_Velim observes, in omnibus his Quadratis lineas longitudinis esse partes -visualium, lineas vero latitudinis esse parallelas lineæ plani, & in -primo Quadrato duci ex punctis, in quibus lineæ ~BD~, ~CD~, tendentes ad -punctum distantiæ, secant visualem ~AO~._ - -_Sub singulis vestigiis Quadratorum, delineavimus alia omnino similia, -per quæ parvo labore fient tres bases, erigendo ad libitum duas primas -perpendiculares æquales; ac ducendo tum duas visuales ad punctum oculi -~O~, tum reliquas, ut in figura. Supponendum est autem, geometricam -altitudinem cujuslibet rei desumi ex lineis normalibus ad lineam plani; -quemadmodum latitudo & longitudo geometrica desumuntur ex eadem linea -plani._ - -_Tres aliæ bases inferiores formantur sine lineis occultis ex vestigio & -ex elevatione longitudinis opticè deformatis, adhibendo solas altitudines -ac latitudines angulorum. Nomine altitudinis intelligimus distantiam -cujuslibet anguli à linea plani; nomine latitudinis intelligimus -distantiam anguli ab una aliqua linea normali ad lineam plani; dummodo -hæ normales eandem habeant positionem respectu basium, & respectu -vestigiorum & elevationum. Quemadmodum autem per concursum altitudinis -~FG~, & latitudinis ~HI~, ope duorum circinorum invenitur unus angulus in -una basi; ita inveniuntur cæteri tum in ea, tum in reliquis._ - - - - -The Fifth Figure. - -_Plans of Squares, with their Elevations._ - - -Besides what has been already said of the fore-short’ning of Squares in -Perspective, it is convenient to observe, That the Foot of the first -Square is here set within the Line of the Plan, as much as the Space BA -optically contracted; because the Line BD has the Distance BA from the -Visual AO: And in like manner, the second Square is distant from the Line -of the Plan the Space EA; and so for the rest. - -I would have you observe in all these Squares, That by the _Length_ I -always understand part of the visual Lines, and by the _Breadth_ those -parallel to the Ground-line; which in the first Square are drawn from -the Points in which the Lines BD, CD, tending to the Point of Distance, -intersect the Visual AO. - -Under the Plans of these Squares are described three others just like -them, which are easily converted into three Bases, by erecting, at -pleasure, the two first Perpendiculars of equal Height, and thence -drawing two Visuals to the Point of Sight O, which also bound the rest, -as in the Figure. Observe also, That the Geometrical Height of every -thing is to be set perpendicularly from the Ground-line, or Line of the -Plan, as the Geometrical Length and Breadth are also placed on the same -Line. - -The three other Bases below are form’d without the Help of Occult Lines, -by making use only of the Heights and Breadths of the Angles, taken -from the Perspective Plan and Upright. By _Height_ I understand the -Distance of each Angle, or Corner, from the Ground-Line; By _Breadth_, -the Distance of an Angle, or Corner, from any Line perpendicular to the -Ground-line; provided these Lines have always the same Place in respect -of the Bases, as they have in respect of the Perspective Plan and -Upright. And as, by the Help of two Compasses, the Height FG, and the -Breadth HI determine the Corner of the first Base; so, in like manner, -are found the Corners of the other Bases. - - - - -[Illustration: FIG. VI.] - - - - -FIGURA SEXTA. - -Modus opticæ delineationis, absque lineis occultis. - - -_In hac figura sexta, vestigium geometricum ~B~ seorsim posui ab -elevatione geometrica ~A~, ut deinceps faciemus. Vestigium ~B~ opticè -contractum in ~E~ est ~NMRS~; elevatio contracta longitudinis vestigii -est ~FTSN~. Posito autem quòd altitudines ~FN~, ~1, 5~, ~2, 6~, sint -æquales; latitudines ~NM~, ~1, 2~, ~5, 6~, sint æquales; & rectæ ~NM~, -~5,6~, sint in linea ~X~ plani; rectæ ~FN~, ~1, 5~, sint in perpendiculo -~V~: anguli ~3~ & ~4~ basis ~C~ habent eandem elevationem seu distantiam -à linea ~X~ plani, quam habet angulus ~T~: anguli ~1~ & ~2~ habent -elevationem, quam angulus ~F~: anguli ~3~ & ~7~ habent eandem latitudinem -seu distantiam à perpendiculo ~V~, quam habet angulus ~R~: anguli ~2~ & -~6~ habent eandem latitudinem, quam habet angulus ~M~._ - - - - -The Sixth Figure. - -_The Manner of designing in Perspective, without occult Lines._ - - -In this sixth Figure, I have design’d the Geometrical Plan B separately -from the Geometrical Elevation A, as I shall always do hereafter. The -Plan B optically contracted, or put in Perspective, in E, is NMRS; the -Elevation of its Length in Perspective is FTSN. Then supposing the -Heights FN, 1,5, 2,6, equal; and the Breadths NM, 1,2, 5,6, equal; the -Lines NM, 5,6, to be in the Line of the Plan X; and the Lines FN, 1,5, in -the Perpendicular V: the Angles 3 and 4 of the Base C have the very same -Elevation or Distance from the Line of the Plan X, as has the Angle T: -the Angles 1 and 2 have the same Elevation with the Angle F: the Angles 3 -and 7 have the same Breadth or Distance from the Perpendicular V, as the -Angle R has: the Angles 2 and 6 have the same Breadth, as the Angle M has. - - - - -[Illustration: FIG. VII.] - - - - -FIGURA SEPTIMA. - -Aliud exemplum vestigii geometrici, cum elevatione longitudinis. - - -_Si delineanda sit basis dissecta in quatuor partes, fiat vestigium ~A~ -cum suis divisionibus longitudinis ~ED~ & latitudinis ~CD~. Easdem vero -divisiones latitudinis habebit in ~EF~ elevatio ~B~ quæ pertingit usque -ad ~X~. Porro ad contractionem opticam vestigii adhibebitur papyrus -complicata in latum & in longum, transferendo in lineam plani latitudinem -& longitudinem vestigii. Deinde nullo negotio fiet optica deformatio -elevationis, ut clarè positum est in figura. Quomodo autem ex vestigio & -ex elevatione longitudinis opticè imminutis eruatur basis nitida sine -lineis occultis, ex præcedentibus manifestum est. Optarem ut per assiduam -circini tractationem in hac methodo exercenda operam sedulò ponas; quum -ex ea pendeat omnis facilitas delineationum opticarum._ - - - - -The Seventh Figure. - -_Another Example of a Geometrical Plan and Upright, put in Perspective._ - - -For drawing in Perspective a Pedestal, or Base, divided into four Parts, -make the Plan A with its Divisions of Length ED, and of Breadth CD; -and the same Divisions of Breadth EF, in the Elevation B, prolong’d -to X. Then make the Perspective-Plan, by transferring the Breadth and -Length into the Ground-line, by means of your Paper folded cross-wise. -From which Plan the Perspective-Upright is very easily made, as may -be plainly seen in the Figure. How the Base below, without occult -Lines, is made from the Perspective-Plan and Upright, is manifest from -what has been said before. I could wish you would be very diligent in -the Practice of this Method by the Compass; because the Dispatch of -Perspective-Delineations chiefly depends thereon. - - - - -[Illustration: FIG. 8.] - - - - -FIGURA OCTAVA. - -Optica projectio stylobatæ. - - -_Si libitum fuerit delineare stylobatam, cum projecturis in summo & -imo, incipies ab elevatione geometrica ~A~, ducendo occultas ad id -necessarias, tum versus perpendicularem ~L~, tum deorsum pro vestigio -geometrico ~B~, cujus distantiæ transferentur in spatium ~G~. Si mensuræ -longitudinis distent spatio ~C~ à mensuris latitudinis, vestigium -deformatum videbitur distare à linea ~K~ plani, quantum est idem spatium -~C~. In construenda optica elevatione ~D~, visuales ex punctis lineæ ~L~ -dabunt lineas latitudinis; lineas vero altitudinis accipies ex lineis -vestigii contracti, ut in figura. In formando stylobata nitido ~EF~, -locum anguli ~H~ dabit concursus latitudinis ex linea ~L~ usque ad ~M~, & -altitudinis ex linea ~K~ usque ad ~I~. Concursus tum ejusdem altitudinis, -tum latitudinis ex ~L~ usque ad ~O~, dabit angulum ~N~. Demum altitudinem -anguli ~P~ accipies ex ~K~ usque ad ~Q~; latitudinem ex ~L~ usque ad ~R~._ - - - - -The Eighth Figure. - -_The Projection of a Pedestal in Perspective._ - - -If you would draw a Pedestal, with the Projecture of its Cap and Base, -you must begin with the Geometrical Elevation A, by drawing such occult -Lines as are necessary, as well sideways to the Perpendicular L, as -downwards for making the Geometrical Plan B, whose Distances must be -transferr’d, and carry’d into the Space G. If the Measures of the Length -be placed the Distance of the Space C, from those of the Breadth, the -Perspective-Plan will then appear removed within the Ground-line K, as -much as the said Space C is. In the Construction of the Perspective -Elevation D, the Visuals drawn from the Points of the Line L give the -Lines of the Breadth; and those of the Height are taken from the Lines -of the Perspective-Plan, as in the Figure. In delineating the clean or -finish’d Pedestal EF, the Intersection of the Breadth from L to M, with -the Height from K to I, gives the precise Place of the Corner H. The -Intersection of the same Height with the Breadth LO gives the Angle N. -Lastly, the Angle P is found by the Intersection of the Height KQ, with -that of the Breadth LR. - - - - -[Illustration: FIG. IX.] - - - - -FIGURA NONA. - -Optica delineatio Architecturæ Jacobi Barozzii; & primum, de Stylobata -Ordinis Etrusci. - - -_Perspectiva nusquam clariùs emicat, quàm in Architectura. Iccirco tibi -ob oculos pono Architecturam Jacobi Barozzii, quem à patria nuncupant ~Il -Vignola~, reliquis fortasse usitatiorem; in eaque continetur elevatio -geometrica singulorum quinque Ordinum, qui vocantur, Etruscus, Doricus, -Ionicus, Corinthius, & Romanus, vel Compositus; delineando seorsim partes -cujuscunque Ordinis in figuris grandioribus. Elevationi geometricæ -suum vestigium nos addemus; ex vestigio autem & ex elevatione opticè -deformatis, eliciemus apparentias solidorum juxta regulam traditam. -Exempli gratia, si delineare velis stylobatam quadratum & pilam Ordinis -Etrusci, præter elevationem geometricam ~A~ delineare oportet vestigium -geometricum ~B~; ex ambobus autem opticè contractis formatur stylobata -nitidus ~D~, cum anta & pila existente ad latus, accipiendo altitudines -à linea plani, latitudines à linea perpendiculari ad ipsum planum. In -alia delineatione posuimus pilam ex adverso, ut eis omni modo delineandis -assuescas._ - -_Ad vitandam confusionem linearum, proderit ut figuræ fiant his nostris -multò grandiores: in quem finem singulis paginis apposita est scala -modulorum. Hoc nomine intelliguntur partes æquales, in quas dividuntur -lineæ latitudinis & altitudinis elevationum geometricarum; ac lineæ -latitudinis & longitudinis vestigiorum geometricorum. Si moduli sint -parvi, subdividuntur singuli in duodecim partes; ac prout fuerint -grandiores, subdividuntur in partes triginta, vel sexaginta, vel -centumviginti. ~Modulos Etruscum Doricúmque in partes duodecim; reliquos -autem in octodecim partiti sunt.~_ - - - - -The Ninth Figure. - -_The Architecture of ~Vignola~ in Perspective; and first, of his Pedestal -of the ~Tuscan~ Order._ - - -Perspective never appears more graceful, than in Architecture; for -which Reason I present you with that of _James Barozzi_, from his -Country generally call’d _Vignola_; which perhaps is more in use than -any other; and contains the Geometrical Upright of each of the five -Orders, _viz._ the _Tuscan_, _Dorick_, _Ionick_, _Corinthian_, and the -_Roman_, or _Composite_; together with a separate Delineation of the -Parts of each Order, in larger Figures. To this Geometrical Elevation -we shall add the Plan, and, from both of them reduc’d into Perspective, -shall draw the Appearances of Solids, according to the Rule before laid -down. For Example: If you would draw the square _Tuscan_ Pedestal, and -its Pilaster, you must, from the Geometrical Elevation A, make the -Geometrical Plan B; and from both of them reduc’d in Perspective, draw -the finish’d Pedestal D, with that of its Pilaster on the Side, by -taking the Heights from the Ground-line, and the Breadths from a Line -perpendicular to the same. On the other Side we have placed the Pilaster -on the Back-part, that you may practise the Drawing them in any manner. - -For avoiding the Confusion of Lines, I advise you to make the Figures -as much larger than ours as you can; for which purpose there is annex’d -a Scale of Modules to each Figure. By this Name we understand the equal -Parts, into which the Lines of the Breadth and Height of the Geometrical -Uprights, and of the Breadth and Length of the Geometrical Plans, are -divided. If the Modules are small, they are subdivided into twelve Parts; -and according as they are larger, into thirty, sixty, or an hundred and -twenty Parts. _I have divided the ~Tuscan~ and ~Dorick~ Module into -twelve Parts, and that of the other Orders into eighteen._ - - - - -[Illustration: FIG. 10.] - - - - -FIGURA DECIMA. - -Optica deformatio stylobatæ Dorici; ubi de modo vitandi confusionem, in -vestigiis delineandis. - - -_Elevatio geometrica ~B~ stylobatæ Dorici continet eandem symmetriam -partium quæ habetur apud Barozzium; ex eaque eruitur vestigium -geometricum ~A~ per lineas occultas, quæ descendant ex punctis -terminativis præcipuarum projecturarum. Earundem projecturarum distantiæ -transferendæ sunt in lineam elevationis, notando puncta quæ necessaria -sunt ad deformandam elevationem longitudinis stylobatæ._ - -_Si ob propinquitatem lineæ plani ad lineam horizontis, vestigium evadat -confusum, fiant in distantia congrua sub linea plani aliæ lineæ planorum -ipsi parallelæ, cum suis vestigiis. Quid autem emolumenti afferat -distantia major præ minori, ostendit vestigium ~E~ distinctiùs vestigio -~D~. Singula hæc vestigia fiunt notando in linea cujuslibet plani -mensuras latitudinis & longitudinis vestigii ~A~, & ducendo lineas ad -eadem puncta oculi ac distantiæ._ - -_Stylobatam nitidum descripsimus ex parte ~G~, tum ex necessitate, tum -ut videas, pro distantia ~FO~, usurpandam esse distantiam ~GO~ penitus -æqualem._ - - - - -The Tenth Figure. - -_A ~Dorick~ Pedestal in Perspective; with the Manner of avoiding -Confusion, in designing the Plans._ - - -The Geometrical Elevation B has the same Members and Proportions, as the -_Dorick_ Pedestal of _Vignola_; and the Geometrical Plan A is form’d, by -letting fall occult Lines from the principal Projectures of the Upright. -Occult Lines are also to be continued to the Perpendicular F, from the -several Members requisite for elevating in Perspective the Length of the -Pedestal. - -When, by reason of the too near Approach of the Ground-line to that of -the Horizon, the Plan becomes thereby confus’d; draw at a convenient -Distance underneath, other Ground-lines parallel to the first; together -with the Plans in Perspective. And of what Advantage the Removal of the -Ground-line is, is evident from the Plan E, which is much more distinct -than the Plan D. Each of these Plans is made, by marking upon its -respective Ground-line the Measures of the Breadth and Length of the Plan -A, and by drawing Lines to the same Points of Sight and Distance, which -were first assign’d. - -We have placed the finish’d Pedestal on the Side G, partly for want of -Room, and partly to shew, that the Point of Distance G is there made use -of, GO being equal to FO. - - - - -[Illustration: FIG. XI.] - - - - -FIGURA Undecima. - -Stylobatæ Ionici deformatio; ubi de vitanda confusione in elevationibus. - - -_Tum in figura præcedenti, tum rursus in hac, ostendimus quid agendum sit -ubi vestigia ~AA~ nimium obliquentur, unde oritur confusio; præcipuè -in lineis parallelis quæ exhibent latitudines. Non minor difficultas -interdum occurret in elevationibus longitudinis opticè deformandis; quòd -videlicet, ob nimiam earum obliquitatem, pervium non sit altitudines -singularum projecturarum probè discernere ac designare. Ad scopulos -istos declinandos, loco elevationis ~B~ adhibebitur elevatio ~C~, quæ -distinctior est, tum illâ, tum duabus intermediis ~D~ & ~E~, ob majorem -distantiam quam habet à puncto oculi._ - -_In delineando stylobata nitido, latitudines accipientur ex ultimo -vestigio, ponendo unam cuspidem circini in linea perpendiculari, quæ -proxima est literæ ~O~: altitudines accipientur ex elevatione ~C~, -ponendo unam cuspidem circini in linea plani, ut in præcedentibus -ostensum est._ - - - - -The Eleventh Figure. - -_The ~Ionick~ Pedestal in Perspective; with the Manner of avoiding -Confusion, in Elevations._ - - -As in the foregoing Figure, so in this also is shewn what is to be done, -where the Plans AA lie so oblique, as to cause Confusion; especially in -the Parallel-lines which give the Breadths. The like Inconvenience often -happens in elevating the Lengths in Perspective; when by their too near -Approach to the Point of Sight, the Contour of the several Mouldings -can’t be distinctly delineated: For avoiding which, instead of B you may -make use of the Elevation C, which is not only more distinct than the -former, but better than either of the two intermediate ones D or E, by so -much as it is more remote from the Point of Sight. - -In designing the finish’d Pedestal, the Breadths are taken from the -lowest Plan, by setting one Point of the Compasses in the perpendicular -Line OL: the Heights are taken from the Elevation C, by placing one Point -of the Compasses in the Ground-line, as has been shewn before. - - - - -[Illustration: FIG. XII.] - - - - -FIGURA Duodecima. - -Deformatio stylobatæ Corinthii, cum duabus pilis. - - -_Ornatus gratiâ, stylobatæ Corinthio additæ sunt pilæ, quæ pone columnas -locari solent. Ut autem pilæ clariùs appareant, columna omissa est, -cujus deformandæ rationem nondum tradidimus. Mensuras omnes ex Barozzio -acceptas esse demonstrat ipsum schema, in quo elevatio geometrica -stylobatæ est ~A~; vestigium ejus geometricum est ~B~: pilæ ~CC~. -Vestigium opticè contractum est ~D~, elevatio longitudinis stylobatæ -opticè contracta est ~E~, ac methodo consuetâ ex iis eruetur stylobata -nitidus cum suis pilis._ - - - - -The Twelfth Figure. - -_The ~Corinthian~ Pedestal, with its Pilasters, in Perspective._ - - -For Ornaments sake, we have added to this _Corinthian_ Pedestal the -Pilasters, which are usually placed behind Columns: And that they may be -the more perspicuous, have left out the Column, not having yet shewn the -Manner of putting it in Perspective. The Scheme shews the Measures are -taken from _Vignola_; in which the Geometrical Upright of the Pedestal is -A; the Geometrical Plan of the same is B; that of the Pilasters CC. The -Plan in Perspective is D, the Elevation in Perspective is E; from which -the finish’d Pedestal and Pilasters are drawn by the usual Method. - - - - -[Illustration: FIG. XIII.] - - - - -Figura Decimatertia. - -Projectio stylobatæ, ordinis Compositi. - - -_Quum pagina non caperet integrum stylobatam tantæ molis, fingere -oportuit detractum illi esse aliquid de trunco; ac partem supremam -stylobatæ sustentari ab infima, non immediatè, sed per quatuor asseres; -eisque impositam fuisse adjumento funium suspensorum ex trochlea. -Elevatio geometrica stylobatæ est ~B~; vestigium geometricum est ~A~. Ex -his eruitur optica delineatio vestigii ~C~ & elevationis ~D~. Ac postea -formatur stylobata nitidus ~E~, accipiendo latitudines ex vestigio ~C~, -altitudines ex elevatione ~D~._ - - - - -The Thirteenth Figure. - -_The Projection of a Pedestal, of the Composite Order, in Perspective._ - - -Wanting Room in this Page to describe so large a Pedestal entire, we -imagine it to have lost part of its Trunk, and the upper part to be set -on the lower; not immediately, but on four Cross-pieces that intervene; -and for placing it thereon, we suppose the Assistance of Ropes and a -Pulley. The Geometrical Elevation of the Pedestal is B; its Plan A; from -whence are found their Projections in Perspective D and C. Then taking -the Breadths from the Plan C, and the Height from the Elevation D, you -complete the finish’d Pedestal E. - - - - -[Illustration: FIG. XIV.] - - - - -Figura Decimaquarta. - -Deformatio circulorum. - - -_Ut stylobatis imponere liceat columnas cum suis basibus & capitellis, -docendus est modus qui servandus est in projectione optica circulorum, -tum singularium, tum duplicium aut multiplicium circa idem centrum._ - -_Vestigium geometricum ~A~ constat quadrato in quatuor partes æquales -diviso, cui circulus inscribitur, additis diagonalibus: & ubi hæ secant -circulum, fiunt rectæ parallelæ ad singula latera ipsius quadrati. -Deinde quadratum cum omnibus divisionibus opticè imminuitur; ac tum per -quatuor puncta ubi tres lineæ rectæ se intersecant, tum per quatuor -extrema reliquarum duarum diametrorum circuli, ducetur cum venustate -circumferentia circuli ~B~. Si addere velimus alium circulum, vestigio -geometrico ~C~ inscribetur aliud quadratum; indeque habebitur optica -delineatio duplicis circuli ~D~. Inter hos duos quomodo liceat describere -tertium, per octo sectiones quadratorum, ostendunt figuræ ~E~ & ~F~. Uno -verbo, circuli describuntur per quadrata, adhibendo sectiones visualium -cum parallelis ad lineam plani; ac nullum est punctum in quadratis & -circulis ~A~, ~C~, ~E~, cui per sectiones illas nequeat inveniri punctum -correspondens in quadratis & circulis ~B~, ~D~, ~F~. Nihilominus ubi opus -habeas pluribus circulis, autor tibi sum ne multiplices quadrata, plus -confusionis allatura tibi quam adjumenti._ - - - - -The Fourteenth Figure. - -_Circles in Perspective._ - - -That upon Pedestals you may be able to place Columns with their Bases and -Capitals, it is requisite you should know the Manner of putting Circles -into Perspective; whether single, double, or many concentrick. - -The Geometrical Plan A consists of a Square with a Circle inscrib’d, -whose Diameters divide it into four equal Parts; and the Diagonals -being drawn where they intersect the Circle, continue Lines parallel -to each Side of the Square. The Square, with all its Divisions, being -put in Perspective; by the four extreme Points of the Diameters, and by -those of the Intersection of the Diagonals, you neatly trace by hand -the Circumference B. If you would add another Circle, you must inscribe -another Square, as in the Plan C; from whence you find in Perspective -the double Circle D. Between these two Circles, you may, by the eight -Intersections of the Squares, describe a third; as is evident by the -Figures E and F. In a word, all Circles are described by the Help of -Squares, tracing them by the Intersections of the visual Lines, with -those parallel to the Ground-line: Nor is there any Point in either the -Squares or Circles A, C, E, whose correspondent Point may not be readily -found by such Sections, in the respective Squares and Circles B, D, F. -Nevertheless, where your Work requires many Circles, I would advise you -to use as few Squares as possible; lest they perplex, rather than assist -you. - - - - -[Illustration: FIG. XV.] - - - - -Figura Decimaquinta. - -Optica delineatio Columnæ. - - -_Descripturi frustum cylindricum ~I~ uniforme, fiet elevatio ~A~, & -vestigium geometricum ~B~, saltem quoad medietatem. Ex hoc opticè -deformato, ut vides in ~C~, ducendæ sunt parallelæ tum latitudinis ad -visualem ~D~, tum elevationis ad visualem ~E~; ex quibus describentur -circuli opticè contracti ~F~ & ~L~, accipiendo latitudines ex vestigio -~C~, altitudines ex perpendiculari ~M~; & juxta hanc methodum circuli -~F~ & ~L~ fiunt sine ope quadratorum. Demum ducendæ sunt perpendiculares -~G~ & ~H~, quæ tangant circulos ~F~ & ~L~ in punctis terminativis maximæ -latitudinis._ - -_Nullum est punctum in vestigio ~C~, cui per lineas latitudinis & -elevationis nequeat inveniri locus correspondens in circulo ~F~. Exempli -gratia; locus puncti ~7~ est punctum ~6~. Hunc autem locum habemus per -tres lineas, ~CD~, ~DE~, ~E7~._ - -_In delineandis duobus frustis cylindricis, cum summo & imo scapo, eandem -regulam servare oportebit._ - - - - -The Fifteenth Figure. - -_A Column in Perspective._ - - -Being to describe Part of the Shaft of a Pillar without Projectures, make -the Elevation A, and the Geometrical Plan B, at least to the middle: -From this brought into Perspective, as you perceive in C, must be drawn -Parallels both of Breadth to the Visual D, and of Elevation to the Visual -E; from which are described the Circles in Perspective F and L, taking -the Breadths from the Plan C, and the Heights from the Perpendicular M: -And according to this Method the Circles F and L are made, without the -Help of Squares. Lastly, draw the Perpendiculars G and H, by the Points -which terminate the greatest Breadth of the Circles F and L. - -There is not a Point in the Plan C, but what, by means of the Lines of -Breadth and Elevation, may be found in the Circle F. For Instance; the -Place of the Point 6 is 7, which is found by the three Lines CD, DE, E7. - -In designing the two Pieces of a Pillar, with the Projecture of the -Fillet at Head and Foot, you must observe the very same Rule. - - - - -[Illustration: FIG. XVI.] - - - - -Figura Decimasexta. - -Optica projectio basis Etruscæ. - - -_Ex elevatione geometrica ~A~ eruitur vestigium ~B~. Hoc autem deformato -in ~C~ & ~D~, ex circulis vestigii ~C~ habentur latitudines columnæ, -quadræ, ac tori triplicis basis: & eodem modo ex vestigio ~D~ habentur -latitudines quadræ ac tori ultimæ basis. Ex maximis latitudinibus -circulorum vestigii ~C~ ereximus perpendiculares ad partes quæ ipsis -respondent in basi; ut agnoscas quænam sint puncta maximæ latitudinis in -eisdem partibus. Hæc puncta (quæ in circulo maximo vestigii ~C~ sunt ~M~ -& ~N~) invenientur tangendo circumferentiam uniuscujusque circuli regulâ -parallelâ ad lineam perpendicularem ~E~, nam si figura exactè delineata -fuerit, regula tanget singulos toros trium basium in punctis maximæ hinc -inde latitudinis._ - -_Magis laborandum erit in reperiendis altitudinibus quatuor basium. -Verum si sedulò inspiciatur deformatio elevationis ~F~, aliarumque -duarum, (quæ factæ sunt, notatis in linea perpendiculari ~E~ divisionibus -desumptis ex elevatione geometrica ~A~) constabit, nullum esse punctum -in circulis vestigii ~C~, cui nequeat inveniri punctum correspondens in -toro & quadra ipsius basis, ut ostendunt lineæ occultæ, quæ incipiunt ex -~M~ & ~N~. Earum quælibet ex vestigio ~C~ pervenit ad lineam visualem, -& continuatur cum linea altitudinis ex visuali ad elevationem ~F~, & -cum alia linea latitudinis ex elevatione ~F~ ad basim. Porrò ex figura -constat, superficiem superiorem quadræ subduci oculis à columna, & -aliquid ex parte postica tori quod cæteroqui conspiceretur, abscondi -à quadra. Proinde torus, qui ex punctis maximæ latitudinis retrorsum -flectitur, eousque delineandus est, quoad hinc inde occurrat quadræ ipsum -cooperienti. Præstaret autem singula membra ita exactè delineari, quasi -essent diaphana; ut partes oculis imperviæ, omnino cohæreant cum partibus -quæ ipsis conspicuæ sunt._ - -_Completâ delineatione, si figuram tuam ex perpendiculo puncti oculi -ex debita distantia contemplatus fueris, omnes defectus facilè deteges -& statim corriges. Præcipuam diligentiam pones in formando & emendando -toro, qui habet duas rotunditates; unam quatenus ambit columnam; alteram -quatenus caret angulis, ut ostendit elevatio geometrica in ~I~._ - - - - -The Sixteenth Figure. - -_The ~Tuscan~ Base in Perspective._ - - -From the Geometrical Elevation A, is drawn the Plan B; which being put -into Perspective, as you see in C and D, from the Circles of the Plan -C you have the Breadths of the Column, and of the List, and _Torus_ of -the three Bases: And after the same manner, by the Plan D, you have the -Breadth of the List and _Torus_ of the last Base. From the greatest -Breadth of the Circles of the Plan C, we have erected Perpendiculars to -the Parts that answer them in the Base, to the end that you may see where -the Points fall, which terminate the greatest Breadth of those Parts. -These Points (which in the biggest Circle of the Plan C are M and N) are -found by touching the Extremity of the Circumference with a Line parallel -to the Perpendicular E: for if the Figure were exact, that Line would -touch every _Torus_ of the three Bases in the extreme Points of their -Breadth. - -The Heights of the four Bases are something more difficult to be found. -Nevertheless, if you consider well the Elevation F, and the other two G -and H, (which are made by transporting the Divisions of the Elevation -A upon the Perpendicular E) it will plainly appear that there is no Point -in the Circles of the Plan C, to which there may not be a correspondent -Point found in the _Torus_ and List of the said Base; as the occult -Lines shew, that arise from M and N; each of which is a Continuation -of three Lines: The first of Breadth, from the Plan C to the Visual; -the second of Height, from the Visual to the Elevation F; the third of -Breadth, from the Elevation F to the Base. Now, tho’ it’s plain by the -Figure, that the Body of the Column prevents the Sight of good part of -the Fillet, and the same Fillet takes off from part of the _Torus_, which -would otherwise be visible; for which Reason the Back-part of the _Torus_ -is continu’d only till it meet the same: Yet it’s certainly best to draw -every Member complete, as tho’ the Work were transparent; that the Parts -hidden from the Eye may the better agree with those that are expos’d to -it. - -When your Draught is finish’d, if you view it at the due Distance, and -perpendicularly to the Point of Sight; you’ll readily discover and -rectify what’s amiss. Your chief Care will be employ’d in shaping the -_Torus_, difficult by reason of its Roundness both ways; namely, in the -Contour of its Moulding, as in the Elevation I; and in the Circuit it -makes about the Column. - - - - -[Illustration: FIG. XVII.] - - - - -Figura Decimaseptima. - -Deformatio basis Doricæ. - - -_Ad vitandam satietatem quam pareret nimia uniformitas, unam ex basibus -invertimus. Utraque autem basis delineata est methodo quam tradidimus -figurâ præcedenti. Eademque methodus adeò manifestè patet ex lineis -occultis latitudinum & elevationum, ut superfluum futurum sit ipsam -repetere._ - - - - -The Seventeenth Figure. - -_The ~Dorick~ Base in Perspective._ - - -That you may not be tir’d with practising one and the same thing, I have -here, for Variety-sake, inverted one of the Bases. Both of ’em are drawn -after the Manner explain’d in the foregoing Figure; which is so evident -from the occult Lines of the Plan and Elevation here given, that I think -it superfluous to say any more of it. - - - - -[Illustration: FIG. XVIII.] - - - - -Figura Decimaoctava. - -Optica delineatio basis Ionicæ. - - -_Ex multitudine ac varietate figurarum hujus Operis, disces, mi Lector, -modum deformandi res demissas & sublimes, magnas & parvas. In hac figura, -linea cui bases duarum columnarum incumbunt, est conjunctim linea plani, -& linea horizontalis; linea cui bases trium columnarum incumbunt, est -altior linea horizontali. Quemadmodum autem, si linea plani sit inferior -linea horizontali, lineæ quæ tendunt ad punctum oculi & ad punctum -distantiæ, ascendunt sursum; ita si linea plani sit superior horizontali, -lineæ quæ veniunt ad punctum oculi & ad punctum distantiæ, tendunt -deorsum. Quòd si in eadem tabula sint plura plana, eorumque aliqua sint -altiora, alia verò demissiora linea horizontali, lineæ omnes planorum, -ac linea horizontalis, sunt invicem parallelæ; adeoque ex linea, quæ -omnes eas normaliter secet, statim dignosci potest, in qua proportione, -singula plana sint altiora vel profundiora linea horizontali. Velim -quoque observes, latitudinem columnæ mediæ, minorem esse latitudine -columnarum lateralium; & discrimen inter hujusmodi latitudines eò est -majus, quò punctum distantiæ fuerit vicinius puncto oculi. Quæ dicta sunt -de columnis, intelligere oportet de basibus, & de optica delineatione -ambarum. Nihilominus, si figura ex debito puncto inspiciatur, columnæ -pictæ habebunt eandem apparentiam, quam haberent columnæ solidæ, invicem -æquales._ - - - - -The Eighteenth Figure. - -_The ~Ionick~ Base in Perspective._ - - -By the Multitude and Variety of Figures in this Work, the Reader will be -instructed in delineating things, however different in Size or Situation. -In this Figure, the Line on which the two Columns rest, is both the -Horizontal and the Ground-line; that on which the three Columns are -plac’d, is so much higher than the Horizontal Line. And as, where the -Ground-line is beneath the Horizontal, the Lines drawn to the Points -of Sight and Distance tend upwards; so, where the same is above the -Horizontal, the Lines to the Points of Sight and Distance tend downwards. -If in the same Picture there are different Grounds, some higher, -others lower than the Horizontal Line; yet are all those Ground-lines, -and the Horizontal, parallel one to another; and therefore, by a Line -cutting them all perpendicularly, you presently know in what proportion -each Plan or Ground is higher or lower than the Horizontal. I would -have you observe, That the Breadth of the middle Column is, by the -Perspective, render’d less than that of the Side-Columns; and that this -Difference is the greater, as the Point of Distance approaches nearer -to the Point of Sight. What has been said of the Columns, is also to -be understood of the Bases, and the Projections of all their Parts in -Perspective: Nevertheless, if the Picture be view’d from its due Place, -the Columns will have the same Effect, as if solid; and all appear equal -one to the other. - - - - -[Illustration: FIG. XIX.] - - - - -Figura Decimanona. - -Optica imminutio basis Corinthiæ. - - -_Hæc basis juxta regulas traditas opticè contracta est. Porrò altitudo -superficiei ~A~ est eadem cum altitudine lineæ visualis ~CD~; latitudo -crucis ~A~ est eadem cum latitudine crucis secundi circuli vestigii ~B~, -incipiendo à minimo omnium. Duæ lineæ normaliter infixæ basi, ostendunt -maximam latitudinem quam habere debet columna supra imum scapum. Maxima -latitudo tori superioris & utriusque astragali, est eadem cum maxima -latitudine tertii circuli. Maxima latitudo tori inferioris est eadem cum -maxima latitudine ultimi circuli._ - - - - -The Nineteenth Figure. - -_The ~Corinthian~ Base in Perspective._ - - -This Base is put in Perspective by the Rules before laid down. The -Height of the Superficies A is the same with that of the visual Line -CD; the Breadth of the Cross A is the same with that of the second -Circle of the Plan B, beginning with the least. The two Lines that stand -perpendicularly on the Surface of the Base, shew the greatest Breadth of -the Columns Shaft above the Fillet. The Extent of the upper _Torus_ and -the two Astragals, is the same with that of the third Circle; and the -Extent of the lower _Torus_ is the same with that of the outward Circle. - - - - -[Illustration: FIG. XX.] - - - - -FIGURA Vigesima. - -Basis Acticurga opticè imminuta. - - -_Basis Acticurga Pictoribus præ reliquis familiaris est, quia cum -omnibus ferè Ordinibus egregiè consentit. Porrò ex punctis ~E~ & ~F~ -maximæ utrinque latitudinis extimi circuli vestigii, habetur maxima -latitudo tori inferioris ~CD~. Ac cætera quæ spectant ad ipsum & ad torum -~AB~, petenda sunt ex dictis de basi Etrusca._ - - - - -The Twentieth Figure. - -_The ~Attick~ Base in Perspective._ - - -The _Attick_ Base is more frequently made use of by Painters, than any -other; because it suits well with most of the Orders. The Points E and F, -the greatest Breadth of the outward Circle of the Perspective-Plan, give -the greatest Breadth of the lower _Torus_ CD. And whatever else relates -either to this or the upper _Torus_ AB, is to be sought in the same -Manner, as has been shewn in the _Tuscan_ Base. - - - - -[Illustration: FIG. XXI.] - - - - -Figura Vigesimaprima. - -Optica imminutio capitelli Etrusci. - - -_Eâdem cum reliquis formâ, eâdemque methodo capitella delineanda sunt: -quum habeant ipsa quoque suum cimatium quadratum, & sint rotunda. Linea -plani solet in iis fieri altior lineâ horizontali: quia quum capitella -imponenda sint columnis homine altioribus, plerumque apparent sublimiora -nostris oculis._ - - - - -The Twenty-first Figure. - -_The ~Tuscan~ Capital in Perspective._ - - -The Manner before deliver’d concerning Bases, is of the same Use in -delineating Capitals; forasmuch as these also have their square _Abacus_, -and their round Members. The Ground-line in Capitals is usually plac’d -above the Horizon; because when they are set upon Columns which exceed a -Man’s Height, they are generally represented above the Eye. - - - - -[Illustration: FIG. XXII.] - - - - -Figura Vigesimasecunda. - -Optica projectio capitelli Dorici. - - -_Capitellum hoc pluribus membris constat, adeóque operosius est quàm -præcedens. Nihilominus accurata delineatio vestigii geometrici omnes -difficultates complanabit._ - - - - -Twenty-second Figure. - -_The Projection of a ~Dorick~ Capital, in Perspective._ - - -This Capital consisting of more Members than the foregoing, will be more -troublesom to put in Perspective; but an accurate Delineation of the -Geometrical Plan will certainly remove many seeming Difficulties. - - - - -[Illustration: FIG. XXIII.] - - - - -Figura Vigesimatertia. - -Deformatio capitelli Ionici. - - -_Capitellum Ionicum poscit duas elevationes geometricas distinctas, -alteram faciei, alteram lateris; ex iisque conflatur vestigium -geometricum ~A~, quod opticè contrahitur, translatis in ~B~ punctis -latitudinis ~C~, & in ~E~ punctis longitudinis ~D~ more consueto: ut ex -punctis ~B~ latitudinis, lineæ tendant ad punctum oculi; ex punctis verò -~E~ longitudinis, lineæ tendant ad punctum distantiæ._ - -_Ex vestigio capitelli opticè contracto eruenda est elevatio longitudinis -ut in figura. Ex utrisque verò juxta morem fiet capitellum nitidum, -acceptis latitudinibus ex vestigio, altitudinibus ex elevatione -longitudinis. Hæc quoque dabit maximam latitudinem singularum volutarum._ - -_Modum delineandi capitellum Ionicum, in quo helices volutarum -obliquentur, dabimus infra figurâ trigesimâ._ - - - - -Twenty-third Figure. - -_The ~Ionick~ Capital in Perspective._ - - -The _Ionick_ Capital requires two distinct geometrical Elevations, -one of the Front, the other of the Side; from both which is found the -geometrical Plan A, which is put in Perspective by transferring into B -the Points of Breadth C, and into E the Points of Length D, after the -usual Manner; that from the Points of Breadth B, Lines may be drawn -towards the Point of Sight; and from the Points of Length E, towards the -Point of Distance. - -From the Plan of the Capital in Perspective, is to be drawn the Upright -of the Length, as in the Figure; and from both, as usual, the finish’d -Capital is wrought, by taking the Breadths from the Plan, and the -Heights from the Elevation; this giving the utmost Height, and that the -utmost Breadth of each of the Volutes. - -The Manner of describing the _Ionick_ Capital, whose Volutes lie -obliquely, we shall hereafter treat of in the Thirtieth Figure. - - - - -[Illustration: FIG. XXIV.] - - - - -Figura Vigesimaquarta. - -Optica projectio capitelli Corinthii. - - -_Capitellum Corinthium absolvere non poteris, nisi elevatione geometrica -ejusque vestigio exactissimè delineatis juxta regulas Barozzii._ - -_Ad formandum ex vestigio ~B~ vestigium ~E~, rectis occultis fient -quadrata necessaria ad contractionem opticam quatuor vel trium saltem -circulorum; translatis in lineam ~D~ divisionibus lineæ ~C~, & aliis, -more consueto. Contrahentur deinde lineis occultis vestigia foliorum, & -absolventur cætera quæ posita sunt in vestigio_ E. - -_Ut fiat optica elevatio longitudinis ~F~, in lineam perpendicularem -~H~ transferentur ex elevatione ~A~ omnes ejus divisiones. Complebitur -autem per lineas rectas, quæ ex punctis divisionum ducantur ad punctum -oculi, ac per rectas ex circulorum summitate ac profunditate, quæ rectæ -sint parallelæ ad lineam ~D~, ac perveniant ad visualem ~G~; indeque -descendant, ac sint parallelæ ad lineam perpendicularem_ H. - -_Capitellum nitidum exordieris ab infimo circulo ~I~, ostendente ambitum -columnæ. Succedent folia ~1~, ~2~, quorum latitudines accipientur -ex vestigio ~E~ per circinum, positâ unâ ejus cuspide in linea ~H~; -altitudines verò accipientur ex elevatione ~F~, posita una cuspide -circini in linea ~D~. Idipsum dico tum de foliis ~3~, ~3~, ~4~, ~4~, tum -de folio ~5~, ac de aliis, & demum de cymatio. Descensus verò lineæ curvæ -ipsius cymatii incipiet ex acie ~L~._ - - - - -Twenty-fourth Figure. - -_The ~Corinthian~ Capital in Perspective._ - - -There is no Completing the _Corinthian_ Capital, unless you most -accurately describe its Geometrical Elevation and Plan, according to the -Rules of _Vignola_. - -Being to form the Plan E from the Plan B, you must, with occult Lines, -make the Squares necessary for bringing four, or at least three of the -Circles into Perspective; transferring into the Line D the Divisions -of the Line C, and the rest as usual. Then, with other occult Lines, -contract the Plans of the Leaves, and finish what’s farther requisite in -the Plan E. - -To make the Optick Elevation of the Length F, you must transfer into the -Perpendicular H all the Divisions of the Elevation A; and complete the -same, by Lines drawn toward the Point of Sight, till they meet their -respective Perpendiculars; which proceeding from all parts of the Circles -parallel to the Line D, intersect the Visual G; from whence they descend, -Parallels to the Perpendicular H. - -In working the clean Capital, you should begin with the lowest Circle I, -which denotes the Compass of the Column. Then make the Leaves 1, 2, by -taking their Breadths from the Plan E, with the Compasses, and keeping -one Point of them upon the Line H; and their Heights from the Elevation -F, keeping one Point on the Line D. The same must be done, as well by the -Leaves 3, 3, 4, 4, as by the Leaf 5, and the others; and last of all, by -the _Abacus_ also; the Sinking of the Horns whereof answers that of the -visual Line L. - - - - -[Illustration: FIG. XXV.] - - - - -Figura Vigesimaquinta. - -Optica descriptio capitelli Compositi. - - -_Ex iis quæ diximus de capitello Corinthio, didiceris modum faciendi -capitellum Compositum. Velim autem tibi persuadeas, cum lectione harum -regularum quæ sunt magistri inanimes, circini usum perpetuò conjungi -oportere. Hic enim vivi magistri defectum unicè supplere potest._ - - - - -The Twenty-fifth Figure. - -_The ~Composite~ Capital in Perspective._ - - -From what has been said of the _Corinthian_ Capital, may be learnt the -Manner of putting the _Composite_ also into Perspective. I wish I could -prevail with you, that to the Reading of the Rules, which in themselves -are but lifeless Masters, you would constantly add a diligent Practice of -the Figures by the Compasses; this being the only way to supply the Want -of a living Master. - - - - -[Illustration: FIG. XXVI.] - - - - -Figura Vigesimasexta. - -Deformatio coronicis Etruscæ. - - -_Post capitella sequuntur coronices, quæ utpote quadratæ, minimam habent -arduitatem. Inter coronices verò, nulla est Etruscâ simplicior ac -facilior. Ex elevatione geometricâ, more solito, formatur vestigium -geometricum; ex eoque opticè contracto eruitur similis elevatio -longitudinis. Demùm ex elevatione & vestigio componitur coronix nitida. -Memineris autem duas esse lineas, quæ hinc inde terminant latitudinem -elevationis opticæ. Linea quæ altior est, dat altitudinem anterioris -faciei coronicis, alia quæ est depressior, dat altitudinem faciei -posterioris. Et ita erit in posterum._ - - - - -Twenty-sixth Figure. - -_The ~Tuscan~ Entablature in Perspective._ - - -After Capitals we proceed to _Entablatures_, which because they are -square, are less difficult than the former. And of all Entablatures, -that of the _Tuscan_ Order is the most simple and easie to be put -in execution. From the Geometrical Upright is drawn, as usual, the -Geometrical Plan; from the Plan put in Perspective is describ’d the -Optick Elevation of the Length; and from both the latter is wrought the -clean Entablature requir’d. You may observe, here are two Lines that -terminate the Breadth of the Perspective on one side and the other. The -Line which proceeds from the higher Corner of the Visual, gives the -Height of the most advanc’d Part; that from the lower determines the -Height of the Back-part. And so for the future. - - - - -[Illustration: FIG. XXVII.] - - - - -Figura Vigesimaseptima. - -Optica delineatio coronicis Doricæ. - - -_In faciendâ coronice Doricâ, quæ majorem operam poscit, ob denticulos -& triglyphos; communis regula servanda est. Si autem libeat coronicem -nitidam describere in papyro separatâ ab ejus præparationibus, id -profectò licet, tum in hoc, tum in quocunque alio schemate._ - - - - -Twenty-seventh Figure. - -_The ~Dorick~ Entablature in Perspective._ - - -In making the _Dorick_ Entablature, which has something more Work in it -than the former, on account of its Dentels and Triglyphs; the common Rule -is to be observ’d. And if you would delineate the finish’d Entablature in -a Paper distinct from that of its Preparations, you are at liberty so to -do, either in this or any other Figure. - - - - -[Illustration: FIG. XXVIII.] - - - - -Figura Vigesimaoctava. - -Præparatio figuræ sequentis. - - -_In figurâ vigesimaoctavâ, quæ continet vestigium & elevationes -geometricas figuræ vigesimænonæ, oportuit latus ~C~ delineare seorsim à -facie ~B~; quia facies exhibet latitudinem ædificii, latus verò exhibet -longitudinem; atque una non est alteri æqualis. In vestigio geometrico -solidus paries est ~A~: circuli referunt summum scapum columnarum. Cætera -dant projecturas coronicis, cum suis mutulis._ - - - - -Twenty-eighth Figure, - -_Preparatory to the following Figure._ - - -In this Twenty-eighth Figure, which contains the Plan and Geometrical -Elevations of the Twenty-ninth Figure, it was requisite to delineate the -Side C separately from the Front B; because the Front, which signifies -the Breadth of the Building, and the Side, which shews its Length, are -not equal one to the other. In the Geometrical Plan the solid Wall is A: -the Circles express the Nakeds of the Pillars Shafts at top. The rest is -the Projecture of the Cornice, with its Mutules. - - - - -[Illustration: FIG. XXIX.] - - - - -Figura Vigesimanona. - -Optica projectio ædificii Dorici. - - -_Habes in hac figura vigesimanona, opticam delineationem vestigii, & -unius ex elevationibus figuræ vigesimæoctavæ; nimirum, elevationis -longitudinis; ex quibus eruitur imago nitida ædificii Ordinis Dorici, cum -summitatibus & capitellis trium columnarum; ejusque epistylium, zophorus, -& corona._ - -BO _est linea horizontis; ~AC~ est linea plani; in quam, ex lineis -~D~ & ~C~ figuræ vigesimæoctavæ, transferuntur puncta latitudinis & -longitudinis duarum elevationum; prolongando versus ~C~ ipsam lineam -plani, ut oportet. Operaberis autem, ut diximus figurâ vigesimatertia; -nimirum, in puncto ~V~ desinet latitudo vestigii, incipiet longitudo; -& ex punctis latitudinis lineæ tendent ad punctum oculi; ex punctis -longitudinis lineæ occultæ tendent ad punctum distantiæ. Ubi verò hæ -lineæ secant visualem ~VO~, fient parallelæ ad lineam ~AC~, cum cæteris -quæ necessaria sunt ad complendam delineationem opticam vestigii._ - -_Elevatio ~C~ figuræ vigesimæoctavæ opticè contrahetur more consueto, -translatis in lineam ~AB~ divisionibus lineæ ~E~ vel ~F~, ex quibus -fient visuales ad punctum oculi; ac demissis ex linea visuali ~AO~ -perpendicularibus ad lineam ~AC~, ita ut lineæ parallelæ ad lineam plani -~AC~ continuentur cum aliis lineis parallelis ad lineam ~AB~._ - -_Hic quoque locum habet observatio illa, cujus meminimus figura -vigesimasexta, de lineis quæ deorsum excurrunt, & hinc inde terminant -membra elevationis opticæ. Ex iis autem desumuntur projecturæ omnes -coronicis & capitellorum._ - - - - -Twenty-ninth Figure. - -_A Projection of the ~Dorick~ Order in Perspective._ - - -In this Twenty-ninth Figure, you have in Perspective the Plan, and one -of the Uprights of the Twenty-eighth Figure; namely, that of the Length; -from whence is drawn this finish’d Piece of the _Dorick_ Order, which has -the upper Part and Caps of three Pillars, with their Architrave, Freeze, -and Cornice. - -BO is the Horizontal-line; AC that of the Plan; into which, from the -Lines D and C of the Twenty-eighth Figure, are transferr’d the Points -of Breadth and Length of the two Elevations; first prolonging the Line -itself, as much as is needful, through C. The Work is then perform’d, -as was shewn in the Twenty-third Figure; namely, the Divisions of the -Breadth of the Plan end in the Point V, at which those of Length begin. -From the first, Lines are drawn to the Point of Sight; and from the -latter, occult Lines are directed to the Point of Distance: And where -these cut the Visual VO, Lines are drawn parallel to AC; with those that -are farther necessary for completing the Plan in Perspective. - -The Elevation C of the Twenty-eighth Figure is put in Perspective, as -usual, by transferring the Divisions of the Line E, or F, into that of AB -in this Plate; from whence drawing Visuals to the Point of Sight, they -are intersected by Perpendiculars let fall from those Divisions of AO -made by the Parallels to the Ground-line AC, and again continu’d parallel -to the Perpendicular AB. - -The Observation, mention’d in the Twenty-sixth Figure, is also pertinent -in this place; That the Lines, which, in the Perspective-Elevation, tend -downward, give the Advance and Recess of the several Members of the -Work; and from them are taken all the Projectures of the Entablature and -Capitals. - - - - -[Illustration: FIG. XXX.] - - - - -FIGURA Trigesima. - -Optica projectio ædificii Ionici; ubi de modo jungendi fictum cum vero. - - -_Si tibi Pictor quum sis, occasione apparatûs quadraginta horarum, vel -sepulcri Domini, mutare ad tempus libeat formam architecturæ alicujus -Ecclesiæ jungendo fictum cum vero, ut mihi sæpius contigit Mediolani ac -Romæ, cum ingenti spectatorum delectatione & admiratione; paucis ostendam -tibi modum quem servare debeas in operando._ - -_Sectio coronicis veræ, quæ, ut suppono, videri debet continua esse -cum coronice picta in telario, est ~A~; elevatio geometrica coronicis, -& reliquorum quæ delineanda sunt, est ~B~; vestigium geometricum est -~C~. Porrò, tum vestigium tum elevatio longitudinis opticè contrahentur -more consueto, ut vides in ~C~ & ~B~: ex iisque formabitur in telario -coronix nitida cum columna & anta; ipsumque telarium depictum, normaliter -coagmentandum erit veræ coronici._ - -_Ut fiat ea pars longitudinis, quæ coronicem pictam continuare videatur -cum vera, & erui non potest ex elevatione deformata; oportet sectionem -~A~ transferre in ~D~, ducendo visuales ex punctis terminativis membrorum -sectionis ~D~, usque dum occurrant lineis latitudinis eorundem membrorum. -Quod si colores in telarium scitè inducantur, angulus in ~E~, quamvis -merè depictus, videbitur verus; & ex adverso, anguli quos telarium ipsum -depictum facit cum diversis adeò crepidinibus coronicis veræ, nusquam -apparebunt, præterquàm in quadra simæ dumtaxat; & unio architecturæ veræ -cum ficta dignosci non poterit._ - - - - -The Thirtieth Figure. - -_An ~Ionick~ Work in Perspective; with the Manner of reconciling the -fictitious to the solid Architecture._ - - -If, being a Painter, you were requir’d, against the Solemnity of the -Holy-Week, to alter for a while the Architecture of some Altar-piece, by -joining Painting to the real Work; as I have often done, both at _Rome_ -and _Milan_, to the great Satisfaction and Surprize of the Beholders: I -shall briefly shew the Method to be observ’d in performing the same. - -The Dissection of the solid Cornice, which I here suppose shall appear -continu’d in that painted on the Canvass, is A; the Geometrical Elevation -of the Cornice, and other Parts to be drawn, is B; the Geometrical Plan -is C. The Plan and Elevation of the Length are put in Perspective after -the usual manner, in C and B; from those the finish’d Cornice, with the -Pillar and Pilaster, are delineated on the Canvass; and the Picture is -then conjoin’d, at right Angles, to the true Cornice. - -For adjusting the Members so, that the painted Cornice may seem to be the -real one continu’d, (which can’t be done by the Perspective Upright) you -must transfer the Section A to D; and from the terminating Points of the -several Members thereof, draw visual Lines, till they meet those of their -respective Members in the Perspective. And if the Colours are laid by a -skilful Hand, the Angle at E, tho’ painted only, will appear as real; -and on the contrary, the Angles which the Members of the painted Cornice -make with the different Projectures of those of the true, will never be -discern’d, unless in the very uppermost Fillet; but the Conjunction of -the real with the painted Architecture, will be altogether imperceptible. - - - - -[Illustration: FIG. XXXI.] - - - - -Figura Trigesimaprima. - -Optica projectio coronicis Corinthiæ, cum capitello & summitate columnæ. - - -_In hoc schemate linea plani est ~CIE~, horizontis est ~DFO~; punctum -oculi est ~O~, distantiæ est ~D~. Elevatio geometrica capitelli Corinthii -cum sua coronice est ~A~, quorum divisiones cernuntur in perpendiculari -~CD~. Vestigium geometricum ~B~ habet longitudinem æqualem latitudini: -opticè autem contrahitur methodo consueta. Nimirum, translatis -divisionibus latitudinis & longitudinis in lineam plani ~CIE~; ex punctis -latitudinis fiunt visuales ad punctum oculi; ex punctis verò longitudinis -fiunt occultæ ad punctum distantiæ: hoc modo habes quicquid necessarium -est ad contractionem opticam vestigii. Nam lineæ longitudinum sunt partes -visualium, ut patet in ~GN~, ~HL~: lineæ latitudinum, parallelæ ad lineam -plani fiunt ex punctis in quibus lineæ tendentes ad punctum distantiæ -secant visualem ~HO~, ut vides in ~NL~. Porro, si tantundem prolongaretur -horizontalis ~DO~, ita ut haberet duo puncta distantiæ remota æqualiter -ab ~O~, medietas diagonalium, quæ sunt in quadrato majori ~GNLH~ opticè -deformato, & in quadratis ejus minoribus, tendent ad unum punctum -distantiæ; altera medietas ad aliud punctum distantiæ._ - -_Elevatio longitudinis opticè contrahitur ductis parallelis ad ~CE~, -quæ ubi pervenerint ad visualem ~IO~, continuentur cum aliis parallelis -ad ~IK~. Præterea, translatis in lineam ~IK~ divisionibus lineæ -perpendicularis ~CD~, ex punctis divisionum fiunt visuales ad punctum -oculi, ac ducuntur singula membra ipsius elevationis, cujus latitudines -sunt partes visualium, altitudines verò sunt partes linearum parallelarum -ad ~IK~. Demùm ex vestigio & ex elevatione longitudinis, formatur coronix -nitida cum capitello. Ut autem faciliùs delineentur mutuli, primùm fient -quadratâ formâ, ut in ~M~; deinde congruus flexus in singulos inducetur._ - - - - -The Thirty-first Figure. - -_The Optick Projection of a ~Corinthian~ Cornice, with the Capital and -PART of the Column._ - - -In this Figure the Line of the Plan is CIE, that of the Horizon is -DFO; the Point of Sight is O, the Point of Distance D; the Geometrical -Elevation of the _Corinthian_ Capital, with its Entablature, is A; whose -Divisions are seen in the Perpendicular CD. The Length and Breadth of the -Geometrical Plan B are equal, and the Plan is put into Perspective after -the usual Method; to wit, by transferring the Divisions of Breadth and -Length into the Line CIE; from the Points of Breadth drawing Visuals to -the Point of Sight; and from those of Length occult Lines to the Point -of Distance: by which Intersections you have all that’s necessary for -putting the Plan into Perspective. For the Lines of Length are Parts of -visual Rays, as is manifest by GN, HL; and the Lines of Breadth are made -Parallels to the Ground-line, from the Intersections before-mention’d, -as is seen in NL. Moreover, if the Horizontal-line DO were so prolong’d, -as to receive another Point of Distance equidistant from O; half the -diagonal Lines of the great Square GNLH, and of the lesser Squares -contain’d therein, would tend to one Point of Distance, and the other -half to the other. - -The Elevation of the Length is put in Perspective, by continuing the -Parallels to CE, till they cut the Visual IO; and from thence dropping -Lines parallel to IK: Then transferring into IK the Divisions of the -Perpendicular CD, from them make visual Lines to the Point of Sight, and -draw the several Members of the Upright; whose Breadths are Parts of -Visuals, and their Heights Parts of Perpendiculars, or Lines parallel -to IK. Lastly, from the Plan and Elevation of the Length, you delineate -the finish’d Cornice and Capital: But that you may more easily draw the -Modillions, first make them in a square Form, as in M; and that will very -much assist you to give the Scroll of each a more agreeable Turn. - - - - -[Illustration: FIG. XXXII.] - - - - -Figura Trigesimasecunda. - -Delineatio geometrica coronicis, Ordinis Compositi. - - -_Ut hoc schema grandius ac distinctius esset, ejus medietatem dumtaxat -suscepi delineandam. ~PN~ est vestigium geometricum. ~M~ est solidus -paries. ~OO~ spatia columnarum. In ~H~ sunt crepidines coronicis. -Elevatio geometrica latitudinis ædificii constat epistylio ~T~, zophoro -~L~, & coronâ ~V~, supra quam eminet fastigium ~S~._ - -_Jam ut inveniatur centrum arcuum, distantiæ ~AV~ fiat æqualis distantia -~AC~. Positaque una cuspide circini in ~C~, alia extendatur usque ad ~V~: -ita fient arcus, quorum ultimus est ~BD~, omnesque sunt concentrici. -Elevatio ~F~ ostendit longitudinem ædificii ex parte ~GI~; elevatio ~E~ -ostendit longitudinem ipsius ex parte ~DR~._ - - - - -Thirty-second Figure. - -_The Geometrical Design of a Cornice, of the ~Composite~ Order._ - - -That this Figure might be larger and more distinct, I have here describ’d -only the Half of it. PN is the Geometrical Plan. M is the solid Wall. OO -are the Places of the Columns. H shews the Projectures of the Cornice. -The Geometrical Elevation of the Breadth of the Frontispiece, consists of -the Architrave T, the Freeze L, and the Cornice V, over which is rais’d -the Pedament S. - -For finding the Center of the arch’d Lines of the Pedament, make the -Distance AC equal to that of AV; and placing one Point of the Compasses -in C, extend the other to V, and describe the Arch. The other Arches, of -which BD is the utmost, have all the same Center. The Elevation F shews -the Length of the Work on the Side GI. The Upright E shews the Length of -the same on the Front DR. - - - - -[Illustration: FIG. XXXIII.] - - - - -Figura Trigesimatertia. - -Deformatio coronicis Compositæ. - - -_Figura hæc trigesimatertia minus ardua tibi videbitur, si ex ea -delineandam primùm suscipias medietatem quæ respondet vestigio ~PN~ & -elevationi ~BR~ figuræ trigesimæsecundæ; rejecto in ultimum fastigio, -postquàm cætera compleveris. Linea ~BV~ est horizontalis. Punctum oculi -est ~V~, punctum distantiæ remotum est ab ~V~ spatio ~BV~, additis -modulis quatuordecim cum dimidio. Linea plani est ~AR~, in quam ex ~Q~ -versus ~A~ transfertur latitudo ~P~; ex ~Q~ versus ~R~ transfertur -longitudo ~N~, cum omnibus earum divisionibus; ut ex punctis latitudinis -fiant visuales ad punctum oculi; & ex punctis longitudinis fiant -occultæ ad punctum distantiæ. Ex his habes quicquid necessarium est ad -projectionem opticam vestigii, ut ostendimus figurâ trigesimaprimâ. -Eademque methodo, quam ibi servavimus, contrahes elevationem ~P~ -longitudinis coronicis: ac tum ex illa, tum ex vestigio, eruetur coronix -nitida more consueto._ - -_Ut delineetur fastigium, transferendæ sunt in lineam ~AB~ divisiones -ipsius ex elevatione ~F~ figuræ trigesimæsecundæ, ac ducendæ visuales -ad punctum oculi, additis lineis terminativis uniuscujusque membri, -quæ accipientur ex vestigio ~Q~ opticè deformato. Centrum ~O~ arcuum -fastigii nitidi, remotum est à summitate coronicis, medietate distantiæ, -quam habent ungues quadræ cui fastigium ipsum incumbit. Ac proinde, si -accipias ex elevatione ~P~ diversas altitudines membrorum fastigii; -latitudines verò accipias ex vestigio ~Q~; opus tuum feliciter absolves._ - - - - -The Thirty-third Figure. - -_A ~Composite~ Cornice in Perspective._ - - -This Thirty-third Figure will be found the less difficult, if you -first attempt that Half which answers to PN in the Plan, and BR in the -Upright of the Thirty-second Figure; leaving the Pedament, till all -the rest be finish’d. The Line BV is the Horizontal. V is the Point of -Sight; the Point of Distance is fourteen Modules and a half without -the Point B, more than the Interval BV. The Line of the Plan is AR, in -which from Q toward A you have the Divisions of Breadth of the foregoing -Plan P; and from Q to R those of the Length thereof N: From the former, -Visuals are drawn to the Point of Sight; and from the latter, occult -Lines to the Point of Distance. And from these you have all that’s -necessary for putting the Plan in Perspective; as was shewn in the -Thirty-first Figure. By the Method there observ’d, you may also describe -the Perspective-Elevation of the Length P; and from this, and the Plan, -delineate the finish’d Cornice after the usual Manner. - -For making the Pedament, the Divisions of the Elevation F in the -Thirty-second Figure, must be transferr’d into the Line AB, and Visuals -drawn from them to the Point of Sight; giving to each Member its proper -Out-line and Contour, as may be taken from the Perspective-Plan Q. The -Center O of the Arches in the finish’d Pedament, is plac’d below the -upper Member of the Cornice, as much as half the Extent of the upper -Fillet from whence the Pedament springs. And by taking the several -Heights of the Members thereof, from the Elevation P; and the Breadths -from the Plan Q; you will successfully finish and complete your Work. - - - - -[Illustration: FIG. XXXIV.] - - - - -Figura Trigesimaquarta. - -Præparatio ad figuram trigesimamquintam. - - -_Si placuerit conferre figuram trigesimamtertiam cum præsenti figura -trigesimaquarta, dignosces vestigium & elevationem coronicis Compositæ -alio modo hic deformari, mutando scilicet longitudinem in latitudinem, & -latitudinem in longitudinem. Propterea hæc figura tantum spatii occupat, -ut eam seorsim à coronice nitida delineare oportuerit._ - -_Divisiones latitudinis in vestigio incipiunt ex ~V~ versus ~R~, & sunt -eædem cum divisionibus rectæ ~IG~ figuræ trigesimæsecundæ. Divisiones -longitudinis incipiunt ex ~V~ versus ~S~, & sunt eædem cum divisionibus -rectæ ~IP~ duplicatis. Ex divisionibus latitudinis fiunt visuales ad -punctum oculi; ex divisionibus longitudinis fiunt rectæ ad punctum -distantiæ; cum reliquis quæ necessaria sunt ad complendum vestigium -~AVDC~._ - -_Elevatio longitudinis coronicis & fastigii, opticè contrahitur per -lineas parallelas ad lineam plani ~AS~; quæ ubi pervenerint ad visualem -~AC~, continuentur cum aliis parallelis ad perpendiculum ~P~, ut diximus -figurâ trigesimaprimâ. In idem perpendiculum ~P~ transferuntur ex figurâ -trigesimasecundâ divisiones rectæ ~DR~; & insuper altitudines, quas -puncta ~KXZ~ habent supra rectam ~VA~; fientque visuales ad punctum -oculi: sectiones autem visualium cum parallelis ad perpendiculum ~P~, -dabunt sex puncta simæ fastigii, respondentia punctis ~KXZ~ duplicatis, -figuræ trigesimæsecundæ; earumque ductu formandus est supremus arcus. -Eodem artificio fient reliqui omnes._ - -_Faciliùs delineabitur coronix, cujus maximam partem occupant lineæ -visuales ad punctum oculi: porrò, membra omnia, exceptâ simâ, communia -sunt coronæ & fastigio. Adeoque puncta similia in lineis terminativis -membrorum singulorum, ex quibus desumuntur crepidines & ungues figuræ -nitidæ, sunt parallela ad perpendiculum ~P~._ - - - - -The Thirty-fourth Figure, - -_Preparatory to the Thirty-fifth._ - - -If you please to compare the Thirty-third Figure with this Thirty-fourth -Figure, you will perceive the Plan and Elevation of this _Composite_ -Cornice to be delineated differently from that; to wit, by making the -Length of that the Breadth of this, and the Breadth of that the Length of -this: On which account, this Figure takes up so much Room, that there was -a necessity of drawing the finish’d Cornice on a separate Paper. - -The Divisions of Breadth in the Plan begin from V toward R; and are the -same with those of the Line IG in the Thirty-second Figure. The Divisions -of Length are set from V toward S; and are the same with those of the -Line IP in the Thirty-second Figure; which being the Half, is here -doubl’d. From the Divisions of Breadth, Lines are drawn to the Point of -Sight; and from those of the Length, Lines to the Point of Distance; with -the farther Requisites for completing the Plan AVDC in Perspective. - -The Upright of the Length of the Cornice and Pedament, is made by -producing Parallels to the Ground-line AS; till they intersect the Visual -AC; and thence continuing Lines parallel to the Perpendicular P, as was -directed in the Thirty-first Figure. Into the same Perpendicular P are -transferr’d the Divisions of the Line DR in the Thirty-second Figure; -and also the Heights which the Points KXZ have above VA in the same -Figure. From all which, Visuals are drawn to the Point of Sight; which -being intersected by the Perpendiculars, give six Points on the _Cima_ of -the Pedament, which answer to the said Points KXZ of the Thirty-second -Figure, doubl’d: By these the outward Arch is form’d. And by the same -Rule, you find Points for all the others. - -You will more easily draw the Cornice, the greatest Part of it consisting -of visual Lines to the Point of Sight: Moreover, all the Members, except -the upper _Cima_, are common both to the Cornice of the Entablature, -and to the Pedament; so that the corresponding Points, in the Out-lines -of their several Members, from whence the Breaks and Contours of the -finish’d Piece are taken, are found in the same Parallels to the -Perpendicular P. - - - - -[Illustration: FIG. XXXV.] - - - - -Figura Trigesimaquinta. - -Deformatio coronicis Compositæ, ad latus inspectæ. - - -_Artificium nitidæ coronicis, ex vestigio & elevatione figuræ -trigesimæquartæ eruendæ, non differt ab eo quod sæpè traditum est. Itaque -supposito, quòd linea plani & horizontis, ac puncta oculi ac distantiæ, -habeant in hoc schemate situm omnino eundem, quem habent in præcedenti; -ope duorum circinorum, invenientur distantiæ, quas anguli necessarii ad -integram delineationem coronicis, habent à linea plani, & à linea normali -ad ipsam lineam plani. Nam ducendo lineas visuales, aliasque lineas -parallelas ad ipsum perpendiculum, cum terminis & flexibus qui conveniunt -singulis membris, complebitur delineatio._ - -_In fastigio visuales sunt penitus occultæ: puncta autem similia ~H~ -& ~L~, ex quibus fastigium incipit introrsum flecti, incidunt in unam -eandemque visualem. Idipsum dico de aliis punctis similibus. Nam -lineæ rectæ omnes, quæ in figura trigesimatertia sunt parallelæ ad -lineam plani, in figuris trigesimaquarta & trigesimaquinta sunt partes -linearum visualium._ - - - - -The Thirty-fifth Figure. - -_A Side-View of the ~Composite~ Cornice, in Perspective._ - - -The Manner of drawing this finish’d Cornice, from the preceding Plan and -Elevation, is the same with that so often shewn you. Admitting therefore, -that the Lines of the Plan and Horizon, and the Points of Sight and -Distance, have the very same Position in this, that they had in the -preceding Scheme; all the Angles necessary for delineating the entire -Cornice, are readily found by the help of two pair of Compasses; taking -their Distances one way from the Ground-line; and the other way from a -Line perpendicular to the same: Then drawing the visual and perpendicular -Lines, and keeping the Place and Contour of the several Mouldings, you -complete your Design. - -In the Pedament the visual Lines are wholly occult; and the Points H -and L, where the Pedament begins to break back, being of like Height, -are found in one and the same Visual: And the same may be said of all -Points that are of equal Height from the Plan; for all the right Lines, -which in the Thirty-third Figure are Parallels to the Ground-line, in the -Thirty-fourth and Thirty-fifth Figures are Parts of the visual Lines. - - - - -[Illustration: FIG. XXXVI.] - - - - -FIGURA Trigesimasexta. - -Præparatio ad figuram trigesimamseptimam. - - -_In vestigio geometrico ~C~, & in ejus elevatione ~AB~, præcipuas tantùm -lineas adnotavi, ne figuram confunderem, & ut studiosorum industriæ -aliquid relinquerem. Linea plani ~EG~ habet divisiones latitudinis ~P~, -& longitudinis ~Q~, vestigii geometrici ~C~. Ex punctis latitudinis -ducentur more solito visuales ad ~O~ punctum oculi; ex punctis -longitudinis fient occultæ ad punctum distantiæ, quod extra lineam -~AB~ protenditur modulis quatuordecim: & ubi occultæ ex divisionibus -longitudinis secant visualem ~FO~ fiunt parallelæ ad lineam plani ~EF~, -adhibitis sectionibus talium parallelarum cum visualibus, ad complendam -deformationem vestigii._ - -_Eædem lineæ quæ in vestigio deformato sunt parallelæ ad ~EF~, -prolongantur usque ad visualem ~EO~, & continuantur cum aliis parallelis -ad perpendiculum ~DE~. Fiunt quoque visuales ad punctum oculi ex -divisionibus elevationis ~AB~ translatis in perpendiculum ~DE~; -adhibitis sectionibus talium parallelarum cum visualibus, ad complendam -deformationem longitudinis elevationis._ - - - - -The Six and thirtieth Figure, - -_Preparatory to the Thirty-seventh._ - - -In the Geometrical Plan C, and in the Elevation thereof AB, I have only -mark’d the principal Lines, as well for avoiding Confusion in the -Figure, as that something might be left to the Industry of the Studious. -The Line of the Plan EG has the Divisions of Breadth P, and of Length -Q, of the Geometrical Plan C. From the Points of Breadth are drawn, as -usual, Visuals to the Point of Sight O; From the Points of Length occult -Lines are produc’d to the Point of Distance, which lies fourteen Modules -without the Line AB: And where the occult Lines from the Divisions of -Length cut the Visual FO, Parallels are made to the Ground-Line EF; and -from the Intersections of those Parallels with the Visuals, you complete -the Delineation of the Plan in Perspective. - -The Lines which in the Plan are parallel to EF, being prolong’d to the -Visual EO, are then continu’d parallel to the Perpendicular DE. And from -the Divisions of AB, produc’d to DE, visual Lines are drawn to the Point -of Sight; which intersecting the Perpendiculars aforesaid, you from -thence find the Length of the Elevation in Perspective. - - - - -[Illustration: FIG. XXXVII.] - - - - -FIGURA Trigesimaseptima. - -Deformatio columnæ Etruscæ. - - -_Ex præparatione quam exhibuimus figurâ trigesimasextâ, eruitur columna -hæc nitida Ordinis Etrusci, opticè imminuta per latitudines & altitudines -partium singularum; quæ accipiuntur ope duorum circinorum, ut sæpiùs -dictum est._ - - - - -The Thirty-seventh Figure. - -_A ~Tuscan~ Column in Perspective._ - - -From the Preparation exhibited in the Thirty-sixth Figure, is drawn this -complete Piece of the _Tuscan_ Order, brought into Perspective by means -of the Breadths and Heights of the several Parts, exactly taken off with -the Compasses, as has been often said. - - - - -[Illustration: FIG. XXXVIII.] - - - - -FIGURA Trigesimaoctava. - -Præparatio ad figuram trigesimamnonam. - - -_Hæc figura est simillima figuræ trigesimæsextæ. In vestigio ~P~ limes -prominentiæ coronicis est ~R~; coronæ verò in stylobatâ est ~T~. -soliditas stylobatæ est ~V~. ambitus columnæ in imo est ~X~, in summo -~Z~._ - - - - -The Thirty-eighth Figure. - -_Preparatory to the Thirty-ninth._ - - -This Figure is very much the same with the Thirty-sixth. In the Plan -P, the utmost Projecture of the Cornice is R; that of the Cap of the -Pedestal is T; the Trunk of the Pedestal is V; the naked Shaft of the -Column at bottom is X, at top is Z. - - - - -[Illustration: FIG. XXXIX.] - - - - -FIGURA Trigesimanona. - -Deformatio ædificii Dorici. - - -_Habes hoc loco ædificium Doricum, addito statuæ unius ornamento. Velim -autem, ut si figuram aliquam ex his desumptam, delineandam assumas, -aliquid mutes saltem in loco punctorum oculi aut distantiæ. Hoc modo -majores in hac arte progressus facies; & si alicubi cælator aberraverit, -ex lapsu illius nullum senties detrimentum._ - - - - -The Nine and thirtieth Figure. - -_A Piece of ~Dorick~ Architecture in Perspective._ - - -In this Plate you have a _Dorick_ Composition, with the additional -Ornament of a single Statue; but I would advise, when you undertake to -work after any of these Designs, you would at least place the Points -of Sight and Distance somewhat differing from those here given; which -Practice will both greatly further your Progress in this Art, and prevent -any Inconvenience, that may arise from a Mistake of the Engraver. - - - - -[Illustration: FIG. XL.] - - - - -FIGURA QUADRAGESIMA. - -Vestigium geometricum ædificii Ordinis Dorici. - - -_Vt studiosorum, qui sedulò se exercuerint in praxibus hucusque traditis, -& ad majora inhient, utilitati serviam, delineandam suscepi medietatem -arcûs cum tribus columnis, ac totidem statuarum loculamentis. Ad vitandam -autem confusionem, ea dumtaxat membra in vestigio adumbrantur, quæ -recensuimus figurâ trigesimaoctavâ, & ostendunt characteres ~A~, ~B~, -~C~, ~D~, ~E~._ - - - - -The FORTIETH FIGURE. - -_The Geometrical Plan of a Design, of the ~Dorick~ Order._ - - -For the Benefit of the Studious, who, having reduc’d to Practice the -Rules hitherto laid down, aim at yet greater Things; I have here -undertaken to delineate half an Arch adorn’d with three Columns, and as -many Niches for Statues. But to avoid Confusion, I have given full Lines -to those Members only, which were mention’d in the Thirty-eighth Figure, -and which are here denoted by the Characters A, B, C, D, E. - - - - -[Illustration: FIG. XLI.] - - - - -FIGURA Quadragesimaprima. - -Elevatio geometrica ædificii Dorici. - - -_Ex vestigio geometrico eruitur hæc elevatio geometrica longitudinis -ædificii nostri. Et iccircò figura ista quadragesimaprima, cujus -mensuræ omnes desumptæ sunt ex Barozzio, congruit longitudini figuræ -quadragesimæ._ - - - - -The Forty-first FIGURE. - -_The Geometrical Elevation of the foregoing Design._ - - -This Upright is drawn from the foregoing Geometrical Plan; and therefore -all the Parts of this Design, whose Measures are taken from _Vignola_, -exactly answer those of the Fortieth Figure. - - - - -[Illustration: FIG. XLII.] - - - - -FIGURA Quadragesimasecunda. - -Modus vitandi confusionem, in contractione vestigiorum, & elevationum. - - -_Contractiones vestigii figuræ quadragesimæ, & elevationis figuræ -quadragesimæprimæ, ob nimiam obliquitatem quam habent, valde confusæ -sunt. Medebimur tamen incommodo isti, uti fecimus figuris decimâ & -undecimâ. Et ostendit chartula, exhibens in parvo tum figuram hanc -quadragesimamsecundam, tum quatuor sequentes._ - - - - -The Forty-second FIGURE. - -_The Manner of avoiding Confusion, in reducing Plans and Elevations into -Perspective._ - - -The Reducing into Perspective the Plan of the Fortieth Figure, and -the Upright of the Forty-first Figure, would become very confus’d, -through the great Obliquity of the Rays: We have therefore remedy’d -the Inconveniences of both, by the Methods explain’d in the Tenth and -Eleventh Figures. And this Plate contains in little, what is more at -large describ’d in Parts, as well in this, as the four subsequent Figures. - - - - -[Illustration: FIG. XLIII.] - - - - -FIGURA Quadragesimatertia. - -Contractio vestigii figuræ quadragesimæ. - - -_Linea plani multò remotior est à lineâ horizontali in hoc schemate, quàm -in præcedenti. Ideo istud vestigium vacat omni confusione. Cætera patent -ex iis quae sæpiùs dicta sunt, & ex figuræ hujus inspectione. Oportet -autem, rectas parallelas ad lineam plani, prolongari usque ad visualem -~TO~, (quæ cadit extra paginam) ut adminiculo parallelarum, fiat elevatio -longitudinis nostri ædificii, de quâ dicemus figurâ quadragesimaquartâ._ - - - - -The Forty-third FIGURE. - -_The Plan of the Fortieth Figure in Perspective._ - - -By placing the Ground-line in this, much more remote from the Horizontal, -than it is in the foregoing Figure, all Confusion is here avoided. The -rest is evident from what has been often said on this Head, and a bare -Inspection of the Figure. Parallels to the Ground-line must nevertheless -be continu’d to the Visual TO, which falls without this Page; that from -them may be rais’d the Elevation of the Length of this Design, which we -shall handle in the next Figure. - - - - -[Illustration: FIG. XLIV.] - - - - -FIGURA Quadragesimaquarta. - -Contractio elevationis figuræ quadragesimæprimæ. - - -_Rectæ parallelæ ad lineam plani figuræ quadragesimætertiæ, ubi -pervenerint ad visualem ~TO~, continuandæ sunt, more solito, cum -parallelis ad lineam perpendicularem. In hanc autem transferre oportet -omnes divisiones, quas ex Barozzio habet elevatio hujus ordinis; ac -ducere visuales. Quomodo autem, adminiculo visualium & parallelarum, -compleatur elevatio, constat ex figura, & clarius ex chartula figuræ -quadragesimæsecundæ. Numeri ~1~, ~2~, ~3~, ~4~, geminati, ostendunt -centra & altitudines semicirculorum seu arcuum figuræ quadragesimæquintæ; -videlicet, numerus inferior designat centrum, superior verò designat -altitudinem semicirculi._ - - - - -The Forty-fourth FIGURE. - -_The Elevation of the Forty-first Figure in Perspective._ - - -When the Parallels to the Ground-line in the Forty-third Figure, are -prolong’d to the Visual TO, they are then, as usual, to be continu’d -Parallels to the Perpendicular: On which Perpendicular, those Divisions -given by _Vignola_, for the Proportions of this Order, are to be -transferr’d; and Visuals drawn from them to the Point of Sight. How by -these Visuals and Parallels the Elevation is rais’d in Perspective, is -manifest in part from this Figure, but more clearly from the Forty-second -Figure. The Numbers 1, 2, 3, 4, which you here see doubl’d, give the -Centers and Heights of Semicircles of the Arches in the Forty-fifth -Figure; the lower Numbers denoting the Centers, and the upper Numbers the -Heights of the Semicircles of the same. - - - - -[Illustration: FIG. XLV.] - - - - -FIGURA Quadragesimaquinta. - -Dimidium ædificii Dorici opticè deformati. - - -_Huic figuræ delineandæ plures præiverunt, ejusdemque latitudines mutuati -sumus ex figura quadragesimatertia, altitudines ex quadragesimaquarta. -Superest autem, ut lumina & umbræ scitè inducantur in singulas partes -ædificii._ - - - - -The Forty-fifth FIGURE. - -_One Half of the ~Dorick~ Design in Perspective._ - - -The foregoing Figures being preparatory to this, the Breadths are taken -from the Forty-third, and the Heights from the Forty-fourth Figure. It -only remains, that the Lights and Shades be skilfully dispos’d to each -Part of the Work. - - - - -[Illustration: FIG. XLVI.] - - - - -FIGURA Quadragesimasexta. - -Alterum dimidium ejusdem ædificii. - - -_Supersedere poteram delineatione alterius medietatis ædificii nostri. -Verùm operæ non peperci, ut ostenderem diversitatem luminum & umbrarum, -quæ conveniunt partibus cæteroqui omnino similibus._ - - - - -The Forty-sixth FIGURE. - -_The other Half of the same Design._ - - -I might very well have omitted this Half of the Design, but that I spar’d -no Pains, to shew the Diversity of the Lights and Shadows, that must be -given to those Parts of the Work, which in other Respects are alike. - - - - -[Illustration: FIG. XLVII.] - - - - -FIGURA Quadragesimaseptima. - -Vestigia ædificii Ionici. - - -_Vestigium geometricum ~A~ ædificii Ionici, sub se habet suam -deformationem ~B~. Hæc autem ut evadat distinctior, lineam plani, quæ in -sequentibus figuris habebit distantiam ~PE~ ab horizontali ~OE~, deorsum -protraximus in ~CD~, ut etiam fecimus figurâ quadragesimasecundâ & -quadragesimatertiâ. Linea visualis ~OM~ eundem habet usum, quem visualis -~OT~ figuræ quadragesimætertiæ; videlicet, ut in ea terminentur parallelæ -ad lineam plani ex membris vestigii ~B~, eademque continuentur cum aliis -parallelis ad rectam ~EC~, pro deformandâ elevatione quam apponemus -figurâ quadragesimanonâ._ - - - - -The Forty-seventh FIGURE. - -_The Plan of an ~Ionick~ Building._ - - -The Geometrical Plan of this _Ionick_ Work is A, underneath is its -Perspective B; to render which more distinct, the Ground-line that in -the following Figures has only the Distance PE from the Horizontal -EO, is here remov’d downward to CD, as was done in the Forty-second -and Forty-third Figures foregoing. The visual Line OM is of the same -use as that of OT in the Forty-third Figure; namely, to terminate the -Lines which are drawn from the Members of the Plan B parallel to the -Ground-line; from whence they are again continu’d parallel to the -Perpendicular EC, for making in Perspective the Elevation inserted in the -Forty-ninth Figure. - - - - -[Illustration: FIG. XLVIII.] - - - - -FIGURA Quadragesimaoctava. - -Elevatio geometrica ædificii Ionici. - - -_Ex hac elevatione quæ clarè ostendit membra totius ædificii secundum -longitudinem dissecti, desumuntur altitudines ac terminationes membrorum -singulorum. Peritiores tamen hac figurâ delineandâ supersedere -solent, quia terminationes haberi possunt ex vestigio ~A~ figuræ -quadragesimæseptimæ, altitudines verò ponendæ iterum sunt figurâ -sequenti._ - - - - -The Forty-eighth FIGURE. - -_The Geometrical Upright of the foregoing ~Ionick~ Design._ - - -From this Figure (which distinctly shews the Composition of the whole -Work, in respect of its Length) are taken the Heights and Terminations -of the several Members thereof. But those that are skill’d in this Art, -usually omit the delineating these Elevations; because the Terminations -may be taken from the Plan A in the Forty-seventh Figure; and the Heights -must be repeated in the following Figure. - - - - -[Illustration: FIG. XLIX.] - - - - -FIGURA Quadragesimanona. - -Deformatio elevationis ædificii Ionici. - - -_Hæc figura continens deformationem præcedentis elevationis, perficitur -methodo illa, quam ostendimus figurâ quadragesimasecundâ; nimirum, ex -vestigio ~B~ figuræ quadragesimæseptimæ, ducere oportet parallelas ad -lineam plani ~CD~, quæ ubi pervenerint ad visualem ~OM~, continuandæ -sunt cum aliis parallelis ad lineam ~EC~. Easdem parallelas in hanc -figuram translatas secant visuales ex linea recta ~AB~, in qua positæ -sunt altitudines ædificii Ionici, desumpta vel ex figura præcedenti, vel -ex Barozzio. Nullum autem est punctum in membris hujus elevationis, quod -non inveniatur per sectiones visualium ex linea ~AB~, cum parallelis ad -eandem lineam._ - - - - -The Forty-ninth FIGURE. - -_The Elevation of the ~Ionick~ Design in Perspective._ - - -This Plate containing the Perspective of the foregoing Upright, is -drawn by the Method laid down in the Forty-second Figure; to wit, from -the Plan B of the Forty-seventh Figure, Parallels to the Ground-line -CD are prolong’d to the Visual OM; and thence are continu’d Parallels -to the Perpendicular EC. These being transferr’d into this Figure, are -intersected by the visual Lines that proceed from AB, which contains the -Heights of this _Ionick_ Composition, agreeable to the foregoing Figure, -and the Rules deliver’d by _Vignola_. Now there is no Point in any Member -of this Upright, but may be found by the Intersection which the visual -Line from AB makes with its respective Perpendicular. - - - - -[Illustration: FIG. L.] - - - - -FIGURA Quinquagesima. - -Architectura Ionica. - - -_Ex vestigio figuræ quadragesimæseptimæ, & ex elevatione figuræ -quadragesimænonæ, eruitur hoc ædificium Ionicum, quod esse poterit -vel principium alicujus turris campanariæ, aut basis cujuspiam arcûs -triumphalis. Vereor ut cælator suam diligentiam in hoc schemate -satis probaverit. Ejus tamen errata facilè ipse deteges, & omni studio -cavebis._ - - - - -The Fiftieth FIGURE. - -_A Design of ~Ionick~ Architecture._ - - -From the Plan of the Forty-seventh Figure, and from the Upright of the -Forty-ninth Figure, is drawn this _Ionick_ Piece; which might well serve -for the lower Order of a Turret, or for part of a Triumphal-Arch. I fear -the Engraver has not been so exact in this Scheme, as he ought; but you -will readily discover his Mistakes, and carefully beware of them. - - - - -[Illustration: FIG. LI.] - - - - -FIGURA Quinquagesimaprima. - -Ordo Corinthius. - - -_Complectitur hæc pagina molem contractam Ordinis Corinthii, cum suis -præparationibus. Vestigium ~A~ exhibet parietem pone columnas cavum -instar canalis. Idem vestigium opticè deformatur in ~D~: omissâque -elevatione geometricâ, per ejus altitudines notatas in lineâ ~BC~ -projicitur elevatio; ac methodo consuetâ, ex vestigio & elevatione -componitur ædificium, addito statuæ unius ornamento._ - - - - -The Fifty-first FIGURE. - -_A ~Corinthian~ Design in Perspective._ - - -This Plate contains the Perspective of a _Corinthian_ Work, with its -Preparations. The Geometrical Plan A shews the Wall wrought hollow -behind the Columns. The said Plan in Perspective is D: and leaving -out the Geometrical Elevation, the Perspective thereof is describ’d, -by transferring the Heights of the former into the Line BC. From the -Perspective-Plan and Upright the Design is finish’d after the usual -Manner; to which is added the Ornament of a single Statue. - - - - -[Illustration: FIG. LII.] - - - - -Figura Quinquagesimasecunda. - -Delineatio columnæ spiralis, Ordinis Compositi. - - -_Posita elevatione geometrica columnæ rectæ, ac divisione illius in -vigintiquatuor partes æquales, columna spiralis absolvitur per partes -circumferentiæ circulorum, quorum diametri sunt æquales diversis -latitudinibus columnæ rectæ, ut ostendit figura in ~A~. Ad projectionem -opticam elevationis, notandæ sunt quatuor occultæ rectæ, quæ ex terminis -convexitatis & concavitatis infimarum spirarum ejusdem elevationis -~A~, descendunt ac desinunt in duos circulos vestigii geometrici ~B~. -Vestigium ipsum opticè imminutum habetur in ~C~: eædem autem sunt -maximæ hinc inde latitudines, tum in circulo majori, tum in convexitate -infimarum columnæ spirarum; eædem sunt maximæ latitudines, tum in circulo -minori, tum in concavitate ipsarum spirarum; ut dignosces applicando -regulam spiris simul & circulis. Ex quatuor punctis maximæ latitudinis -duorum circulorum, incipiunt quatuor lineæ parallelæ ad lineam plani, -quæ ubi pervenerint ad visualem ~ED~, continuandæ sunt cum parallelis ad -perpendiculum ~DF~. In eandem lineam ~DF~, ex elevatione ~A~ transferre -oportet vigintiquatuor partes æquales altitudinis columnæ, ac ducere -visuales ad ~O~ punctum oculi. Per sectionem autem visualium cum -prædictis quatuor parallelis ad lineam ~DF~, ducuntur lineæ undulatæ -~MN~, ~PQ~, ex quibus eruuntur lineæ utrinque terminativæ columnæ -spiralis nitidæ. Ex linea verò ~GH~ habetur facies anterior stylobatæ, -columnæ & coronicis; ex linea ~IL~ habetur facies eorum posterior._ - - - - -The Fifty-second FIGURE. - -_The Description of a wreath’d Column, of the Composite Order._ - - -Having made the Geometrical Elevation of a streight Column, and divided -the Height of its Shaft into Four and twenty equal Parts; the Wreathing -is describ’d by Parts of the Circumference of Circles, whose Diameters -are equal to the several Breadths, or Diameters, of the streight Column; -as is shewn in the Figure A. For putting the Upright into Perspective, -four streight occult Lines are of use, which descend from the Extent -of the Swellings and Sinkings of the lower Wreaths of the Column A; -and terminate in two Circles of the Geometrical Plan B. The said Plan -laid down in Perspective is C. The utmost Extent of the greater Circle -determines that of the Convex Parts of the lower Wreaths: The greatest -Breadth of the lesser Circle gives that of the hollow Parts of the said -Wreaths; as may be perceiv’d, by applying a Ruler from the Wreaths to -the Circles of the Plan. From the four Points of greatest Breadth in -those Circles, four Lines parallel to the Ground-line are continu’d to -the Visual ED, and thence again continu’d parallel to the Perpendicular -DF. From the Elevation A, the Four and twenty equal Parts of the Columns -Height are transferr’d into the Line DF, and Visuals drawn from each to -the Point of Sight O. By the Intersections of those Visuals with the -four Perpendiculars aforesaid, are drawn the wav’d Lines MN, PQ; from -which, both the Out-lines of the finish’d Column are describ’d. But the -Fore-part of the Pedestal, Column, and Cornice, is taken from the Line -GH; the Back-part of the same from the Line IL. - - - - -[Illustration: FIG. LIII. A.] - - - - -Fig. Quinquages. tertia A. - -Ordines Architecturæ, desumpti ex Palladio & Scamozzio. - - -_De Ordinibus Architecturæ, præter Barozzium, egregiè scripserunt -Palladius & Scamozzius; ac singuli, jure merito, suos habent asseclas & -patronos. Ut ergò, etiam juxta laudatissimorum Autorum placita, opticas -projectiones facere possis, omnes Ordines in hac paginâ exhibere volui, -ut in eorum Libris inveniuntur._ - - - - -The Fifty-third Figure A. - -_The Orders of Architecture, taken from ~Palladio~ and ~Scamozzi~._ - - -Besides _Vignola_, _Palladio_ and _Scamozzi_ have also written -excellently well of the Orders of Architecture; and each of ’em have -deservedly their Followers and Admirers. That you might therefore be -enabl’d to make Designs in Perspective, after the Proportions of the most -celebrated Masters, I have in this Plate given you the Measures of all -the Orders, as deliver’d by them in their Books. - - - - -[Illustration: FIG. LIII. B.] - - - - -Fig. Quinquages. tertia B. - -Modus triplex delineandi columnas spirales. - - -_Columnæ figuræ superioris carent ea concinnitate, qua præditæ sunt -columnæ spirales æneæ celeberrimi Equitis Bernini ad sepulcrum S. Petri -in Vaticano. Itaque methodum triplicem exhibeo ad minuenda spatia totius -altitudinis columnæ._ - -1. _Recta ~OA~ sit æqualis altitudini ~AB~ columnæ. Fiat autem recta -~OB~, & arcus ~AP~ ex centro ~O~, divisus in partes duodecim æquales, -ducendo rectas, quæ per puncta divisionum desinant in columnam rectam; -ac demum fiant parallelæ ad basim: Spatia inter has parallelas dabunt -aperturam circini pro triangulis æquilateris & pro spiris, ut ostendit -columna ~1~._ - -2. _Translatâ in ~C~ tertiâ parte altitudinis columnæ ab ejus imo scapo, -habeat circinus aperturam ~CD~; ac posito uno ejus crure prius in ~D~, -postea in ~C~, fiant duo parvi arcus ad ~E~: sectio illorum arcuum erit -centrum arcûs ~DC~, quem oportet dividere in duodecim partes æquales, -& ex punctis divisionum ducere parallelas ad basim. Tum spatiis inter -parallelas divisis in quatuor partes æquales, tres ex illis partibus -dabunt longitudinem crurum pro triangulis isoscelibus; vertices autem -triangulorum erunt centra singularum spirarum, ut ostendit columna ~2~._ - -3. _Ductâ ex medio summitatis ~G~ rectâ ~GF~, spatium ~HF~ transferatur -in ~I~, & fiat recta ~IL~ parallela ad basim ~HF~; spatium ~IL~ -transferatur in ~N~, ac fiat ~NM~, & sic deinceps. In parvis columnis -triangula sine sensibili errore duci possunt per diagonales: in columnis -tamen grandioribus, alterutrum ex modis antea explicatis adhibere necesse -est._ - - - - -The Fifty-third Figure B. - -_Three different Ways of delineating wreath’d Columns._ - - -The wreath’d Columns describ’d in the Fifty-second Figure, being divided -into Twenty-four equal Parts, want very much of that Elegancy of Contour, -which is visible in those brass Pillars, made by the famous Cavalier -_Bernino_, for S. _Peter_’s Sepulcher in the _Vatican_. Wherefore I here -lay before you three several Ways of diminishing the Spaces through the -whole Height of the Column. - -1. Make the right Line OA equal to AB the Height of the Column; then draw -the Line OB, and on the Center O describe at pleasure the Arch AP, which -divide into twelve equal Parts, and by the Divisions draw streight Lines -from the Center O to the Line of the Column; and lastly continue the same -Parallels to the Base. The Spaces between these Parallels, shall be the -Sides of equilateral Triangles, wherewith you are to describe the Wreath -of the Column, as is seen in Column 1. - -2. Having set the third Part of the Columns Height, from the Bottom of -the Shaft to the Point C; with the Interval CD, from the Centers D and -C, describe the Parts of Arches intersecting at E. On the Center E, -with the same Interval, describe the Arch DC, which divide into twelve -equal Parts; and from the Points of those Divisions, draw Parallels -to the Base. Then dividing each Space between the Parallels into four -equal Parts; three of those Parts shall be the Sides of the _Isosceles_ -Triangle; whose _Vertex_ is the Center whereon to describe each Wreath of -Column 2. - -3. Having drawn from the midst of the Columns top G, the Line GF, make HI -equal to HF, and draw IL parallel to the Base HF: Again, make IN equal to -IL, and draw NM also parallel, and so on. In small Pillars, the Centers -of the Diagonals of these Spaces may, without sensible Errour, serve for -describing the Wreaths; but in greater Columns, either of the other two -Methods is rather to be chosen. - - - - -[Illustration: FIG. LIV.] - - - - -FIGURA Quinquagesimaquarta. - -Vestigia ædificii Ordinis Corinthii. - - -_Descripturi ædificium Corinthium octangulare, ponimus hic vestigia unius -ex quatuor partibus pilarum, quibus imponetur fornix in modum tholi, ut -constabit in figurâ quinquagesimaoctava. Ad faciliorem descriptionem, -in parte inferiori paginæ posui vestigium geometricum stylobatæ, -in superiori vestigium geometricum coronicis, cum latitudinibus & -longitudinibus membrorum singulorum; ut eas transferendo in lineam -plani more consueto, utrumque vestigium opticè deformetur. Ad vitandam -confusionem, prius notare oportebit puncta quæ spectant ad membra -propinquiora solido parieti, deinde alia._ - - - - -The Fifty-fourth FIGURE. - -_The Plan of a Design of the ~Corinthian~ Order._ - - -Being to describe an Octangular _Corinthian_ Work, I have here inserted -the Plan of one Quarter of the Composition; which is vaulted in Form of a -_Cupola_, as is seen in the Fifty-eighth Figure. To render the Plan less -confus’d, I have, in the lower part of the Plate, given the Geometrical -Plan of the Pedestal; and in the upper part, that of the Cornice; with -the Breadths and Lengths of each Member: so that by transferring the same -into the Ground-line, after the usual Manner; you delineate each Plan -in Perspective. For avoiding Confusion, ’twill be requisite first, to -transfer the Points of those Members that are next the Solidity of the -Wall; and then proceed to the others. - - - - -[Illustration: FIG. LV.] - - - - -FIGURA Quinquagesimaquinta. - -Elevatio ædificii Ordinis Corinthii. - - -_Elevatio geometrica ædificii octangularis congruit cum duobus ejus -vestigiis figuræ antecedentis. Quia verò elevatio parietis abscondit -secundam ex quatuor columnis, eademque in ædificio deformato conspicua -futura est; iccircò eam lineis occultis designare oportuit._ - - - - -The Fifty-fifth FIGURE. - -_The Geometrical Elevation of a ~Corinthian~ Work._ - - -The Geometrical Elevation of this Octangular Design, is wholly -correspondent to the two Plans of the foregoing Figure: But because the -Wall in this Upright takes off the Sight from the second of the four -Columns, which is notwithstanding visible in the finish’d Perspective -that follows; ’tis requisite to delineate the same with occult Lines, as -in the Figure. - - - - -[Illustration: FIG. LVI.] - - - - -FIGURA Quinquagesimasexta. - -Deformatio vestigiorum & elevationis ædificii Corinthii. - - -_In hac figurâ, lineam plani coincidere volui cum linea horizontis. -Itaque videri non posset vestigium inferius, nisi ut alias deorsum -protraxi lineam plani, hic è converso sursum promovissem lineam -horizontis, quam constitui mediam inter lineas plani utriusque vestigii, -ut ambæ projectiones essent æquè distinctæ. In elevatione, columna -secunda, quam, ut dixi, paries abscondit, lineis occultis designanda est._ - - - - -The Fifty-sixth FIGURE. - -_The Perspective Plans and Upright of the ~Corinthian~ Design foregoing._ - - -In this Figure, I have made the Ground-line coincident with that of -the Horizon, in which case the lower Plan can’t be seen, unless the -Ground-line be sunk lower, as before intimated; or contrariwise, the -Point of Sight rais’d higher, as I have here done, keeping it in the -midst between the Ground-lines of the two Plans, that the Perspective -of both might be equally distinct. In the Elevation, the second Column, -which I mention’d to be hidden by the Wall, should be design’d with -occult Lines. - - - - -[Illustration: FIG. LVII.] - - - - -FIGURA Quinquagesimaseptima. - -Adumbratio figuræ sequentis. - - -_Figuram hanc seorsim delineavi, ut videas quomodo facienda sit operis -totius adumbratio, accipiendo altitudines membrorum singulorum ex -elevatione; latitudines & longitudines ex vestigiis. Quæ omnia ex -diagrammatis inspectione clarissimè apparent._ - - - - -The Fifty-seventh FIGURE. - -_The rough Draught of the following Figure._ - - -I have drawn this Figure apart, that you may see the Manner of describing -the Out-line of the whole Work, by taking the Heights of the several -Members from the Elevation, and their Breadths and Lengths from the -Plans; all which is very plain, upon Inspection of the Figure. - - - - -[Illustration: FIG. LVIII.] - - - - -FIGURA Quinquagesimaoctava. - -Ædificium Ordinis Corinthii octangulare. - - -_Hucusque descripsimus pilas anticas sinistras ædificii Corinthii. En hoc -loco medietatem dexteram totius Operis. Integrum verò ædificium habebis -figurâ sexagesimâ._ - - - - -The Fifty-eighth FIGURE. - -_Part of an Octangular Work of the ~Corinthian~ Order._ - - -Hitherto the nearest left-hand Quarter of this _Corinthian_ Design has -been describ’d. In this Plate you have the right-hand Half of the whole -Work; and in the Sixtieth Figure, the entire Perspective compleat. - - - - -[Illustration: FIG. LIX.] - - - - -FIGURA Quinquagesimanona. - -Vestigia tabernaculi octangularis. - - -_Projectiones rerum octangularium sunt quadratis difficiliores: ideò -in eis explicandis diligentiæ non peperci. Moles cujus vestigia -vides in ~A~ & ~B~, convenit in multis cum eâ quam ereximus figurâ -quinquagesimaoctavâ. Visualis ~CD~ recipit sectiones perpendicularium, -quæ deserviunt pro elevatione figuræ sequentis, ut sæpius dictum est. Si -facies interior delineanda sit seorsim à facie anteriori, illam perficies -ope linearum ~CE~, istam ope linearum ~FD~._ - - - - -The Fifty-ninth FIGURE. - -_The Plans of an Octangular Tabernacle._ - - -Octangular Figures being more difficult to be put in Perspective, -than the Square; I shall use my best Endeavours to render the Method as -plain as possible. The Composition whose Plans you see in A and B, has -much Affinity with that describ’d in the Fifty-eighth Figure. The Visual -CD receives the Sections, from which Perpendiculars are rais’d for the -Elevation and Profile of the following Figure, as has been often said. If -you would delineate the Back-part separate from the Fore-part, you may do -the former by means of the Line CE, and the latter by that of FD. - - - - -[Illustration: FIG. LX.] - - - - -FIGURA SEXAGESIMA. - -Tabernaculum octangulare. - - -_Hoc tabernaculo aliquoties usus fui pro expositione quadraginta horarum. -Si colores scitè inducti fuerint in duos ordines telariorum, resectis -omnibus quæ ad molem ipsam non pertinent, spectatoribus imponet, & solida -videbitur. Oportebit autem exemplar externæ faciei eruere ex parte ~DF~ -vestigii & elevationis; exemplar interioris faciei eruere ex parte ~EC~, -servando in omnibus regulas quas hucusque tradidimus._ - - - - -The SIXTIETH FIGURE. - -_An Octangular Tabernacle in Perspective._ - - -I have sometimes made use of this Tabernacle for the Exposition of the -_Forty Hours_. If the Colours are laid by a skilful Hand, on two Ranges -of Cloth, and the Frame cut away according to the Out-line of the Work, -they will wonderfully deceive the Eye, and appear as solid; but then the -outer Range must be drawn after the Plan and Elevation of the Part DF in -the foregoing Figure; and the inner Range after that of EC; in all things -observing the Rules hitherto deliver’d. - - - - -[Illustration: FIG. LXI.] - - - - -FIGURA Sexagesimaprima. - -Modus erigendi machinas, quæ constant pluribus ordinibus telariorum. - - -_Ex figuræ inspectione addisces modum erigendi machinas quæ constant -pluribus ordinibus telariorum. Tabernaculum hoc nostrum indiget duobus -tantum ordinibus; nam telaria propinquiora oculo exprimunt faciem -externam, remotiora exhibent faciem internam. Ne autem lateant stipites -quibus telaria sustinentur, medietatem telariorum adumbrare omisimus. -Recta ~LS~ est linea plani, recta ~DG~ est linea horizontalis; ac -punctum distantiæ quod cadit extra paginam in recta ~CG~ prolongatâ, -debet esse remotum à puncto ~C~, quantum in superiori parte figuræ -quinquagesimænonæ, punctum distantiæ est remotum à puncto oculi. Eadem -horizontalis ~DG~ secatur normaliter in ~C~ à recta ~EF~, quæ est sectio -externæ faciei tabernaculi, & ex ~C~ incipiunt divisiones in partes -æquales pro reticulatione anterioris faciei telariorum, ut dicemus figurâ -sexagesimasecunda. Recta ~IL~ quæ est sectio internæ faciei tabernaculi, -distat ad libitum à recta ~EF~ cui est parallela. Porrò, per divisiones -rectæ ~EF~ (ut vides in ~M~, ~N~, ~O~) ex puncto distantiæ ducendæ sunt -visuales ad rectam ~IL~ pro reticulatione aliorum telariorum: distantia -enim ~DC~ facit ut augere oporteat ea quæ in telariis pinguntur, alioquin -justo minora viderentur. Atque hinc dignosces, cur arcus qui in telariis -anterioribus pertingeret solum ad ~B~, in posterioribus elevetur usque ad -~H~._ - -_Figura sequenti proponemus modum delineandi faciem internam telariorum, -adhibita reticulatione externæ faciei: ad intelligentiam verò illius -methodi, fiat in hac figurâ recta ~HP~ parallela ad ~DC~, ac recta ~BC~ -dividatur in totidem partes æquales, in quot partes divisa fuerit recta -~PC~._ - - - - -The Sixty-first FIGURE. - -_The Manner of erecting Machines, that consist of several Ranges of -Frames._ - - -By casting your Eye on the Figure, you’ll readily apprehend the Manner -of erecting the several Ranges of Frames. This Tabernacle last describ’d -needs only two of them; the Frame next the Eye represents the outer Face, -and the hinder Frame the inner Face thereof. I have here describ’d but -the Half-Breadth of the said Frames, that you might have a Sight of the -Poles and Braces which support them. The Line LS is the Line of the Plan, -or Ground-line; the Line DG is that of the Horizon; and the Point of -Distance, which falls without the Page CG prolong’d, is as far from the -Point C, as the Point of Distance is from the Point of Sight in the upper -Part of the Fifty-ninth Figure. The Horizontal DG is cut perpendicularly -in C by the Line EF, which is the Section of the outer Face of the -Tabernacle; and from the Point C begin the equal Divisions for the -Net-work of the foremost Frame, as is shewn in the Sixty-second Figure. -The Line IL, which is the Section of the inner Face of the Tabernacle, -may at pleasure be set nearer or farther from the Line EF, to which it is -parallel. By the Divisions of the Line EF (as M, N, O) Lines are drawn -from the Point of Distance to the Perpendicular IL, for the Net-work of -that Frame; for the Distance DC obliges the Parts of D to be painted -larger, otherwise they will appear less than they really ought. And from -hence you may discern, why the Arch, which in the foremost Frame would -reach only to B, does in the hindmost rise up to H. - -In the following Figure is shewn the Manner of delineating the inner -Frame, from the Net-work of the outer Face; for the better understanding -of which, make the Line HP in this Figure parallel to DC, and let the -Line BC be divided into as many equal Parts, as the Line PC was. - - - - -[Illustration: FIG. LXII.] - - - - -FIGURA Sexagesimasecunda. - -De reticulandis telariis, quæ repræsentent ædificia solida. - - -_Duo exemplaria tabernaculi quæ seorsim delineanda sunt, conjunctim -habes in ~A~. Utrisque deservit eadem reticulatio, quam suis numeris -insignivimus. Postquam ergo designaveris amplitudinem totius ædificii, -cum proportione ad ipsam reticulabis pavimentum ~B~ aulæ cujuspiam quod -capiat rem totam, ascriptis eisdem numeris quos habet exemplar: ejusque -retis ope, ducentur in pavimento lineæ terminativæ totidem membrorum, -quot futura sunt telaria exprimentia faciem externam tabernaculi. Ubi -hæc parata fuerint, singula disponentur exactè suis locis in ipsomet -pavimento; ac funiculis colore nigro imbutis, repetetur in telariis eadem -reticulatio, additis ad libitum pluribus visualibus; quarum adjumento -dum seorsim pinguntur telaria, duci queant rectæ tendentes ad punctum -oculi seu perspectivæ. Alia quoque reticulatio super pavimento necessaria -est pro internâ facie tabernaculi: ac duæ reticulationes pavimenti eam -inter se proportionem habebunt, quam habent divisiones rectarum ~IL~, -~EF~, figuræ sexagesimæprimæ. Hujus retis ductu fient lineæ terminativæ -telariorum cum reliquis, ut jam indicavimus._ - -_Juxta hanc methodum nequeunt duci lineæ terminativæ interioris faciei, -nisi fiat in pavimento aliud rete deleto priori, quod esset valdè -laboriosum. Postquam ergo ex vestigio figuræ quinquagesimænonæ eruta -sint duo exemplaria, in exemplar faciei externæ transferatur recta ~PC~ -figuræ sexagesimæprimæ, in exemplar faciei internæ transferatur recta -~BC~. Si autem recta ~PC~ divisa fuerit in quindecim partes æquales, -dividetur ~BC~ in quindecim partes æquales, atque ope harum divisionum -reticulare oportebit utrumque exemplar. Porrò licet quadrata in reti -exemplaris faciei externæ sint majora quadratis exemplaris internæ -faciei, nihilominus idem rete pavimenti deserviet pro ducendis lineis -terminativis utriusque faciei. Quæ dicta sunt de duobus exemplaribus, -valent de aliis quotcunque. Exempli gratiâ; si construere placeat quinque -ordines telariorum, fient quinque exemplaria in papyro. Si in omnibus -exemplaribus usurpetur eadem reticulatio, in pavimento facere oportet -quinque diversas reticulationes. Si autem in exemplaribus fiant -quinque diversæ reticulationes, in pavimento sufficit una reticulatio._ - -_Curandum est ut singula retis quadrata in telariis sint exacta, omnesque -illorum anguli sint recti. Modus expeditissimus faciendi angulos rectos -est hujusmodi. Posito uno crure circini in puncto ~F~ lineæ rectæ ~EF~, -alioque crure posito ubilibet in ~O~, fiet circulus ~GFI~, & ex puncto -~G~ diameter ~GI~. Si recta ~HF~ transeat per puncta ~I~ & ~F~, est -normalis ad ~EF~._ - - - - -The Sixty-second FIGURE. - -_Of making the Net-work on Frames, for representing the Architecture as -solid._ - - -You have jointly in A, the two Designs of a Tabernacle, which are to -be drawn separately; the same Net-work serving for both, which is also -mark’d with Numbers. When you have therefore resolv’d on the Size of -your Work, on the Pavement of some Room capacious enough make a Net-work -answerable, and affix thereto the Numbers, as in your Copy: By the Help -of which, you may on the Pavement describe the Out-line of all those -Members that are requisite to the outer Frame of the Tabernacle. This -being done, let the Frame be laid exactly in its place on the said -Pavement, and with a black Line strike thereon the same Net-work; adding -as many visual Lines as you please, which will be of Use for drawing -Lines to the Point of Sight, when you come to paint the Frames asunder. -Another Net-work on the Pavement is also necessary for the inner Face -of the Tabernacle, which should bear such Proportion to this, as the -Divisions of the Line IL do to those of EF in the Sixty-first Figure; and -by this means the Out-lines of the inner Frame, _&c._ may be drawn, as -has been shewn already. - -Thus the Out-line of the inner Face can’t be describ’d, without rubbing -out the first Net-work, and making a second on the Pavement; which would -be very troublesom. Wherefore, from the Plan of the Fifty-ninth Figure, -take the two Designs, and transfer the Line PC of the Sixty-first Figure -on the outer Face, and the Line BC on the inner Face. Then if PC were -divided into fifteen equal Parts, BC shall be divided in the same manner, -and by these Divisions make the Net-work on each Design. And although -the Squares of the outer Face be larger than those of the inner one, the -same Net-work may nevertheless serve for giving the Out-line of both. -What has been said of these two Designs, may be understood of many. For -Instance; if five Ranges of Frames were requir’d, five Designs must be -made in Paper. If in all the Designs the same Net-work be us’d, then five -several Net-works must be made on the Pavement; but if the Designs have -five different, then one Net-work on the Pavement will suffice. - -You must be very careful that all the Squares of the Net-work be exactly -divided, and at right Angles. The ready way of making a right Angle is -thus: Placing one Foot of the Compasses in the Point F of the Line EF, -and the other at pleasure in O, describe the Circle GFI; and from the -Point G draw the Diameter GI. The Line FH drawn by the Points FI, shall -be perpendicular to FE. - - - - -[Illustration: FIG. LXIII.] - - - - -FIGURA Sexagesimatertia. - -Vestigia ædificii quadrati. - - -_Vestigium geometricum ~A~ hujus ædificii habet in ~B~ suam -deformationem. Discrimen inter pilas ~C~ & ~D~ oritur ex eo, quòd in ~C~ -posita sint vestigia stylobatarum, in ~D~ autem posita sint vestigia -coronicum._ - - - - -The Sixty-third FIGURE. - -_The Plan of a square Design._ - - -The Geometrical Plan of this Design A, is brought into Perspective in B. -The Difference between the Parts C and D arises from hence, that the Plan -of the Pedestals is plac’d in C, and that of the Cornice in D. - - - - -[Illustration: FIG. LXIV.] - - - - -FIGURA Sexagesimaquarta. - -Ædificium quadratum. - - -_Ex deformatione vestigii & elevationis, methodo consuetâ eruitur imago -totius ædificii, quæ potest esse exemplar aræ maximæ alicujus Ecclesiæ. -Hanc machinam, non sine communi approbatione, aliquoties adhibui, in -apparatu quadraginta horarum; locum in medio vacuum occupantibus Angelis -cum nubibus, additâ figurarum aliquot copiâ in parte inferiori. Modus -faciendi in telariis remotioribus ab oculo partem tholi rotundi quam hic -vides, deducitur ex iis quæ tradidimus in projectione circulorum._ - - - - -The Sixty-fourth FIGURE. - -_A square Design in Perspective._ - - -From the Plan and Upright in Perspective, this finish’d Piece of the -whole Work is delineated after the usual Manner, and may serve for -the Design of a great Altar in a Church. I have sometimes, for the -Solemnity of the _Forty Hours_, expos’d this painted on a Machine, with -an universal Satisfaction; Angels with Clouds possessing the higher part -of the Hemisphere within, and Groups of Figures the lower part. The -Manner of designing on the inner Frame, that part of the said _Cupola_ -which you here see, is deduc’d from what has been before said of putting -Circles into Perspective. - - - - -[Illustration: FIG. LXV.] - - - - -FIGURA Sexagesimaquinta. - -Vestigium ædificii rotundi opticè imminutum. - - -_Qui sedulam operam in circulis deformandis non posuerint, eosque minimo -negotio ex usu describere nequiverint, frustra conabuntur projicere -vestigia ædificiorum rotundorum. Ad vitandam confusionem, proderit in -vestigio notare primùm lineas occultas membrorum præcipuorum; iisque -translatis in elevationem, addere sensim reliquas. Hac industriâ ego -ipse in hoc schemate usus sum. Quum autem experimento didicerim summam -arduitatem harum descriptionum, aliam regulam adhibere jamdiu cœpi, quam, -ut suprà diximus, in aliud Opus reservamus._ - - - - -The Sixty-fifth FIGURE. - -_The Plan of a Circular Work in Perspective._ - - -They that have not diligently apply’d themselves to the putting Circles -into Perspective, and, by a constant Practice, render’d the Work familiar -to them, will in vain attempt that of the Plans of round Buildings. To -prevent Confusion, you’ll do well, first to mark the occult Lines of the -principal Members; and after those are transferr’d into the Upright, then -proceed to the rest, as I myself did in this Figure. But having found -by Experience, the great Difficulty of describing these round things, I -have long since made use of another Method, which, as I said before, is -reserv’d for another Volume. - - - - -[Illustration: FIG. LXVI.] - - - - -FIGURA Sexagesimasexta. - -Projectio ædificii rotundi. - - -_Mirifice oculis imponunt imagines rerum rotundarum, si omnibus resectis -quæ ad eas non pertinent, exactè delineatæ ac depictæ fuerint. Hanc -figuram ex vestigio eruere oportebit methodo consuetâ, eamque in -Templo S. Ignatii Collegii Romani construxi pro feriâ V & VI Hebdomadæ -sanctioris. Intra arcum, super altari, locus erat urnæ sepulcrali, cum -Venerabili Sacramento. Sub altari visebatur simulacrum Christi Domini è -Cruce depositi: in medio columnarum, imago Beatæ Virginis dolentis; super -balaustiis Angeli lugentes, cum instrumentis cruciatuum Salvatoris._ - - - - -The Sixty-sixth FIGURE. - -_A Circular Design in Perspective._ - - -The Appearance of round things, if well design’d, masterly painted, and -the Frame cut away to the Out-line of the Work, do wonderfully deceive -the Eye. This Figure is drawn from the Plan, as usual; and was put in -execution by me, in the Church of S. _Ignatius_ of the _Roman_ College, -for the _Thursday_ and _Friday_ of the Holy Week. Within the Arch, on the -Altar, was plac’d a sepulchral Urn containing the Holy Sacrament. Beneath -the Altar was laid a Figure of our Saviour Christ taken down from the -Cross. In the midst of the Tambour, was a Picture of the Blessed Virgin -in extreme Sorrow; and on the Ballustrade, Angels mourning, bearing the -Instruments of the Passion. - - - - -[Illustration: FIG. LXVII.] - - - - -FIGURA Sexagesimaseptima. - -Vestigium geometricum, ac prima præparatio ad figuram septuagesimamprimam. - - -_Egregiam adeò speciem præsetulit, atque oculis adeò imposuit machina -quam construxi anno 1685, pro supplicatione quadraginta horarum, in -Templo Urbis Farnesiano, ut decreverim satisfacere Studiosis, publici -juris faciendo non modò imaginem totius ædificii, sed etiam illius -vestigia & elevationes: quæ omnia eâ diligentiâ delineavimus, veluti -Opus ipsum non pennicillo colorandum, sed lapidibus extruendum fuisset. -Spatia nigrantia soliditatem designant parietum & columnarum. Cæteræ -lineæ sunt crepidines stylobatarum & coronicum. Initium delineationis -fiet ab iis membris, ex quibus oriuntur lineæ occultæ positæ in ~A~, (quæ -autem dicuntur de hac medietate, intelligi debent de aliâ) ne multitudo -linearum confusionem pariat. In ~B~ lineæ curvæ occultæ sunt vestigium -tholi qui complet summitatem ædificii. Vestigium ~C~ exhibet ambulacrum -interius. Omisimus autem vestigium theatri, quia paginæ angustia illud -non capit._ - - - - -The Sixty-seventh FIGURE. - -_The Geometrical Plan, and first Preparation to the Seventy-first Figure._ - - -The Machine which I erected in the Year 1685, in the Church _Farneze_, -or _Jesuits_ Church at _Rome_, for the Devotions of the _Forty Hours_; -had so admirable an Effect, and so pleasantly deceiv’d the Eye, that -I resolv’d to gratify the Studious, not only with a general View, but -with the Plan and Elevation thereof; all which was perform’d with such -Exactness, that the Work itself seem’d rather to consist of solid Stones, -than to be wrought by the Painter’s Hand. The hatch’d Part denotes -the Solidity of the Walls and Columns. The other shews the Breaks and -Projectures of the Pedestals and Cornices. Lest many Lines should cause -Confusion, begin with those Members, which produce the occult Lines on -the Side A; understanding the same also of the other half. In B the -occult curv’d Lines are the Plan of the _Cupola_ which crowns this -Structure. The Plan C is that of the inner Vestibule, but that of the -Theater is here omitted, through Want of Room in the Page. - - - - -[Illustration: FIG. LXVIII.] - - - - -FIGURA Sexagesimaoctava. - -Elevatio geometrica vestigii præcedentis, & secunda præparatio ad figuram -septuagesimamprimam. - - -_In hoc schemate habes elevationem ædificii sectam in longum, quam figurâ -septuagesimâ opticè projiciemus: eisdemque membris constare videbis -elevationem deformatam, quibus constat elevatio geometrica. Hinc disces -ad excogitandas hujusmodi machinas, eandem Architecturæ scientiam in -Pictore necessariam esse, quæ ad construenda solida ædificia exigitur -in Architecto._ - - - - -The Sixty-eighth FIGURE. - -_The Geometrical Elevation of the foregoing Plan, and second Preparation -to the Seventy-first Figure._ - - -In this Figure you have the Elevation of the aforesaid Structure -dissected lengthwise; the Perspective thereof is describ’d in the -Seventieth Figure; and you may observe that both of them consist of the -same Members: whence you may perceive, that for designing things of this -kind, the Painter ought to have no less Skill in Architecture, than is -requir’d for the Execution of solid Works. - - - - -[Illustration: FIG. LXIX.] - - - - -FIGURA Sexagesimanona. - -Deformatio vestigii figuræ sexagesimæseptimæ, & præparatio tertia ad -figuram septuagesimamprimam. - - -_Artificium projectionis vestigii hujus, explicatum à nobis est figurâ -quadragesimasecundâ. Nimirum, ut parallelæ sint invicem distantiores, -lineam plani deorsum protraximus, ut ex intuitu figuræ statim cognosces._ - - - - -The Sixty-ninth FIGURE. - -_The Plan of the Sixty-seventh Figure in Perspective, and third -Preparation to the Seventy-first Figure._ - - -The Artifice us’d in projecting the Perspective of this Plan, has been -already shewn in the Forty-second Figure; namely, that for giving the -greater Distance between the Parallels, the Ground-line is drawn much -lower than its true Place; as is manifest on Inspection of the Figure. - - - - -[Illustration: FIG. LXX.] - - - - -FIGURA SEPTUAGESIMA. - -Deformatio elevationis figuræ sexagesimæoctavæ, & præparatio quarta ad -figuram septuagesimamprimam. - - -_Quæ dicta sunt de projectione vestigii nostri ædificii, habent locum -in elevatione. Nimirum, ut parallelæ invicem notabiliter distarent, usi -sumus industriâ quam declaravimus figurâ quadragesimasecundâ._ - - - - -The Seventieth FIGURE. - -_The Perspective of the Elevation of the Sixty-eighth Figure, and the -fourth Preparation to the Seventy-first Figure._ - - -What has been said of the Perspective-Plan of this Structure, is also -here practis’d in the Elevation; namely, that the Parallels might be -sufficiently distinct, the Perpendiculars are drawn more remote from the -Point of Sight, as was shewn in the Forty-second Figure. - - - - -[Illustration: FIG. LXXI.] - - - - -FIGURA Septuagesimaprima. - -Theatrum repræsentans Nuptias Canæ Galilææ, constructum Romæ, anno 1685. -in expositione Ven. Sacramenti in Templo Farnesiano Societatis JESU. - - -_Ex antecedentibus præparationibus eruimus projectionem nobilis hujus -Architecturæ, quæ oculos implebat tum ad lucem solis diurnam, tum -præcipuè ad lumen candelarum; ex quibus multæ palam erant expositæ, -aliæ omnino latebant, ut illuminarent sex diversos ordines telariorum -quibus tota machina constabat, non computando in hoc numero telaria, -quæ in medio arcûs maximi exprimebant nubes refertas Angelis adorantibus -Venerabile Sacramentum. Nubes istas omisimus, ne absconderentur -partes interiorum ædificiorum. In disponendis autem ordinibus -telariorum, servatus est modus quem declaravi figurâ sexagesimaprima -& sexagesimasecunda; ac præterea in eligenda eorum distantia curatum -fuit, ut candelæ in parte postica telariorum collocatæ, illuminarent -faciem telariorum interiorum. Porrò quot membra præcipua in duabus -faciebus majoribus, totidem distincta telaria numerabantur, quorum -proinde connexiones discerni vix poterant; eorumque aliquot paria ferreis -hamulis copulata erant, ut explicari ac replicari possent, ad faciliorem -tractationem diuturnioremque conservationem._ - -_Qui hucusque sequuti me fuerint, nihil dubito quin suum iter felicissimè -sint prosequuturi; atque Opera his nostris majora melioraque inventuri._ - - - - -The Seventy-first FIGURE. - -_A Theater representing the Marriage of ~Cana~ in ~Galilee~, erected in -the ~Jesuits~ Church at ~Rome~, in the Year ~1685~; for the Solemnity of -exposing the Holy Sacrament._ - - -From the foregoing Preparations, is drawn the Perspective of this noble -Piece of Architecture; which struck the Eye when seen by Day-light, but -was more especially surprizing by Candle-light; many of the Candles being -expos’d to Sight, and others altogether hidden, to illuminate the six -different Ranges of Scenes, of which the whole Work consisted, without -reckoning that in the midst of the great Arch, representing Clouds fill’d -with Angels adoring the blessed Sacrament. Those Clouds are here omitted, -that the inner Parts of the Work might be the better seen. In disposing -the several Ranges of Scenes, the same Method was observ’d, which was -deliver’d in the Sixty-first and Sixty-second Figures; and great Care was -also taken in their Distances, that the Candles plac’d on the Back of one -of them might illuminate the Face of the other behind it. Moreover, each -Scene consisted of as many parts, as there were principal Members in the -two greater Façades; so that the Joints were scarcely discernible: and -some Pairs of them being coupl’d with Hinges, folded and unfolded, for -the more easy managing and preserving them. - -I doubt not but those who have follow’d me thus far, will be encourag’d -so to prosecute their Studies, as to be able to design even greater and -more noble Works, than these of mine. - - - - -[Illustration: FIG. LXXII.] - - - - -FIGURA Septuagesimasecunda. - -De theatris scenicis. - - -_Theatris quæ jam delineavimus affinia sunt theatra scenica: in his tamen -non adeò facilè reperitur punctum oculi seu perspectivæ. Præterea, quia -ex obliquitate canalium intra quos moventur scenæ, oritur ut lineæ rectæ -quæ videri debent parallelæ ad lineam plani, non debeant esse parallelæ -sed obliquæ, harum delineatio difficultate non caret. Incommodum istud -vitari posset adhibendo canales parallelos ad poscenium, ut alicubi -fieri solet, præsertim in Germaniâ. Nihilominus usus Italicus affert -hoc adjumentum, ut illi quibus incumbit suggerere actoribus, vel scenas -movere, aliisque similibus præesse, facilius lateant & liberius fungantur -munere suo._ - -_Ut brevem summam habeas eorum quæ deinde latius declaraturi sumus, -hanc figuram contemplare. ~1~, ~2~, ~3~, ~4~, est vestigium aulæ quæ -habet in longitudine centumviginti palmos Romanos, in latitudine -sexaginta palmos; ut ostendit scala ~S~ triginta palmorum. Medietatem -loci occupat theatrum, medietatem obtinent podia & loca spectatorum. -~O~ punctum in quo uniuntur lineæ visuales, ~D~ locus pro apparentiis -rerum magis ac magis distantium. ~BC~ locus poscenii. ~HH~ sunt canales -obliqui, quorum latitudo est dupla latitudinis scenarum. ~FG~ frons -& facies theatri. ~AO~ ejus profunditas aut longitudo. ~E~ locus pro -psaltibus, tibicinibus, & fistulatoribus. ~K~ spatium pro spectatoribus. -~I~ vestigium podiorum. ~L~ scalæ podiorum. ~N~ ipsorum elevatio. ~M~ -declivitas tabulati, cum sectione & elevatione theatri, & scenis ex -latere inspectis, quæ cum suis canalibus congruunt, ut demonstrant lineæ -occultæ. ~OO~ linea normalis ad lineam horizontalem. ~P~ & ~Q~ elevatio -scenarum coram inspectarum, quæ introrsum flectuntur; & in latitudine -congruunt cum canalibus vestigii ~B~, in altitudine cum sectionibus -elevationis ~M~; ut constat ex lineis occultis. In eâdem elevatione ~M~ -pars altitudinis tribuenda est scenis, pars laquearibus ~R~, per quæ -jungitur unumquodque par telariorum. ~VV~ lineæ ad explorandum an detur -vacuum inter scenas & laquearia, vel inter scenas, vel inter laquearia. -In quibusdam autem scenis, loco laquearium pinguntur nubes & aer._ - - - - -The Seventy-second FIGURE. - -_Of Scenes for the Stage._ - - -Scenes for the Stage have very much Affinity with those lately describ’d, -but the Point of Sight is not so easily found in these; and from the -Obliquity of the Grooves in which the Scenes run, it comes to pass, that -the right Lines which ought to appear parallel to the Line of the Plan, -must not be drawn parallel thereto, but oblique; which is a Work of some -Difficulty. This indeed may be avoided, by fixing the Grooves parallel -to the Poscene; as is usual in some Places, especially in _Germany_. -Nevertheless, the _Italian_ Manner has this Advantage; That those who -are employ’d to prompt the Actors, and shift the Scenes, _&c._ are less -expos’d to Sight, in the Performance of their Business. - -In this Figure I have given you an Abridgment of those things, which -shall hereafter be more enlarg’d on. The Numbers 1, 2, 3, 4, denote the -Area of a Hall an hundred and twenty _Roman_ Palms in Length, and sixty -in Breadth; as is manifest from the Scale of thirty Palms mark’d S. Half -this Space is taken up by the Stage, the other half by the Spectators. O -is the Point in which the visual Lines concenter. D is the Place of those -things that are to appear most remote. BC is the Place of the Poscene. -HH are the oblique Grooves, whose Lengths are double the Breadth of -the Scenes. FG is the Front of the Stage. AO is its Depth or Length. -E is the Place for the Musick. K is the Room for Spectators. I is the -Plan of the Galleries. L the Stairs to the same. N is the Elevation of -the Galleries. M shews the Declivity of the Floor, with the Section -and Elevation of the Stage and Scenes view’d on the Side; answering -their respective Grooves, as the occult Lines demonstrate. OO is a Line -perpendicular to that of the Horizon. P and Q are the Elevation of the -Scenes view’d in Front, turning inwards, in Breadth agreeing with the -Length of the Grooves of the Plan B; and in Height answering that of the -Sections of the Elevation M; as is evident from the occult Lines. In this -Profile M, part of the Height belongs to the Scenes, and part to their -Soffites, or Ceilings, R; where each Pair of these Frames are join’d. VV -are the Lines by which is espy’d what Vacancy there is either between -the Scenes and their Ceilings, between the Scenes themselves, or between -their respective Ceilings; though in some Scenes the Place of these last -is supply’d by painting therein the Air with Clouds, _&c._ - - - - -[Illustration: Fig. lxxiii.] - - - - -FIGURA Septuagesimatertia. - -Aliud vestigium theatri, ubi de modo inveniendi ejus punctum. - - -_Si pingendæ sint scenæ theatri alicujus antea constructi, delineare -oportebit vestigium geometricum ex ipso erutum, (ad formam vestigii quod -cernis in hac paginâ) ut inveniatur longitudo theatri, seu distantia quam -ejus punctum habet à puncto ~A~: id autem nullo negotio fiet, accipiendo -distantias ~BC~ inter primos canales, & ~DE~ inter ultimos, ac ducendo -visuales ~MO, NO~: nam theatrum habebit longitudinem ~AO~, ac punctum -perspectivæ in vestigio theatri erit ~O~. Præterea scire oportebit -longitudinem & latitudinem canalium, eorumque numerum, distantias, & -flexus; ac præcipuè curandum est, ut licet sint obliqui ad lineam ~MN~, -sint invicem paralleli in unoquoque latere, ac singuli tangant lineas -~MO, NO~. Jam si rectæ ~AO~ fiat æqualis recta ~FA~, in ~F~ erit punctum -distantiæ: adeoque si theatrum juxta methodum à nobis tradendam depictum -fuerit, spectatori qui consistat in ~F~ apparebit veluti tabula picta -juxta leges perspectivæ, posita in ~A~._ - - - - -The Seventy-third FIGURE. - -_Another Plan of a Theater, with the Method of finding the Point of Sight -therein._ - - -If it be requir’d to paint the Scenes of some Theater already built, the -Geometrical Plan thereof must first be carefully drawn, (as you see, for -Example, in this Plate) that the Length of the Theater may be found; or -the Distance of its Point from that of A; which is easily done, by taking -the Interval BC of the first Grooves, and DE of the latter; and drawing -the Visuals MO, NO: for AO is the Length of the Theater, and the Point -of Sight, or Perspective, therein, is O. Moreover the Length and Breadth -of the Grooves must be known, as also their Numbers, Distance, and -Obliquity; and especial Care must be taken, that though they be oblique -to the Line MN, that on each Side they be Parallels between themselves, -and that they all touch the Lines MO, NO. If you then make AO equal to -FA, the Point of Distance will be F; and if the Theater be painted -according to the Rules hereafter given, it will appear to him that views -it from F, as a regular Piece of Perspective plac’d in A. - - - - -[Illustration: FIG. LXXIV.] - - - - -Figura Septuages. quarta. - -Sectio Scenarum Theatri. - - -_Præter vestigium Theatri delineanda est sectio scenarum. Itaque si -acceptis mensuris altitudinis, quam punctum ~A~ unde incipit tabulatum, -ac punctum ~D~ poscenii, habent supra planum horizontale ~FV~, fiant ex -perpendiculo ~NV~ tum recta ~ADO~ ex qua innotescit declivitas tabulati, -tum recta ~NO~, quæ sit parallela ad ~FV~ & æqualis rectæ ~AO~ figuræ -septuagesimætertiæ; punctum theatri in elevatione est ~O~; in poscenio -verò punctum theatri est ~Q~. Si maxima scenarum altitudo sit ~EB~, recta -~OE~ dat altitudinem omnium reliquarum. Vera tamen altitudo cujuslibet -scenæ est illa quam habet linea major, ex minori autem dignoscitur -quantum obliquitas cujusque scenæ apparenter minuat altitudinem extremæ -illius lineæ. Porro excessus quo linea major superat minorem tum in summo -tum in imo, diligenter notandus est, hinc enim pendet intelligentia -figuræ septuagesimæquintæ. Punctum ~M~ quod est remotum ab ~N~ quantum in -figura septuagesimatertia punctum ~F~ est remotum ab ~A~, designat locum -unde Theatrum spectari oporteat, ut ibidem notavimus._ - -_In construendo tabulato solet servari hæc regula, ut altitudo puncti ~O~ -sit æqualis altitudini oculi, & elevatio ex ~A~ usque ad ~D~ sit nona -circiter vel decima pars ipsius longitudinis ~AD~. Expediret autem ad -scenas facilius movendas, pavimentum ~F~ esse profundius pavimento ~G~, -ut erecto corpore sub tabulato ambulari possit._ - - - - -Seventy-fourth Figure. - -_The Section or Profile of Scenes for Theaters._ - - -Besides the Plan of the Theater, the Section of the Scenes is also to -be delineated, for finding the Point of the Theater in the Elevation. -Wherefore, setting the Measures of the Heights which the Point A, where -the Floor of the Stage begins, and the Point D of the Poscene, have above -the Level of the Horizontal FV; from the Perpendicular NV draw the right -Line ADO, which gives the Declivity of the Stage; then make NO parallel -to FV, and equal to AO of the Seventy-third Figure: The Point of the -Theater in Elevation is O; the Point of the same on the Poscene is Q. If -EB be the greatest Height of the first Scene, the Line OE determines the -Height of all the others. The longest of the two Lines gives the true -Height of each Scene; and the shorter discovers how much of that Height -the Sight loses on the Out-line, by the oblique Position of the Scenes. -Moreover, the Excess of the longer Line above the shorter, as well at -top as at bottom, is to be well observ’d; for on this depends the right -Understanding of the Seventy-fifth Figure. The Point M, which is as far -distant from N, as that of F is from A in the Seventy-third Figure, -denotes the Place from whence the Stage ought to be view’d; as is there -mention’d. - -In laying the Floor of the Stage, this Rule is commonly observ’d, That -the Height of the Point O be made equal to the Height of the Eye, and -that the Rise of the Floor from A to D, be about a Ninth or Tenth Part of -the Length AD. ’Tis also requisite, for the better shifting the Scenes, -that the Pavement F be sunk lower than that of G, that a Man may walk -upright under the Floor thereof. - - - - -[Illustration: FIG. LXXV.] - - - - -FIGURA Septuagesimaquinta. - -Elevatio scenarum coram inspectarum: ubi docetur artificium ut scenæ -obliquæ appareant rectæ. - - -_Scenæ quas vides in ~S~, habent suam latitudinem à vestigio figuræ -septuagesimætertiæ, altitudinem ab elevatione figuræ septuagesimæquartæ, -ac censentur erectæ & canalibus insertæ, quæ omnia repræsentantur etiam -figurâ septuagesimasecunda in ~P~ & ~Q~. Velim observes quantum elevetur -tabulatum in principio ~A~, in poscenio ~D~, & in puncto theatri ~O~. -Similiter notare oportet elevationem singularum scenarum, quæ propter -obliquitatem canalium flectuntur introrsum: iccirco lineæ ~BL~, ~KI~, -partis ~C~, non videntur parallelæ ad lineam plani, ut reipsa sunt; ac -visualis ~LF~ non tendit ad punctum oculi ~O~, sed ad punctum ~F~. Si -autem excessus apparens, quem recta ~BK~ habet in summo & imo supra -rectam ~LI~ transferatur in partem ~E~ scenarum, (iidem excessus desumi -etiam possunt ex figura septuagesimaquarta) ac ducantur rectæ ~LG~, ~IH~, -habebuntur lineæ apparenter parallelæ ad lineam plani. Si fiat recta -~LO~, quæ cum ~LG~ faciat angulum ~GLO~ æqualem angulo ~BLF~, eadem ~LO~ -tendet exactissimè ad punctum ~O~ oculi, eâque utendum erit ut visuali._ - -_In ~P~ supponimus scenas ~M~ & ~N~ jacere super pavimento unas super -aliis, ac duas lineas ~RT~ habere distantiam eandem cum duabus ~LI~, & -ita in reliquis scenis. Ubi notandum est, lineas ~RS~, ~TV~, easdem esse -cum lineis ~LG~, ~IH~, scenarum ~E~: nihilominus lineas ~RS~, ~TV~, non -esse parallelas, quum tamen ~LG~, ~IH~, videantur parallelæ. Proinde, si -fiat recta ~RL~, & anguli ~SRL~, ~GLO~, sint æquales, rectâ ~RL~ utendum -erit tanquam visuali, in ~L~ erit punctum accidentale oculi pro pingendis -scenis ~N~, ac lineæ ~RS~, ~TV~, habebuntur ut parallelæ: id autem quod -superest in telario ultra tales lineas, pro nihilo computabitur, ibique -pingetur aer aut aliquid aliud. Punctum accidentale oculi pro pingendis -scenis ~M~ erit in ~I~._ - - - - -The Seventy-fifth FIGURE. - -_The Elevation of Scenes in Front, and how the oblique Scenes are made -to appear direct._ - - -The Scenes in S have their Breadth from the Plan of the Seventy-third -Figure, and their Height from the Elevation of the Seventy-fourth -Figure; and are suppos’d to stand perpendicularly in their Grooves; all -which is also represented in P and Q of the Seventy-second Figure. I -would have you observe, how much the Floor rises, from its Edge A, to -the Poscene D, and to the Point of the Theater O. You should also note -the Elevation of each Scene, which, by reason of the Obliquity of the -Grooves, turn inward: Wherefore the Lines BL, KI, of the Part C, do not -seem Parallels to the Ground-line, as they really are; and the Visual LF -tends not to the Point of Sight O, but to the Point F. But if the seeming -Excess, which the Line BK has at top and at bottom, above the Line LI, be -transferr’d on the Side of the Scenes E, (which Excess may also be taken -from the Seventy-fourth Figure) and you draw the Lines LG, IH; these -Lines will appear Parallels to the Line of the Plan. Then drawing the -Line LO, so as to make the Angle GLO equal to the Angle BLF, the said LO -shall tend directly to the Point of Sight O; and serve for a visual Line. - -In P, I suppose the Scenes M and N to lie one upon another on the Floor, -and the two Lines RT to have the same Distance as the Lines LI; and so -of the others. Where you are to take Notice, that the Lines RS, TV, are -the same with the Lines LG, IH, of the Scenes E: and that the Lines RS, -TV, are not Parallels; altho’ LG, IH, seem to be so. Therefore, if you -draw the Line RL, so that the Angles SRL, and GLO, be equal; the Line RL -shall serve as a Visual, and L shall be the accidental Point of Sight, -for painting the Scenes of the Side N; and the Lines RS, TV, shall be -us’d as Parallels. What remains on the Frame, beyond those Lines, is to -be reckon’d as nothing; but you may paint there Air, or what you please. -The accidental Point of Sight for painting the Scenes of the Side M, is I. - - - - -[Illustration: FIG. LXXVI.] - - - - -FIGURA Septuagesimasexta. - -Modus delineandi exemplar scenarum. - - -_Iterum delineavimus scenas erectas super tabulato; in ~B~ nudas, in -~A~ depictas, additis projecturis coronicum & aliorum ornamentorum. -Deformatio scenarum ~A~ eruitur methodo consuetâ ex vestigio ~C~, in quo -videbis lineam plani deorsum protractam. Vestigium autem geometricum est -in ~D~._ - - - - -The Seventy-sixth FIGURE. - -_The Manner of delineating the Designs of Scenes._ - - -In this Plate you have another Design of Scenes erected on the Floor; the -naked Scenes are B; the painted ones A; with the additional Projectures -of Cornices and other Ornaments. The Draught of the Scenes A is produc’d -from the Plan C, after the usual Manner; in which you may observe the -Ground-line to be lower than its true place, for the greater Distinction -of the Parallels. The Geometrical Plan is D. - - - - -[Illustration: FIG. LXXVII.] - - - - -FIGURA Septuagesimaseptima. - -Modus reticulandi & pingendi scenas theatri. - - -_Postquam in pavimento exactissimè disposueris tum poscenium, tum -ex ordine scenas reliquas, unam alteri incumbentem, ut figurâ -septuagesimaquintâ declaravimus, fiet linea horizontalis, in qua notanda -sunt tria puncta perspectivæ, unum in ~O~ usui futurum in pingendo -poscenio, ac duo reliqua hinc inde, singula videlicet pro scenis partis -oppositæ. Jam supponendo quòd in parvo exemplari ~A~ primæ scenæ facta -fuerit reticulatio per quadrata perfecta; proportionalis divisio -fiet tum in recta ~HI~ primæ scenæ ~B~, tum in recta ~CD~. Postea ex -puncto ~E~, per singula puncta divisionum rectæ ~HI~, fient visuales, -adhibendo funiculum colore nigro imbutum; earumque ope, ut figura -ostendit, reticulare oportebit scenam ~B~, tum remotâ ea scenam illi -subjectam, & eodem modo aliam & aliam; ac demum per divisiones quas -in recta ~LM~ faciunt visuales ex puncto ~E~, absolvetur reticulatio -poscenii, cujus quadrata esse debent perfecta, secus quadrata scenarum. -In parte inferiori paginæ, duæ scenæ ~G~ & ~F~ ostendunt ornamenta quæ in -scenis depingi possunt. Velim autem observes, tum lineas transversas -coronicum, quæ non sunt invicem parallelæ, tum visuales, quæ tendunt -ad puncta opposita. Nam ejusmodi lineæ continent duas peculiares -difficultates projectionum theatralium; easque ut superes, exactè -servandæ sunt regulæ quas declaravimus._ - - - - -The Seventy-seventh FIGURE. - -_The Manner of making the Net-work or Squares, and painting the Scenes of -Theaters._ - - -After you have with great Exactness dispos’d the Poscene on the Pavement, -and the others in order one upon another, as was mention’d in the -Seventy-fifth Figure; draw the horizontal Line, and mark therein three -Points of Sight: That in O, for the Use of the Poscene; and the Points -on the Sides, for the Service of the opposite Scenes respectively. Then, -supposing that the Net-work of the small Draught of the first Scene A, -consists of perfect Squares; transport the same Divisions both on the -Lines HI and CD of the first Scene B; and with a black Line strike the -Visuals from the Point E, by the Points of the Divisions of HI; and -by the Help of those Visuals make the Net-work of the Scene B, as is -done in the Figure. When that’s done, lay it aside; and do the next in -the same manner; and so of the others. Lastly, by the Divisions, which -the Visuals from the Point E make on the Perpendicular LM, finish the -Net-work on the Poscene, which consists of perfect Squares, though that -of the Scenes does not. The two Scenes of the lower part of the Plate, G -and F, shew what Diversity of Ornament the Painter may introduce. I would -have you also take particular Notice, both of the transverse Lines of the -Cornice, which are not Parallels to each other; and of the Visuals which -are directed to their opposite Points: because in these two Particulars -lies the greatest Difficulty of describing Theatrical Designs; for the -surmounting which, it’s absolutely necessary, that you carefully regard -the Rules hitherto deliver’d. - - - - -[Illustration: FIG. LXXVIII.] - - - - -FIGURA Septuagesimaoctava. - -De projectionibus horizontalibus. - - -_Quemadmodum facilior est deformatio columnarum jacentium, quàm -columnarum erectarum; (nam lineæ quæ in istis sunt perpendiculares, -in illis sunt visuales, ac nullus circulus amittit suam formam) ita -projectiones horizontales, quas in laquearibus delineare necesse est, -contra quàm Pictores imaginantur, expeditiores & faciliores sunt -verticalibus, quas hucusque tractavimus. Nam ut stylobatæ & columnæ -appareant erectæ, pingendæ sunt veluti jacentes._ - -_Deformationes horizontales auspicamur à mutulis, quia columnæ ac -stylobatæ identidem iis imponuntur, ut magis in prospectu sint. Ob -diversitatem verò quam habet latus mutuli à sua facie, utriusque -delineationem geometricam seorsim in hac figura exhibemus._ - - - - -The Seventy-eighth FIGURE. - -_Of horizontal Perspective._ - - -As it is easier to describe in Perspective Columns lying on the ground, -than those that are erect, (the Lines in these last being Perpendiculars, -which in the former are Visuals, wherein no Circle loses its Form) so -the horizontal Projections of Perspective, proper for Ceilings, contrary -to the Judgment Painters usually make, are perform’d with more Ease -and Expedition, than the vertical, which we have hitherto treated of; -forasmuch as the Pedestals and Columns that must appear erect, are -painted as if lying on the ground. - -I have usher’d in these horizontal Designs with those of Corbels, -because, for setting the Pedestals and Columns more in View, they -generally seem to be supported by them. And the Side of this Corbel being -different from its Face, I have here inserted a Geometrical Description -of each distinct. - - - - -[Illustration: FIG. LXXIX.] - - - - -FIGURA Septuagesimanona. - -Projectiones vestigii & elevationis mutuli. - - -_Facies mutuli quam delineavimus figurâ septuagesimaoctavâ, gerit -hic munus vestigii; latus verò gerit munus elevationis; ut ostendunt -lineæ occultæ, quæ ex divisionibus faciei tendunt ad punctum oculi, -ex divisionibus lateris tendunt ad punctum distantiæ (puncta oculi -ac distantiæ in hac & sequentibus figuris cadunt extra paginam.) Per -sectiones harum linearum ducuntur lineæ quæ terminant singulas partes -vestigii deformati; hujusque adjumento ducitur elevatio lateris, ac -methodo consuetâ latitudines & longitudines mutuli solidi eruuntur ex -vestigio, altitudines ex elevatione. Hic & deinceps nomina longitudinis -& altitudinis usurpamus, veluti planum cujuslibet perspectivæ esset -verticale; in quâ suppositione, ~IL~ esset latitudo mutuli, ~SR~ -altitudo, ~RL~ longitudo: quum ~SR~ reverà sit longitudo, ~RL~ altitudo. -Ad faciliorem descriptionem hujus figuræ observandum est, rectis ~IL, -LM, GH,~ hujus paginæ inesse divisiones rectarum ~DC, FE, AB,~ figuræ -septuagesimæoctavæ._ - - - - -The Seventy-ninth FIGURE. - -_The Plan and Elevation of a Corbel in Perspective._ - - -The Face of the Corbel describ’d in the Seventy-eighth Figure, in this -does the Office of a Plan; and the Side serves here for the Elevation; -as is plain from the occult Lines, which from the Divisions of the Face -tend to the Point of Sight, and from those of the Side tend to the Point -of Distance; both which Points, in this and the succeeding Figure, fall -without the Plate. From the Intersections of these Lines are drawn -others, that determine each Part of the Perspective-Plan; by means of -which, the Elevation of the Side being also form’d, the Breadths and -Lengths of the solid Corbel are taken, as usual, from the Plan, and the -Heights from the Elevation. Here and henceforward, the Terms of Length -and Height are made use of, as though the Plan of each Perspective were -vertical; according to which Supposition, IL is the Breadth of the -Corbel, SR the Height, and RL the Length; whereas in reality SR is the -Length, and RL the Height. For the more ready Description of this Figure -you will do well to observe, that the Lines IL, LM, GH, of this Plate, -bear the same Divisions as DC, FE, AB, of the Seventy-eighth Figure. - - - - -[Illustration: FIG. LXXX.] - - - - -FIGURA OCTOGESIMA. - -Horizontalis projectio mutuli inumbrati. - - -_In hac figurâ suas umbras mutulo addidimus: eumque si in altum supra -oculum elevaveris, & ex distantiâ quam ipsi dedimus suspexeris; miraberis -profectò, in alium longè concinniorem subitò mutatum fuisse._ - - - - -The EIGHTIETH FIGURE. - -_The Horizontal Projection of a shaded Corbel._ - - -In this Figure you have the Corbel finish’d with its proper Shades; -which, if plac’d above the Eye, and beheld from the Distance here -assign’d it; you’ll be strangely surpriz’d at the sudden and most -agreeable Alteration you’ll find therein. - - - - -[Illustration: FIG. LXXXI.] - - - - -Figura Octogesimaprima. - -Stylobatæ Corinthii horizontaliter contracti. - - -_In deformandis hisce stylobatis, usi sumus projectione vestigii & -elevationis, quam exhibet figura duodecima; ut figuram illam cum istâ -conferenti manifestissimè constabit. Porrò stylobatas pingi solere -incumbentes mutulis, diximus figurâ septuagesimaoctavâ._ - - - - -The Eighty-first Figure. - -_~Corinthian~ Pedestals in an Horizontal Perspective._ - - -In delineating these Pedestals, I have made use of the Plan and Upright -put into Perspective in the Twelfth Figure; as will evidently appear, -by comparing that Figure with this. I have already mention’d, in the -Seventy-eighth Figure, that in painting these Pedestals, they are -generally suppos’d to be upheld by Corbels. - - - - -[Illustration: FIG. LXXXII.] - - - - -Figura Octoges. secunda. - -Columna Corinthia horizontaliter deformata. - - -_Vestigium & elevatio stylobatæ, quem delineavimus figurâ duodecimâ, -suppeditat mensuras pilarum hoc loco deformandarum, ut ex iis eruatur -contractio columnæ. Huic autem soli suas umbras addidimus, ut clariùs -appareat modus & artificium totius operationis. Ex his vides, quadrata & -circulos in perspectivâ horizontali omninò retinere suam figuram, eamque -dumtaxat restringi paulatim & coarctari: quicquid in contrarium & verbis -& pennicillo docuerint Pictores nonnulli._ - - - - -Eighty-second FIGURE. - -_A ~Corinthian~ Column in Horizontal Perspective._ - - -The Plan and Elevation of the Pedestal delineated in the Twelfth Figure, -gives also the Measures for reducing these Pilasters into Perspective; -from which the Contraction of the Column is taken. I have shadow’d -only this last, that the Manner of the whole Work might be the more -conspicuous. By this you see the Squares and Circles in Horizontal -Perspective always retain their Figures, without any Alteration, save -that of being gradually diminish’d and made less; notwithstanding what -some Painters have taught and practis’d to the contrary. - - - - -[Illustration: FIG. LXXXIII.] - - - - -Figura Octogesimatertia. - -Capitella Corinthia horizontaliter contracta. - - -_Habes in hac paginâ deformationes vestigii & elevationis capitelli -Corinthii, quas desumpsimus ex delineationibus geometricis, transferendo -mensuras earum in lineas plani ~AB~, & elevationis ~AC~, ita ut facillimè -dignosci possit unde nascantur singulæ partes capitellorum nitidorum. -Nihil dubito quin deformationes horizontales sis experturus faciliores -verticalibus quas dedimus figurâ vigesimaquartâ. Nam in horizontalibus -gyrus foliorum circulis clauditur, quorum centra mutuantur latitudines -à suis vestigiis in punctis ~1~, ~2~, ~3~, ~4~; altitudines verò à -capitellis elevationis in punctis ~5~, ~6~, ~7~, ~8~._ - - - - -Eighty-third FIGURE. - -_A ~Corinthian~ Capital horizontally contracted in Perspective._ - - -You have in this Plate the Perspective both of the Plan and Elevation of -the _Corinthian_ Capital, drawn from the Geometrical Descriptions, by -transferring their Measures into the Ground-line AB, and into that of the -Elevation AC; so that you may readily discover from whence every part of -the finish’d Capital is produc’d. I don’t doubt but you’ll experience -these horizontal Perspectives to be much less difficult than the vertical -propos’d in the Twenty-fourth Figure. For in these the Circuit of the -Leaves is determin’d by perfect Circles, whose Centers take their -Breadths from the Plan at the Points 1, 2, 3, 4; and their Heights from -the Capitals of the Elevation, at the Points 5, 6, 7, 8. - - - - -[Illustration: FIG. LXXXIV.] - - - - -Figura Octogesimaquarta. - -Coronix Corinthia. - - -_Si faciendæ sint coronices quæ habeant angulos, elevatio geometrica -~A~ repræsentabit unum latus, alterum sectio ~B~. Curandum est autem, -ut crepidines partium, quas fingere volumus incumbere columnis, non -obsint concinnæ distributioni mutulorum. Ad contractionem elevationis -~A~ & sectionis ~B~, in lineam plani ~EF~ & elevationis ~EG~ transferre -oportet puncta diversarum latitudinum, quas habent in elevatione A ungues -epistylii, zophori, & coronæ, ducendo ex iis lineas ad punctum oculi; -in partem verò ~FH~ lineæ ~FE~ transferre oportet puncta longitudinis, -ducendo lineas ad punctum distantiæ. Hac industriâ perficies utramque -deformationem, quarum una geret munus vestigii, altera elevationis. -Utrobique autem designabis lineas terminativas partium coronicis, ac -sectionum ~C~ & ~D~._ - - - - -Eighty-fourth FIGURE. - -_A ~Corinthian~ Cornice._ - - -If you are to describe Cornices having Angles, admit the Elevation A to -represent one Side, and the Section B the other. But Care is to be taken, -that the Breaks of those Parts which are suppos’d to be set directly over -the Columns, do not obstruct the regular Distribution of the Modillions. -For contracting into Perspective the Elevation A, and the Section B, you -must transfer into the Ground-line EF, and into that of the Elevation -EG, the Points of the several Breadths made by the Projectures of the -Architrave, Freeze, and Cornice of the Elevation A; and from them draw -Lines to the Point of Sight: Then on the Part FH of the Line FE, you -must note the Points of Length, and draw Lines from them to the Point of -Distance. By this Practice you complete these two Contractions, one of -which does the Office of a Plan, the other that of an Elevation. It’s -also requisite, that you draw the Out-line of the Members of the Cornice -on each side the Angle, & the Sections C and D. - - - - -[Illustration: FIG. LXXXV.] - - - - -Figura Octogesimaquinta. - -Coronix Corinthia horizontaliter contracta. - - -_Soliditas coronicis cum omnibus projecturis eruta est ex vestigio & -elevatione figuræ octogesimæquartæ. Hic autem finem imponimus partibus -rerum, ad integra ædificia gradum facturi._ - - - - -The Eighty-fifth Figure. - -_A ~Corinthian~ Cornice in Horizontal Perspective._ - - -The Solidity of this Cornice, with all its Projectures, is deduc’d from -the Plan and Elevation of the foregoing Figure. With this therefore I -shall conclude the Description of Parts of things, and proceed to that of -entire Structures. - - - - -[Illustration: FIG. LXXXVI.] - - - - -Figura Octogesimasexta. - -Horizontalis projectio columnæ. - - -_Postquam sigillatim descripsimus mutulum, stylobatam, columnam & -coronicem, omnia ista conjungere placuit: ita clariùs apparebit quomodo -disponere oporteat delineationes geometricas, ut ex iis eruantur -projectiones horizontales._ - -_Linea plani est ~CD~, perpendicularis ~CI~. In ~A~ est elevatio -geometrica longitudinis columnæ, (supponimus columnam delineari veluti -jacentem humi.) In ~B~ ejus vestigium geometricum, cum divisionibus -latitudinis in lineâ ~ER~. Puncta longitudinis transferentur in lineam -plani ~CG~, puncta altitudinis ~EC~ transferentur in ~CF~, ducendo rectas -ex divisionibus ~CG~ ad punctum distantiæ, ex divisionibus ~CF~ ad -punctum oculi. Per sectiones verò visualis ~CO~ erigentur perpendicula, & -complebitur elevatio ~H~, ex quâ eruetur columna nitida ~L~._ - -_Si super vestigio ~M~ formare placeat aliam columnam, ejus latitudines -accipiendæ sunt ex columna ~B~; ac sectio projicienda est in ~N~, ut -ex hac tamquam ex elevatione eruatur columna ~P~. Si aliam columnam in -angulo addere libitum fuerit, ope sectionum ~HN~ facilè illam complebis._ - - - - -The Eighty-sixth Figure. - -_A Column in horizontal Perspective._ - - -After the separate Description of a Corbel, Pedestal, Column, and -Cornice; I have here conjoin’d them all, that you might the better -perceive how to dispose Geometrical Elevations for the Business of -horizontal Perspective. - -The Line of the Plan is CD, the Perpendicular CI; the Geometrical -Elevation of the Length of the Column, suppos’d to be lying on the -Ground, is A. The Geometrical Plan thereof is B, with the Divisions -of its Breadth on the Line ER. The Points of Length being transferr’d -on the Line of the Plan CG, and the Points of Height EC into CF; from -the Divisions of CG Lines are drawn to the Point of Distance; and from -those of CF to the Point of Sight. From the Sections of the Visual CO, -Perpendiculars are erected, and the Elevation H completed, from whence is -taken the finish’d Column L. - -If upon the Plan M you would delineate another Column, the Breadths -thereof must be taken from the Column B, and another Profile design’d -in N, which serves as an Elevation for making the Column P. If another -Column were requir’d in the Angle, the Profiles HN assist you in the -ready Performance thereof. - - - - -[Illustration: Fig. lxxxvii.] - - - - -FIGURA Octogesimaseptima. - -Præparatio necessaria ad sequentem figuram, & ad projectiones -horizontales in laquearibus vel testudinibus. - - -_Exhibet hæc figura in ~AA~ unum ex quatuor parietibus aulæ, cujus -altitudinem veram ~IH~ velis attollere apparenter usque in ~L~, pingendo -in laqueari, vel in testudine, seriem balaustiorum. In ~B~ est vestigium -geometricum quartæ partis laquearis. In ~C~ habetur elevatio medietatis -latitudinis. In ~D~ est sectio coronicis & mutulorum. In ~E~ posita -est elevatio medietatis longitudinis. In ~F~ est punctum oculi, in ~G~ -punctum distantiæ: adeóque tota distantia est ~GF~._ - - - - -The Eighty-seventh FIGURE. - -_The Preparation necessary to the following Figure, and to all other -horizontal Perspectives, whether on flat or vaulted Ceilings._ - - -The Figure AA represents one of the four Walls of a Hall, whose true -Height IH you would have appear rais’d to L, by painting a Ballustrade in -the Ceiling thereof. B is the Geometrical Plan of the fourth part of the -said Ceiling; C is the Elevation of half the Breadth; D is the Section -of the Cornice and Corbels; E is the Elevation of half the Length. In F -is the Point of Sight, in G the Point of Distance; so that the Distance -itself is FG. - - - - -[Illustration: FIG. LXXXVIII.] - - - - -Figura Octogesimaoctava. - -Horizontalis projectio balaustiorum figuræ octogesimæseptimæ, cum brevi -distantia. - - -_Claritatis gratiâ totum laquear divisum est in quatuor partes. Prima -continet contractionem vestigii & elevationis, quæ perficiuntur methodo -consueta. Nam linea ~AOV~ est horizontalis, ~BC~ est linea plani. Punctum -oculi est ~O~, distantiæ ~E~. Secunda pars continet sectionem ~L~, quæ -dat projecturas mutulorum aliarumque partium, desumendas ex sectione ~D~ -figuræ octogesimæseptimæ, deformando eam in angulis ~B~ & ~C~. Tertia -pars complectitur delineationem integram sine umbris: ultima pars eandem -complectitur cum umbris._ - -_Ob punctum distantiæ parum remotum à puncto oculi, nimiam amplitudinem -ac deformem apparentiam habere videtur hæc delineatio. Nihilominus, si ex -distantia ~EO~ figuram suspexeris, omnis deformitas evanescet._ - -_Ut fucus imperitis fiat, industrii Pictoris interest parare sibi -geminum exemplar suorum Operum, in quibus distantia sit nimis brevis; -unum videlicet palam ostendendum, in quo punctum distantiæ sit remotum à -puncto oculi, quantum necesse est ad vitandam omnem deformitatem. Alterum -verò, in ipsomet Opere clam usurpandum._ - -_Si pingendæ sint testudines, oportet prius facere in eis reticulationem -peculiarem; quæ quia difficilis est, & paucis explicari nequit, in aliud -Opus reservatur._ - - - - -Eighty-eighth Figure. - -_The horizontal Projection of the Ballustrade of the Eighty-seventh -Figure, view’d at a small Distance._ - - -For the better Illustration of this Figure, I have divided the whole -Ceiling into Four Parts. The first contains the Plan and Elevation in -Perspective, after the usual manner; AOV being the horizontal Line, BC -that of the Plan; the Point of Sight O, and that of Distance E. The -second Part contains the Section L, which gives the Projectures of the -Corbels and other Parts taken from the Section D of the Eighty-seventh -Figure, by drawing it in the Angles B and C. The third Part comprehends -the Delineation of the Perspective without Shadows. The fourth Part -contains the same wholly shadow’d and finish’d. - -Through the near Approach of the Point of Distance to the Point of Sight, -you may perhaps imagine this Draught will appear too wide, and so have an -ill Effect: But when once you view it from its due Distance EO, you will -find all such Doubts vanish and come to nothing. - -When you have to deal with Persons unskill’d in these things, and are to -paint for so small a Distance; your best way is to make two Draughts; one -for publick Shew, in which you may place the Point of Distance so far -from the Point of Sight, as is necessary for preventing Deformity; and -the other you may privately make use of in performing your Work. - -If you are to paint arch’d or vaulted Ceilings, a particular kind of -Net or Lattice-work must first be made therein; the Performance whereof -being difficult, and not capable of being explain’d in few words, I have -reserv’d it for another Volume. - - - - -[Illustration: FIG. LXXXIX.] - - - - -Figura Octogesimanona. - -Horizontalis projectio architecturæ in laqueari quadrato. - - -_Si laquear sit quadratum, & valde distans ab oculo, architecturam huic -similem in eo depingere licebit. ~A~ est elevatio geometrica; eadem verò -deformata in ~B~ & ~C~, gerit munus vestigii & elevationis. Medietas -unius ex quatuor partibus, usui esse potest in toto opere, aut premendo -chartam, aut eâ perforatâ, immittendo per foramina carbonem minutissimè -contusum._ - - - - -Eighty-ninth FIGURE. - -_An horizontal Projection of Architecture in a square Ceiling._ - - -If the Ceiling be square, and very remote from the Eye, you may paint -in it some such Piece of Architecture as this. A is the geometrical -Elevation; the same reduc’d into Perspective in B and C does the Office -of a Plan and Elevation. The Half of one of the four Parts may suffice -for the Draught of the whole Work, either by tracing over the Lines of -the Paper, or by pricking small Holes therein, and pouncing them through -with Charcole finely powder’d. - - - - -[Illustration: FIG. XC.] - - - - -FIGURA Nonagesima. - -Horizontalis projectio tholi. - - -_Initium hujus rei fiet à vestigio geometrico, in quo duæ series -circulorum designant columnas; aliæ lineæ designant stylobatas, -ac projecturas & ungues basium & coronicum. Linea plani est ~AB~, -horizontalis ~CD~, perpendicularis ~AD~. Punctum oculi est ~O~, distantiæ -~D~; adeóque figura hæc debet habere supra oculum altitudinem ~DO~. -Punctum oculi positum fuit extra ipsum tholum, ut qui eum aspiciunt, -minus defatigentur, ac plus appareat de architectura & de artificio; -secus verò contingeret si punctum oculi esset in medio. Itaque puncta -lineæ ~EF~ transferentur in partem ~AG~ lineæ ~AD~. Centrum ~I~ vestigii -transferetur in ~H~ & ex omnibus his punctis fient visuales ad ~O~. -Deinde altitudine tholi, ac divisionibus partium singularum tum ipsius, -tum laternæ, translatis in lineam ~AB~, ex punctis divisionum fient rectæ -ad punctum distantiæ ~D~. Ubi autem hæ secant visualem ~AO~, erigentur -perpendicula, quorum sectiones cum visuali ~HO~ dabunt centra pro -singulis circulis. Inter visuales ~AG~ ducere oportet lineas terminativas -columnarum & coronicum; quemadmodum fieret, si ex vestigio eruta fuisset -elevatio geometrica. His positis, aggredieris delineationem opticam -ipsius tholi, translatis in perpendicularem ~EO~ centris ope parallelarum -~HI~, ~LN~; ac semidiametro ~LM~ fiet circulus ~NP~ pro simâ coronicis: -semidiametro ~ST~ fiet circulus ~QR~, & sic de reliquis. Quomodo autem -per rectas ex angulis vestigii ad punctum oculi, habeantur ungues -coronicis, ostendunt numeri ~1~, ~2~, ~3~, ~4~; lineæ verò laterales -unguium tendunt ad centra suorum circulorum, ut videre est in ~N 3, 4~. -In vestigio, ne nimium occupetur, mutulos omisimus._ - -_Ex his patet necessitas faciendi vestigium geometricum totius tholi, ac -non sufficere vestigium unius columnæ; quum singulæ peculiares exigant -deformationes. Quum autem Opus ipsum delineandum ac pingendum fuerit, -ipsum desumere non poteris ex parvo exemplari, ope reticulationis; -Quinimo suis locis ducere oportebit lineas visuales, & invenire centra -omnium circulorum. Figendo autem funiculum in singulis centris, ipsius -adjumento facillimè absolves omnes circumferentias._ - - - - -The Ninetieth Figure. - -_A Cupola in horizontal Perspective._ - - -In the Execution of this Work, you are to begin with the Geometrical -Plan; in which the two Ranges of Circles denote the Columns, the other -Lines shew the Pedestals, with the Projectures and Breaks of the Bases -and Cornices. The Line of the Plan is AB, that of the Horizon CD, the -perpendicular Line is AD. The Point of Sight is O, that of Distance D; -wherefore this Figure ought to be plac’d as much above the Eye, as the -Height DO. I have set the Point of Sight something without the Cupola, -that the Eye might be less weary’d in viewing the Work, and embrace more -of the Architecture, than it could have done, had the Point of Sight been -in the midst. The Points of the Line EF are transferr’d into AG, part of -the Line AD. The Center of the Plan I is continu’d to H, and from all -these Points visual Lines are drawn to O. Then placing the Heights of -every part both of the Cupola and Lantern on the Line AB, from the Points -of those Divisions draw Lines to the Point of Distance D; and where they -cut the Visual AO, erect Perpendiculars intersecting the Line HO; which -Points are the Centers of the several Circles. On the Visuals, between -AG, must be describ’d the Out-lines of the Columns and Cornices, in like -manner as when a Geometrical Upright is rais’d from a Plan. This done, -you proceed to the Delineation of the Cupola itself in Perspective, -by transferring into the Perpendicular EO the several Centers of HO, -by Parallels to HI, as LN, _&c._ On the Center, with the Interval LM, -describe the Circle NP, for the Nose of the Cornice; and with the -Semidiameter ST describe the Circle QR, and so of the rest. The Numbers -1, 2, 3, 4, shew how the Breaks of the Cornice are determin’d by Lines -from the Angles of the Geometrical Plan tending to the Point of Sight, -till they intersect the Circle: The Returns of which Breaks are made by -Lines tending to the Centers of their respective Circles; as is plain -from N 3, and N 4. In this Plan I have omitted the Corbels, lest I should -too much encumber the Work. - -Hence appears the Necessity of making the Geometrical Plan of the whole -Cupola, the Plan of a single Column not being sufficient; by reason each -requires its particular Delineation. And when the Work itself is to be -drawn for painting, you can’t well take it from a small Draught by way of -Net-work or Squares, but the visual Lines should be drawn in their proper -places, and the several Centers found; in which, by fixing Strings, you -may readily describe the Circumferences of all the Circles. - - - - -[Illustration: FIG. XCI.] - - - - -Figura Nonagesimaprima. - -Tholus figuræ nonagesimæ, cum luminibus & umbris. - - -_Tholus quem vides in hac paginâ, pollicetur sibi vitam diuturniorem -illo, quem super telario plano insignis amplitudinis, depinxi anno 1685. -in Templo S. Ignatii Collegii Romani. Proinde si casus aliquis illum -absumat, non deerunt qui ex isto eundem in melius reficiant. Mirati -fuerunt Architecti nonnulli, quòd columnas anteriores mutulis imposuerim, -id enim in solidis ædificiis ipsi non facerent. Verùm eos metu omni -liberavit amicissimus mihi Pictor, ac pro me spopondit, damnum omne se -statim reparaturum, si fatiscentibus mutulis, columnas in præceps ruere -contingat._ - - - - -The Ninety-first Figure. - -_The Cupola of the Ninetieth Figure, with its Lights and Shades._ - - -The Cupola in this Plate will in all Likelihood be of longer Duration, -than that which I painted on a very large Table, for the flat Ceiling -of the Church of S. _Ignatius_ of the _Roman_ College, _anno_ 1685. For -if that suffer by any Accident, with the help of this its place may be -supply’d by a better. Some Architects dislik’d my setting the advanc’d -Columns upon Corbels, as being a thing not practis’d in solid Structures; -but a certain Painter, a Friend of mine, remov’d all their Scruples, -by answering for me, That if at any time the Corbels should be so much -surcharg’d with the Weight of the Columns, as to endanger their Fall, he -was ready to repair the Damage at his own Cost. - - - - -[Illustration: FIG. XCII.] - - - - -Figura Nonages. secunda. - -Tholus octangularis. - - -_Ex circulo fiet octagonum, accipiendo medietatem quadrantis circuli, -ut habeantur singula latera octagoni. In eisdem lateribus distribuetur -vestigium geometricum totius architecturæ, cum projecturis omnium -membrorum, juxta modum quem servavimus in limbo circulari figuræ -nonagesimæ. Utiliter etiam fieret elevatio geometrica totius Operis; -quamvis ob spatii angustias ego eam omiserim. Deinde positâ una cuspide -circini in centro circuli, extendetur alia cuspis ad altitudinem -singularum projecturarum inter spatium ~A~ & ~B~, ut hic vides: atque -ope parallelarum, omnia transferentur in lineam ~CD~, ut fiat optica -deformatio, quam poscit sectio elevationis, cum aliis præparationibus, -ut in figura præcedenti. Nam hic quoque ope circulorum invenire oportet -puncta extrema in prominentiis membrorum singulorum architecturæ: ut -conjungendo puncta per lineas rectas, quæ forment facies octagoni, -compleatur totum Opus._ - - - - -Ninety-second Figure. - -_An Octangular Cupola._ - - -From the Circle describe the Octagon, by taking half the Quadrant of the -former for each Side of the latter. On these Sides the Geometrical Plan -of the whole Architecture is to be dispos’d, with the Projectures of -all the Members thereof, in the same manner as was done in the circular -Border of the Ninetieth Figure. It will also be expedient, to make the -Geometrical Elevation of the whole Work, tho’ thro’ Want of Room I have -here omitted it. Then placing one Point of the Compasses in the Center -of the Circle, extend the other to the Height of the several Projectures -between A and B, as you see in the Figure; and by help of the Parallels -transfer them all into the Line CD, for putting the Profile of the -Upright into Perspective, and drawing the other Requisites, as in the -foregoing Figure. For here also, by means of the Circles, are found -the extreme Points of the Projectures of the several Members of the -Architecture; and by conjoining these Points with strait Lines agreeable -to the Shape of the Octagon, the whole Work is completed. - - - - -[Illustration: FIG. XCIII.] - - - - -FIGURA Nonagesimatertia. - -Vestigium templi Ludovisiani S. Ignatii almæ urbis. - - -_Constitueram huic Libro finem imponere figurâ nonagesimasecunda; -nihilominus ut satisfaciam precibus amicorum, cupientium addiscere modum -reticulationis opticæ, quæ adhibetur in superficiebus irregularibus, -ejusque memini figurâ octogesima octava, publici juris facere decrevi -ejus construendæ methodum. Ipsiusmet retis ope delineavi non solùm -ædificium mox repræsentandum, sed etiam figuras omnes testudinis templi -Ludovisiani, in qua pingenda nunc occupor. Eademque reticulatione, quæ -erit ultima figura hujus Libri, dabimus Operi nostro suum complementum; -quum nulla sit superficies, in qua suas delineationes juxta Perspectivæ -regulas, earum rerum Studiosi absolvere nequeant._ - -_Exhibet hæc figura vestigium totius templi. Quamvis enim non indigeam -nisi testudine inter januam maximam & tholum; proderit nihilominus -Architecturæ Studiosis, universi Operis elegantiam ac symmetriam per -otium contemplari._ - - - - -The Ninety-third FIGURE. - -_The Geometrical Plan of the Church of S. ~Ignatius~ at ~Rome~._ - - -I had once determin’d to end this Book with the Ninety-second Figure; but -at the Request of some Friends, who were desirous to learn the Making -of Perspective Net-work for irregular Surfaces, as was hinted in the -Eighty-eighth Figure; I resolv’d to publish the Manner of performing -the same. By the Help of this Net-work, I delineated not only the -Architecture now to be treated of; but also each Figure in the Vault of -the Church of S. _Ignatius_, which I am at present employ’d in painting. -The Method is laid down in the last Figure of this Book, and entirely -completes the same; there being no Superficies, how irregular soever, but -the Studious may thereon describe, by these Rules, whatever Perspective -he has occasion for. - -This Figure contains the Plan of the whole Church; for though my present -Design requir’d no more than the Vault of the Nave, between the great -Door and the Cupola; I thought it might be nevertheless acceptable to -the Curious in Architecture, to have a View of the whole Design, so -celebrated for the Elegancy and Proportion of its Parts. - - - - -[Illustration: FIG. XCIV.] - - - - -Figura Nonages. quarta. - -Orthographia templi Ludovisiani. - - -_Vt magis tibi gratificer, orthographiam seu elevationem templi -Ludovisiani in longum dissecti delineavi, cum omnibus mensuris quæ -vestigio sunt communes; addito tholo juxta ideam Autoris. Ejus autem -nondum constructi loco, positum est in ~A~ & ~B~ telarium cum tholo -depicto, de quo supra in figuris nonagesimâ & nonagesimaprimâ._ - - - - -Ninety-fourth FIGURE. - -_The Orthography, or Geometrical Elevation of the Inside of S. -~Ignatius~’s Church._ - - -For your greater Satisfaction, I have here given the Geometrical Upright -of the Church dissected lengthwise, with all its Measures agreeable to -those of the Plan; as also the Cupola design’d by the Author: Which not -being yet built, instead thereof is plac’d between A and B, the painted -Cupola before describ’d in the Ninetieth and Ninety-first Figures. - - - - -[Illustration: FIG. XCV.] - - - - -Figura Nonages. quinta. - -Aliæ præparationes ad figuras nonagesimamoctavam & nonagesimamnonam. - - -_Ex hac figura in quatuor partes divisa, disces ex uno intuitu methodum -qua sum auspicatus opticam delineationem templi Ludovisiani. Prima pars -exhibet latus dextrum testudinis inter januam templi ac tholum. Secunda -pars continet vestigium ejusdem testudinis, arcubus ac lunulis distinctæ. -Tertia pars continet latus dextrum testudinis usque ad summitatem -fenestrarum, unde incipit Architectura quam pingimus in fornice. Quarta -pars est vestigium geometricum fornicis, cum prominentia quam habent -arcus in summitate jam dicta fenestrarum. Fingimus autem eandem esse -soliditatem, tum ædificii depicti, tum navis templi; solæ enim columnæ, -quæ respondent pilis templi, prominent extra ædificium._ - - - - -The Ninety-fifth Figure. - -_Other Preparations to the Ninety-eighth and Ninety-ninth Figures._ - - -By this Figure divided into four Parts, you will at first Sight perceive -the Method I observ’d in beginning the Perspective Design of this Church -of S. _Ignatius_. The first Part shews the right-hand Side of the Vault -between the Door and the Cupola. The second contains the Plan of the same -Vault, with its Arches and Lunettes. The third Part represents the same -right-hand Side, to the top of the Windows; where begins the Architecture -painted in the Vault. The fourth Part contains the Geometrical Plan of -that part of the Vault which is painted; with the Lunettes made by the -Arches above the Heads of the aforesaid Windows. The Disposition of the -painted Architecture above, is the same with that of the Nave of the -Church; save that, answerable to the Pilasters below, I have suppos’d -Columns projecting over the Work. - - - - -[Illustration: FIG. XCVI.] - - - - -Figura Nonagesimasexta. - -Aliæ præparationes ad figuras nonagesimamoctavam & nonagesimamnonam. - - -_Prima pars figuræ hujus trifariam divisæ, repræsentat elevationem -geometricam lateris templi supra coronicem, & ædificii in testudine -pingendi. Secunda pars complectitur arcum testudinis maximum, & -elevationem geometricam faciei ejusdem ædificii. Tertia pars exhibet -vestigium totius ædificii pingendi in testudine, cujus amplitudo -eadem est cum amplitudine navis, ut antea dicebamus. Porrò vestigium -geometricum non minus necessarium est ad pingendum ædificium, quàm ad -ipsum ex materiâ solidâ extruendum, ut alibi monuimus._ - - - - -The Ninety-sixth Figure. - -_Other Preparations to the Ninety-eighth and Ninety-ninth Figures._ - - -In this Figure, which consists of three parts, the first represents the -Geometrical Elevation of the Right-side of the Nave above the Cornice, -and of the Design painted in the Vault. The second contains the great -Arch of the Vault, and the Geometrical Elevation of the Front of the -said Design. The third part shews the Plan of the whole Work painted on -the Vault, the Extent and Disposition of which is the same with that of -the Nave, as beforemention’d. The Geometrical Plan, as I have formerly -hinted, is no less necessary for the painting a Design in Perspective, -than it is for raising a Structure with solid Materials. - - - - -[Illustration: FIG. XCVII.] - - - - -Figura Nonages. septima. - -Alia præparatio ad figuras nonagesimamoctavam & nonagesimamnonam. - - -_Ut optica projectio vestigii & elevationis quartæ partis totius Operis -distinctior evaderet, mensuras partium singularum quadruplicavi, -eandemque methodum in hac delineatione tenui, quæ figuris -octogesimasextâ, octogesimaseptimâ, octogesimaoctavâ, & octogesimanonâ, -explicata fuit. Punctum oculi positum est in medio navis Ecclesiæ; -punctum distantiæ est in lineâ ex quâ incipit arcus testudinis._ - - - - -Ninety-seventh Figure. - -_Another Preparation to the Ninety-eighth and Ninety-ninth Figures._ - - -That the Perspective of the fourth part of the Plan and Elevation of -this Work might be more distinct, I have in this Figure made the Measures -of each part four times as big as in the former; and have kept the -same Method in this Delineation, as was deliver’d in the Eighty-sixth, -Eighty-seventh, Eighty-eighth, and Eighty-ninth Figures foregoing. I have -set the Point of Sight in the midst of the Nave of the Church; and the -Point of Distance is in the Line from which the Arch of the Vault springs. - - - - -[Illustration: FIG. XCVIII.] - - - - -Figura Nonages. octava. - -Quadrans Architecturæ horizontalis in fornice, cum luminibus & umbris. - - -_Habes in hac paginâ quadrantem totius Operis, modo consueto erutum ex -præcedenti: nimirùm, cuspide circini ex angulis vestigii accipiuntur -lineæ perpendiculares; ex angulis verò elevationis desumuntur lineæ -parallelæ, ac lineæ visuales ad punctum oculi._ - - - - -Ninety-eighth Figure. - -_A fourth Part of the Architectonical Design, painted on the Vault of S. -~Ignatius~’s Church; with its Lights and Shadows._ - - -In this Figure you have a Quarter of the whole Work, drawn from the -foregoing Figure, after the usual Manner; namely, by taking with the -Compasses the perpendicular Lines from the Angles of the Plan; and the -parallel Lines from those of the Elevation, as also the visual Lines to -the Point of Sight. - - - - -[Illustration: FIG. XCIX.] - - - - -Figura Nonagesimanona. - -Alter quadrans totius Operis. - - -_Ob diversitatem duorum quadrantum, tum in longitudine, tum in luminibus -& umbris, seorsim apponendum utrumque censui; ut in eis delineandis omnem -difficultatem tibi adimerem._ - - - - -The Ninety-ninth Figure. - -_Another Quarter of the whole Design._ - - -By reason of the Difference of the two Quarters, as well in Length, as in -their Lights and Shadows, I resolv’d to describe them separately, that -you might find no Difficulty in designing the whole Work. - - - - -[Illustration: FIG. C.] - - - - -FIGURA Centesima. - -Modus reticulationis faciendæ in testudinibus. - - -_Opera quæ fiunt in planis, contenta sunt duplici reticulatione, ut notum -est. Nam una earum fit in exemplari, altera fit in superficie in quâ -ipsum Opus pingendum est. At verò testudines exigunt tres reticulationes. -Prima fit in exemplari, quod supponimus delineatum esse juxta regulas -Perspectivæ horizontalis. Secunda reticulatio constat ex funiculis, & -est pensilis; cujus formam geometricam habes in ~M~. Locum ubi figendi -sunt clavi qui sustineant funiculos, exhibent rectæ ~AB~, ~EF~: optica -verò deformatio retis est in ~N~. Punctum oculi est ~O~, distantiæ est -~LO~. Itaque si imagineris, tempore nocturno, lumen candelæ aut lucernæ -existere in ~O~, atque à reti ex funiculis projici lineas umbrosas in -testudinem, eædemque lineæ pennicillo colorentur, habebitur tertia -reticulatio ad pingendam testudinem necessaria._ - -_Dixi ~si imagineris~, quia in testudinem obductam tabulato, ac remotam -à reti, & multò magis à lumine, vel projici nequeunt umbræ, vel -nequeunt esse vividæ ac distinctæ, ut oportet. Itaque ubi nimia fuerit -distantia, figes in ~O~ extremitatem fili; eóque usque ad testudinem -extenso, utéris veluti radio ac lumine candelæ, ad notandum umbræ -locum. Proderit etiam, ut super tabulato motum fili obsecundes lumine -alicujus candelæ, quod ipsi filo proximè admoveas. Atque his aliisque -adminiculis, tuâque industriâ, colores induces super lineis umbrosis, ac -tertiam reticulationem absolves. Posset etiam rete ex filis figi in parvâ -distantiâ à coronice, puta in ~GH~, unde incipit basis ædificii: tunc -autem umbræ in fornice sunt magis distinctæ ac visibiles._ - -_Diligentissimè curabis, ne mensuræ exemplaris discrepent ullatenus à -mensuris testudinis: ut rete incidens in angulos, arcus, aut lunulas -testudinis, exactè respondeat reti exemplaris. Demum si in vitia quæ -emendari nequeant, incidere nolis; scito, regulas omnes Perspectivæ -horizontalis, æquè in hominibus aut animalibus, ac in columnis aut -coronicibus pingendis, omnino servari oportere._ - - - - -The Hundredth Figure. - -_The Method of drawing the Net or Lattice-Work on Vaults._ - - -For Works on a flat Superficies, two Net-works are sufficient; as has -been already intimated: One drawn on the Copy; the other on the Table to -be painted. But for arch’d Surfaces, or Vaults, three are requir’d: One -made on the Copy, which I suppose drawn according to Rules of horizontal -Perspective. The second consists of a Frame of small Cords or Threads, -to be hung up; the Geometrical Form of which is M. The Lines AB, EF, -shew the Place where this Frame is to be fix’d, in the same manner as -the Perspective N. The Point of Sight is O; of Distance, LO. Therefore, -if you imagine a Lamp or Candle fix’d in the Night-time at the Point O; -the Shadows of the Thread, thrown thereby on the Vault, being trac’d by a -Pencil, make the third Net-work requir’d for painting the same. - -I say, _if you imagine_ a Lamp thus fix’d; because either the Scaffold -to the Vault, or the great Distance of the Vault from the Net-work, or -the greater of both from the Light, may prevent the Shadows from being -thrown at all, or at least, may render them so faint, as not to be -distinct enough for the purpose. Therefore, where this happens, instead -of the Light fix one End of a Thread in the Point O; and extending the -other to the Vault, make use of it as a Ray from the Lamp or Candle, for -describing the Place of the Shadows. It will be also of great use, to -second the Motion of the Thread with the Light of a Candle you may have -by you on the Scaffold, holding the same near the Thread itself. By this, -and other such Helps, which your own Industry will suggest, you may lay -these Shadows in Colours, and complete the third Net-work requir’d. The -Frame of Threads may also be fix’d nearer the Vault at some Distance -above the Cornice, as at GH, where the painted Architecture begins; for -the Shadows thrown on the Arch will by that means become more visible and -distinct. - -You must be very careful, that the Measures of your Copy are exactly the -same with those of the Vault, that the Net-work thrown into the Angles, -Arches and Lunettes of the Vault, may perfectly correspond with that of -your Copy. Lastly, if you would not run into inextricable Errors; assure -yourself, that all these Rules of horizontal Perspective are as strictly -to be observ’d in the Figures of Men or Animals, as in painting Columns, -Cornices, or the like. - - - - -_Ut Perspectivæ Tyronibus consulerem, qui fortasse non adeo facilè -percipient duodecim primas figurarum explicationes, totidem novas -explicationes hic addo._ - -For the greater Help to Beginners, and those who are less conversant in -the Art of Perspective, I here subjoin a farther Explanation of the first -twelve Figures of this Book. - - -FIGURA PRIMA. - -Explicatio linearum plani, & horizontis, punctorum oculi, & distantiæ; de -hoc ultimo pressiús. - -_Tres lineæ diversi inter se nominis, & muneris, item, & duo puncta -præcipuè necessaria sunt, ut delineatio quælibet opticè reddi queat: -prima vocatur linea plani, secunda horizontalis ubi est punctum oculi; -de tertia loquar in elevationibus: alterum de duobus punctis assignatur -oculo, & vulgò dicitur punctum oculi; alterum verò assignatur distantiæ, -à qua nomen habet. Punctum oculi notissimum est, punctum verò distantiæ -non ità; in hujus igitur explicatione morabor, & ut clariùs ostendam -quid sit, & quomodo formandum sit, selegi descriptionem Ecclesiæ -geometricè habitam, quam in tres partes divisi, in vestigium, sectionem, -& interiorem faciem, in qua facie velit quis pingere, seu delineare -aliquid opticè, ut elongetur ad mensuram aperturæ quadrati ~P~, ut habes -in vestigio, & ad mensuram profunditatis ~Q~, quam habes in sectione._ - -_Super faciem ~CCCC~ quam puta esse delineamentum, habes rationem, qua -debes disponere supradicta puncta, & lineas. ~HI~ erit linea plani: ~NON~ -erit linea horizontalis, quæ fieri solet distans à linea plani altitudine -hominis, ut vides in ~B~. Punctum oculi erit in ~O~; punctum distantiæ -erit in ~N~, ex qua parte malueris. Hoc punctum ~N~ debet tantum abesse -à puncto ~O~, quantum tuo arbitratu tu vis procul esse ut videas -profunditatem illius quadrati ~PQ~, sicut vides in exemplo vestigii, & -sectionis; ubi rem velut in suo statu naturali exhibeo; in iis enim tam -abest ~N~ ab ~O~, quam abest homo ab ~A~ ad ~DE~, & homo ~B~ in sectione, -ab ~FG~, ubi est murus in quo pingendum, vel delineandum est._ - -_Si ulteriùs curiosè descriptionem hanc consideres, videbis quam bene -respondeat quadratum ~P~ in plano, & elevatio ~Q~, ut naturalis status -rei in sectione Perspectivæ positæ in facie ~CCCC~, quæ est delineatio. -Videbis enim visuales, quæ secant in plano spatium ~RS~, ita pariter -secare spatium ~TV~ in elevatione: & segmentum visualium ~XZ~ in sectione -respondere ~YK~ in elevatione, quod demonstratione non caret._ - - -FIRST FIGURE. - -_An Explanation of the Lines of the Plan and Horizon, and of the Points -of Sight and Distance; but more especially of this last._ - -For beginning any Design in Perspective, there are principally requir’d -three Lines, and two Points: One Line where the Feet stand, which is -call’d the Line of the Plan, or Ground-line: The second where the Eye is -plac’d, call’d the horizontal Line: I shall speak of the third in the -Elevations. Of the Points, one is assign’d to the Eye, the other to the -Distance. The first of these is generally known, the latter not so well -understood, though of great Use for giving the Removal or Depth of every -Object. I shall therefore insist a while on the Explanation of the Point -of Distance; and that I may more clearly shew what it is, I have chosen -the Geometrical Description of a Church, which is divided into three -Parts; _viz._ the Plan, Profile, and inner Face; in the midst of which -Face one would paint a Piece of Perspective, that should seem to recede -as much as the Square P in the Plan, and the Depth Q in the Profile. - -On the Face CCCC, which suppose that of the Design, you see the Manner -of disposing the two Lines and the two Points. HI is the Ground-line. -NON is the horizontal Line, which is usually made a Man’s Height above -the Ground line, as in B. The Point of Sight is O, the Point of Distance -N, on which side you will. This Point N must be as far from O, as the -Distance you determine to place yourself at for viewing the Depth of the -Square PQ; as is exemplify’d in the Plan and Profile, where you see the -thing as in its natural Position: And in them N is distant from O, as far -as the Man in A is remov’d from DE; or the Man B in the Profile from FG, -which is the Wall to be drawn or painted on. - -If you farther and more strictly examine this Description, you’ll discern -how well the Square of the Plan P, and the Elevation Q, correspond as if -naturally put into Perspective on the Face CCCC, which is the Draught. -For you see the Visuals which cut the Space RN in the Plan, cut the -same Space TV in the Upright; and the Segment of the Visuals XZ in the -Profile, answer that of YK in the Elevation; which needs no Demonstration. - - -FIGURA SECUNDA. - -Quadratum opticè delineatum. - -_Postquam descripseris in papyro separata quadratum geometricum A, facies -duas lineas parallelas inter se distantes altitudine, quam dederis -puncto oculi; linea inferior erit linea plani, linea superior erit linea -horizontalis, super quam ponuntur puncta oculi ~O~, & distantiæ ~E~, -quod sit ex parte quam mavis: linea distantiæ non debet esse brevior -magnitudine rerum describendarum. Transfer posteà circino latitudinem -quadrati ~A~ in ~CB~, unà cum visualibus ad punctum ~O~; & similiter -transfer longitudinem ipsius quadrati in ~DC~, ducens lineam à puncto -~D~ ad punctum distantiæ ~E~, transeuntem per visualem ~CO~, & ubi illa -secat, habebis terminum quadrati optici ~GFCB~, ducens parallelam ad -lineam plani in ~F~._ - -_Ut autem hoc idem citiùs absolverem, sæpius chartam complicavi, ut habes -in ~A~._ - - -SECOND FIGURE. - -_A Square in Perspective._ - -After you have drawn, on a separate Paper, the Geometrical Square A, -make two parallel Lines as much distant one from the other, as you would -have the Height of the Eye. The under Line is the Plan or Ground-line; -the upper Line is that of the Horizon, on which are plac’d the Points -of Sight O, and of Distance E, on which side you please. The Line of -Distance should not be shorter than the Extent of the thing to be -describ’d in Perspective. Then with your Compasses set the Breadth of -the Square A on CB, and draw Visuals to the Point O; and from the Length -of the Square transferr’d into DC, draw a Line from the Point D to the -Distance E; and where that cuts the Visual CO, by drawing a Line parallel -to GF, you describe the Square in Perspective GFCB. - -For the more quick Dispatch of this, I commonly fold the Paper, as you -see in A. - - -FIGURA TERTIA. - -Rectangulus altera parte oblongior opticé. - -_Quidquid in proximo quadrato vidisti, facies in præsenti. Transferres -latitudinem ~BC~ in ~BC~, & longitudinem in ~CD~, ducens latitudinem ~BC~ -ad punctum oculi ~O~, & longitudinem ~CD~ ad punctum distantiæ ~E~. Ubi -vero hæc linea secat visualem ~CO~, erit terminus rectanguli supradicti -~FG, BC,~ ducens parallelam, ut supra._ - - -THIRD FIGURE. - -_An Oblong Square in Perspective._ - -What was done in the preceding, repeat in this Third Figure. Transfer the -Breadth BC into BC, and the Length into CD, drawing the Breadth BC to the -Point of Sight O, and the Length CD to the Point of Distance E. Where -this cuts the Visual CO, you terminate the Square FG, BC, by drawing the -Parallel, as before. - - -FIGURA QUARTA. - -Quadratum duplex opticé. - -_Eodem modo construes quadratum duplex ~A~, transferens circino, aut -duplicando chartulam, latitudinem cujuscumque lineæ, ut vides in punctis -~1~, ~2~, ~3~, ~4~, ~5~, ~6~, super lineam plani in iisdem numeris, & ab -istis transferes visuales ad punctum ~O~. Postea transfer longitudinem -~7~, ~8~, ~9~, ~10~, super lineam plani in iisdem pariter numeris, & ab -istis duc lineas ad punctum distantiæ ~E~. Ubi hæ lineæ secant lineam ~6, -7, O,~ fiunt lineæ parallelæ ad lineam plani, & quadratum conficitur; -parem constructionem facies de quadrato secundo, & tertio, facilè ex -dictis._ - - -FOURTH FIGURE. - -_A double Square in Perspective._ - -The double Square A is made after the same manner as the former, by -transporting, either with the Compasses, or folded Paper, the Breadth of -every Line, as you see the Points 1, 2, 3, 4, 5, 6, on the Ground-line -mark’d with the same Numbers; and from these draw Visuals to the Point -of Sight. Then transfer the Points of Length 7, 8, 9, 10, into the -Ground-line, as you see also in the same Numbers; and direct their Lines -to the Point of Distance E. Where these intersect the Visual 6, 7, O, -make Parallels to the Ground-line, and the Square is complete. The same -is done in describing the middle Square, and that on the other Side. - - -FIGURA QUINTA. - -Quadratorum vestigia cum elevationibus. - -_Figuram hanc in duas partes divisi; in superiori parte vides tria -quadrata optica aliquantulum adumbrata, eaque tam inter se distantia, -quanta est distributio super lineam plani. ~BC~ erit quadratum primum. -Secundum erit in ~EF~. Si ergo posueris longitudinem quadrati in ~BC~, -eamque duxeris ad distantiam, secabit in ~DD~ visualem ~AO~. Si pariter -posueris alterum spatium longitudinis ejusdem quadrati in ~EF~, & duxeris -ad lineam distantiæ, habebis secundum quadratum opticé. Idem facies de -tertio, & de aliis, quæ distribuenda sunt._ - -_In secunda parte. Si desideres supra totidem vestigia formare -elevationes cuborum, & stylobatarum, ut in inferiori figuræ parte -vides, satis erit ex omni vestigiorum angulo elevare lineas occultas, -& apparentes, determinando altitudinem faciei ~L~ primo cubo, & anguli -ejusdem faciei dabunt altitudinem omnium aliorum._ - -_Immò etiam totidem cubos formare potes sine lineis occultis, ducendo -solùm apparentes, ut vides in tribus expositis adumbratis, & nitidis, -quorum perpendiculares sumuntur ab angulis vestigiorum, ut in superiori -figura habes in ~H~, & lineæ plani translatæ sunt ab angulis elevationis, -ut videtur in ~F~._ - - -FIFTH FIGURE. - -_Several Plans of Squares, with their Elevations._ - -I have divided this Figure into two Parts; In the uppermost you have -three Squares in Perspective a little shadow’d, distant one from another, -according to their Distribution on the Ground-line. BC is the first -Square; EF the second. If you then set the Length of a Square on BC, and -draw Lines to the Point of Distance, they will intersect the Visual AO -in DD. In like manner, if you set another Length of the said Square on -EF, and draw to the Point of Distance, you’ll have the second Square in -Perspective. The same you may do in the third, and as many as you have -occasion for. - -In the second Part you see, that if upon the fore-mention’d Plans the -Elevations of Cubes or Pedestals were requir’d, it would suffice to -elevate the occult and visible Lines from every Angle of the Plan; and -determining the Height of the Face L of the first Cube, the Angles of -that Face drawn to the Point of Sight, give the Height of all the others. - -You may form the same Cubes without occult Lines, drawing only those -that are apparent, as you see in the three Cubes that are finish’d and -shadow’d; the Perpendiculars of which are taken with the Compasses from -the Angles of the Plan, as is shewn in HI of the upper Figure; and the -level Lines are transferr’d from the Angles of the Elevation, as in FG of -the same Figure. - - -FIGURA SEXTA. - -Modus delineandi opticè sine lineis occultis. - -_Desiderans facili methodo figuram hanc exponere, dabo rationem elevandi -corpora sine lineis occultis, ut in superiori tetigi; ostendam igitur -hic, quomodo quinque cubi adumbrati desumantur ab eorum vestigiis, & -elevationibus._ - -_Duas debes facere præparationes, si libeat, in chartis etiam separatis. -Prima erit formare geometricè vestigium, & elevationem, ut vides in ~B~ -& ~A~. Secunda erit distribuere super lineam plani latitudinem vestigii -~B~, puta in ~NM~, & in duabus proximis: Illius longitudo ~MX~ ducta ad -distantiam ~D~, secat visualem ~MO~ in ~R~. Spatium autem obliquatum ~E~ -utile etiam est aliis duobus quadratis positis super eamdem lineam plani; -anguli quorum translati ad distantiam ~B~, totidem angulos dabunt inter -visuales ~NO~, ~MO~. Hoc posito, duces perpendicularem ad angulum ~N~, -quæ in elevationibus geometricis semper necessaria est, eaque tertia -linea est, quam supra dixi. Transfer postea altitudinem ~A~ in ~NF~, cum -visualibus ~FO, NO,~ & invenies altitudinem ~ST~. Hoc pariter de cæteris -eveniet._ - -_Sciendum superest quonam modo supradicta præparatione uti possis ad -construendos stylobatas adumbratos, & inornatos._ - -_Super aliam igitur chartam dispone situm cum duabus lineis, plani -scilicet, & horizontis, una cum puncto oculi ~O~, & perpendiculari ~V~, -ejusdem mensuræ cum supradicta præparatione, & faciens uti me fecisse -vides. Experire postea circino ~NF~ æqualia esse ~1, 5,~ & ~2, 6~. Metire -pariter ~ST~, & invenies æqualia ~7~ & ~3~; facies postea lineas planas, -& visuales ad punctum oculi, & habebis planum superius cubi in ~1~, ~2~, -~3~, ~4~. Hoc idem faciendum est de aliis. Uno verbo: anguli vestigiorum -dabunt tibi lineas perpendiculares, & anguli elevationis dabunt lineas -planas; atque hoc semper erit._ - - -SIXTH FIGURE. - -_The Manner of designing in Perspective without occult Lines._ - -Being desirous to make this Rule as easy as possible, I shall give a -farther Account of raising Solids without the Help of occult Lines, which -I only touch’d upon in the foregoing Figure. I therefore here shew you, -how the five shadow’d Cubes of this Figure are taken from their Plans and -Elevations. - -Two things preparatory are to be done, and, if you please, on separate -Papers. The first is, to describe the Geometrical Plan and Elevation, -as you see in B and A. The second is, to dispose on the Ground-line the -Breadth of the Plan B; as, for Example, in NM, and the two next to it. -The Length thereof MX, drawn to the Point of Distance D, cuts the Visual -MO in R; and the Foreshortning E serves also for the other two Squares -plac’d upon the same Ground-line, whole Angles being directed to the -Distance D, give as many Angles on the Visuals NO, MO. This done, erect a -Perpendicular on the Angle N, which in Geometrical Elevations is always -necessary, and is the third Line mention’d in the first Figure. Then -carry the Height A on NF, drawing the Visuals FO, NO, which determine the -Height ST, and that of the other Squares. - -It remains to be known, how to make use of the foresaid Preparation for -the Construction of the shadow’d Pedestals. - -On another Paper therefore dispose the Horizontal and Ground-lines, -together with the Point of Sight O, and the Perpendicular V, keeping the -same Measures as in the aforesaid Preparation, and doing as I have done. -You may prove by the Compasses, that NF is equal to 1, 5, and 2, 6, and -measuring ST, you’ll find it equal to 7, 3, then drawing the level Lines, -and the Visuals to the Point of Sight, you have the upper Face of the -Cube C in 1, 2, 3, 4. The same must be done in the others. In a word, the -Angles of the Plan give you the perpendicular Lines, and the Angles of -the Elevation give the level Lines, or those parallel to the Ground-line; -and this you are always to understand for the future. - - -FIGURA SEPTIMA. - -Aliud exemplum construendi vestigium geometricum, cum elevatione -longitudinis. - -_Vides hic stylobatam ~P~ in quatuor partes divisum, & adumbratum. Si -illum opticè delineare velis, construere debes supradictas præparationes, -geometricam nempe, & opticam. Nomine geometricæ intelligo vestigium -~A~, & elevationem ~B~; nomine vero opticæ, totum id quod includitur in -~GCDEO~._ - -_Transfer igitur latitudinem geometricam ~CD~ vestigii ~A~ super lineam -plani pariter ~CD~, & transfer longitudinem ~DE~ super lineam plani -pariter ~DE~, operans more solito; & habebis vestigium opticé. Transfer -posteà elevationem ~HX~ in ~CG~ perpendicularis; ducens visualem ~GO~, -eleva ad lineam ~GO~ omnem angulum, quem planum facit in linea ~CO~, & -habebis altitudinem necessariam etiam sectionis._ - -_Transferes denique circino in aliam chartam angulos vestigii, qui dabunt -tibi lineas perpendiculares, & anguli sectionis dabunt lineas planas: -Visuales vero duces ad punctum oculi._ - - -SEVENTH FIGURE. - -_Another Example of a Geometrical Plan, with the Elevation of its -Length._ - -If you would delineate in Perspective the Pedestal P, which you here -see divided into four Parts, and shadow’d; you must make the two -foregoing Preparations; namely, the Geometrical and the Perspective. -By the _Geometrical_, I mean the Plan A, and the Elevation B; By the -_Perspective_, all that’s contain’d within G, C, D, E, O. - -Then transfer the Geometrical Breadth CD of the Plan A, into CD of -the Ground-line; and the Length DE of the said Plan into DE of the -Ground-line working after the usual manner; and you will have the Plan in -Perspective. Again, set the Elevation HX on CG of the Perpendicular, and -drawing the Visual GO, elevate thereto every Angle made by the Plan on -the Line CO, and you have all the Heights necessary for the Profile. - -Lastly, by the Compasses you transport on a clean Paper the Angles of the -Plan, which give the perpendicular Lines; and those of the Profile, which -give the level Lines. The Visuals you draw to the Point of Sight. - - -FIGURA OCTAVA. - -Stylobata opticé. - -_Hic etiam postquam feceris supradictas præparationes, geometricam -scilicet, & opticam; facies præsentem stylobatam adumbratum, transferens -circino angulos vestigii, ut construas perpendiculares; & angulos -sectionis, ut formes lineas planas, ut supra. Nam sic duo anguli -vestigii ~MO~ dabunt lineas perpendiculares ~EF~; angulus vestigii ~R~ -dabit perpendicularem ~P~, & sic reliqui anguli dabunt reliquas lineas -perpendiculares. Similiter à sectione angulus ~I~ dabit lineam planam -~HN~. Breviter, primus terminus sectionis ~ID~ dabit altitudinem linearum -planarum in facie stylobatæ adumbrati ~EFHN~. Secundus terminus ~Q~ dabit -altitudinem faciei oppositæ, & occultæ ~P~._ - -_Duo tamen moneo; primum, ut faciens vestigia geometrica, ducas ab -elevatione ~A~ totidem lineas ad latera vestigii ~B~, quot angulos -invenies in prominentiis supradictæ elevationis ~A~, ut manifestè vides -in lineis quas ex punctis composui, illæ enim à stylobata ~A~ cadunt -super vestigium ~B~; quare prominentia major in elevatione ~L~ facit -lineam majorem ~L~ in vestigio._ - -_Secundum quod moneo sit, ut volens elongare vestigium opticè delineatum -~MOR~ à linea plani ~K~, quantum erit spatium ~C~ in eadem linea plani, -tantumdem elongabitur spatium ~G~ à linea ejusdem plani._ - - -EIGHTH FIGURE. - -_A Pedestal in Perspective._ - -Here also, after you have made the two foregoing Preparations, the -Geometrical and the Perspective; this shadow’d Pedestal is made by -taking with the Compasses the Angles of the Plan, for drawing the -Perpendiculars, and the Angles of the Profile for the level Lines, as -before. Thus the two Angles of the Plan MO, give the perpendicular Lines -EF. The Angle of the Plan R, gives the Perpendicular P; and the other -Angles give their respective Perpendiculars. So likewise in the Profile, -the Angle I gives the level Line HN. In short, the first Out-line of -the Profile ID gives the Height of the level Lines on the Front of the -shadow’d Pedestal. The other Out-line Q gives the Height of the occult -and back part thereof. - -Nevertheless, two things are to be observ’d; first, that in making the -Geometrical Plan, you draw from the Elevation A, as many Lines to the -Side of the Plan B, as you have Angles in the Projectures of the said -Elevation; as is manifest in the pointed Lines, which fall, from the -Upright A, on the Plan B, where that of the greatest Projecture L in the -Elevation makes the outer Line L of the Plan. - -The second thing to be observ’d, is, That if you would have the -Perspective-Plan MOR as far within the Ground-line K, as the Breadth -of the Space C on the same Line, the Space G will then be the Distance -thereof from the said Ground-line. - - -FIGURA NONA. - -Optica delineatio Architecturæ Jacobi Barozzii: & primum, de stylobata -Ordinis Etrusci. - -_Quandoquidem omnibus nota est Architectura Barozzii, eam hic penitus -immutatam cum suis regulis particularibus, & generalibus expono; Metieris -autem illam modulis ut fieri solet; qui igitur illam desiderat, in -sequentibus figuris inveniet totam, simulque discet opticè reddere. Cum -autem non minus Opticæ studioso quam Architecturæ necesse sit, efficere -delineamenta rei construendæ, ab hoc verè, ab illo fictè, id est, cum -uterque facere debeat vestigium, elevationem, sectionem, & faciem, ob id -delineavi hic stylobatam Ordinis Etrusci cum suo vestigio, quem vides -in ~AB~, ut faciliùs percipias quod in proxima figura dixi, à totidem -scilicet angulis prominentiarum elevationis, totidem ducendas esse -lineas super lineam vestigii; cum hoc necesse sit ad inveniendum illorum -angulorum cum istis lineis concursum in suis degradationibus. Nota, -longitudinem, quam voco ~F~ ductam in ~G~ esse illam, à qua non solùm -nascitur vestigii obliquitas, verùm etiam ab illa nascitur obliquitas -illius quam voco sectionem ~E~. Ob id in altero hujus ejusdem figuræ -stylobata totum id è contrario videbis._ - -_Non ampliùs repetam quonam modo eruatur nitida delineatio, de qua -superiùs pluries; dicam tamen angulos primi termini sectionis ~E~ -daturos lineas planas faciei ~D~, & angulos vestigii daturos omnes -perpendiculares._ - - -NINTH FIGURE. - -_The Architecture of ~Vignola~ put in Perspective; and first, the -Pedestal of the ~Tuscan~ Order._ - -Since every one is acquainted with _Vignola_’s Architecture, I determine -not to alter it, but to explain it, with its general and particular -Rules; measuring the same with Modules, after the usual manner. He -therefore that has it not, may find it in the following Figures, and -at the same time learn the Method of putting it in Perspective. And -whereas the Drawing the Plan, Elevation and Profile of what’s to be -built, is no less necessary for him that studies Perspective, than for -the Architect, the first performing in Appearance, what the latter does -in Reality; I have therefore here delineated the _Tuscan_ Pedestal, with -its Plan, as you see in AB, that you may the better apprehend what I said -in the foregoing Figure, That from all the Angles of Projecture in the -Elevation, Lines must be let fall on the Plan; this being of absolute -necessity for finding the Correspondence of the Angles with the Lines in -the Perspective Projection. Observe, that what I always call Length, as -from F to G, is that from which proceeds not only the Foreshortning of -the Plan; but also that which I call the Profile E. Wherefore, in the -opposite Pedestal of the same Figure, you’ll see a contrary Disposition -of the Whole. - -I shall not here repeat, how the finish’d Pedestal is taken from these; -having so largely spoken of that before; but briefly tell you, that the -Angles of the first Out-line of the Profile E give the level Lines of the -Face D, and the Angles of the Plan give all the Perpendiculars. - - -FIGURA DECIMA. - -Stylobata Doricus, & ratio vitandi difficultatem quamdam, quæ occurrit -inter illum opticè delineandum. - -_Hic oritur difficultas hæc. Vestigium ~A~ opticè translatum in ~C~ -adeò contrahitur, ut distinctè videri nequeat ubi collocetur circini -pes, ut transferri possint perpendiculares stylobatæ adumbrati; totaque -hæc difficultas oritur à propinquitate quam habet linea horizontalis, -seu punctum oculi cum linea plani. Ut igitur illam vincas: Duces lineam -plani inferiùs quantum libuerit, & super illam feres denuò latitudinem, & -longitudinem more solito, retinendo puncta oculi, & distantiæ ~OF~, & sic -videbis vestigia magis minusve distincta; Vestigium enim ~E~ distinctius -est vestigio ~D~, & ~D~ distinctius est vestigio ~C~._ - - -TENTH FIGURE. - -_A ~Dorick~ Pedestal, with the Manner of shunning a Difficulty, which -occurs in putting the same in Perspective._ - -In this Figure a Difficulty arises, which is this; That the Plan A put -in Perspective in C, is so foreshorten’d, that one can’t see distinctly, -where to place the Compasses, for transferring the Perpendiculars on -the shadow’d Pedestal; which is caus’d by the too near Approach of the -horizontal Line to the Ground-line. For avoiding this Difficulty, draw -another Ground-line as much below the first as you please, and carry the -Breadth and Length thereon, after the usual manner, still keeping the -same Points of Sight and Distance O and F: And according to the Removal -of the Ground-line, the Plans will be more or less distinct; as you see -the Plan E is more distinct than D, and D is more so than C. - - -FIGURA UNDECIMA. - -Stylobata Ionicus, & ratio vitandi aliam difficultatem in elevationibus. - -_In elevationibus etiam sectionis opticè potest accidere, ut si visualis -~LK~ nimis recta sit, sectio ~B~ restringatur. Elongando lineam plani ab -~L~ ad ~M~, visualis ~MN~ erit inclinatior, & consequenter sectio ~C~ -erit latior, & distinctior._ - -_Nota, difficultatem hanc sæpe sæpiùs te habiturum in figuris præcipuè, -quæ multas lineas habent, ut in figura quadragesimasecunda, ubi pariter -rationem vitandi confusionem reddam._ - -_Neque tibi molestiæ sim, quod in hac figura lineam horizontalem infra -lineam plani collocaverim, id enim feci, ut illarum diversos effectus -videas, utque tu in tuis studiis mutes, & discas._ - - -ELEVENTH FIGURE. - -_The ~Ionick~ Pedestal, and the Way to shun another Difficulty in the -Elevations._ - -In Elevations of the Profile in Perspective, it may sometimes happen, -that the Visual LK may be so direct, as to render the Profile B too close -and narrow; wherefore prolonging the Ground-line from L to M, make the -Visual MN, which being much more oblique, does consequently render the -Profile C more broad and distinct. - -And observe, that this Difficulty will very often occur; especially in -Figures that have many Lines, as the Forty-second Figure has, where I -speak also of the manner of avoiding the same. - -Nor let it trouble you, that in this Figure I have plac’d the horizontal -Line below the Ground-line; which I have done, that you might see their -different Effects, and by changing the Disposition of your Designs, -improve and learn. - - -FIGURA DUODECIMA. - -Stylobata Corinthius cum suis pilis. - -_Fecisse septimam figuram magno tibi documento erit ad construendum, -& dividendum stylobatam ~A~, & vestigium ~B~; cum nihil addere debeas -præter pilas ~C~ cum coronice, quæ duo latera ambit. Opticè hoc vestigium -delineabis in ~D~, quæ delineatio distinctior est, quia inferiùs duxi -lineam plani; & distinctior etiam est sectio ~E~, cum elongaverim -visualem ~FG~. Sic semper agam, ut detur locus figuræ adumbratæ, & ut -etiam videas perpendiculares stylobatæ adumbrati cadere super angulos -vestigii, & lineas planas incidere è diametro super angulos sectionis -~E~. Iterùm libenter moneo, ut facias supradictas præparationes in -chartulis separatis, ut initio assuescas transferendis figuris nitidis -circino; facile enim tibi postea erit integras machinas Perspectivæ -jucundioris delineare, ut videbis: in hoc enim tota regulæ hujusce, & -totius operis facilitas sita est._ - - -TWELFTH FIGURE. - -_A ~Corinthian~ Pedestal, with its Pilasters._ - -The Performance of the Seventh Figure will be a great Assistance to you, -in the Construction and Division of this Pedestal A, and the Plan B; -since you have nothing more to add here, but the Pilasters C, and the -Mouldings which surround the two Sides. This Plan is put in Perspective -in D, and becomes more distinct by my sinking the Ground-line lower; -and the Profile E is also more distinct by the Removal of the Visual -FG, as mention’d in the foregoing Chapter. This I shall always do, that -there may remain Room for the shadow’d Figure, and that you may also see -that the Perpendiculars of the shaded Pedestal fall directly upon the -Angles of the Plan, and that the level Lines directly answer the Angles -of the Profile E. I repeat my Advice, that you would make the foresaid -Preparations on several Papers, and accustom yourself at the beginning -to take off the finish’d Figures with the Compasses; for it will become -very easy to you afterward, to design entire Machines of delightful -Perspectives, as you’ll see hereafter. And indeed in this Practice, the -Facility of this Rule, and of all that follows in this Work, does chiefly -consist. - - - - -_Respondetur objectioni factæ circa punctum oculi opticum._ - - Non omnium sensus est, uni optico operi unicum tantùm punctum - assignare, _e. g._ toti spatio fornicis, tholi, & tribunæ, quam - vocant, expressæ in figura nonagesimatertia, nolunt concedi - unicum punctum, volunt concedi plura. - - -_Respondeo, objectionem hanc dupliciter intelligi posse: vel enim -intelligi posset, non esse assignandum unicum punctum toti illi spatio; -atque in hoc sensu vera est; cum enim spatium illud valde oblongum sit, -dividi debuit in partes, atque assignanda tribunæ, quam dicunt, tholo, -& fornici, propria puncta; cum hoc communiter doceant, ubi situs nimium -est longus, & parùm altus. Vel potest intelligi de qualibet ex dictis -partibus, & sic intellecta penitùs falsa est. Primò, quia præstantiores -fornices aularum, & templorum, qui optico artificio ornati sint, si -unicum opus reddunt, à suismet authoribus determinatum idemque unicum -punctum accepisse compertum est. Secundò, quia cum ars optica sit mera -veri fictio, non id pictor facere potest, ut à qualibet parte simulet -veritatem, verùm ab uno determinato puncto id ostendit. Tertiò, quia si, -~e. g.~ fornici, qui uno integroque optico opere ornetur, plura puncta -assignaveris, nullum reperies locum, unde integrum opus spectare possis, -& ad summum ex quolibet puncto tantùm partem illius spectabis, nusquam -verò totum opus. Ex dictis igitur rationibus concludo ab inducentibus -plura puncta in eodem opere induci malum majus eo, quod unicum punctum -inducit; quare hoc omnino necessarium est situi in quo unicum opus -formandum sit, ad quod collimare debeant ex omni operis parte figuræ -simul & architectura. Quo posito, negari rationabiliter nequit, à -me etiam concedi unicum punctum spectando fornici amplo, aptoque ad -repræsentandum unicum opus, qualis est fornix in D. Ignatii templo. Si -verò propter situm irregularem, ut dicimus, architectura extra punctum -aliquantulum deformetur, & figuræ pariter operi optico intermixtæ extra -commune punctum aliquam patientur deformitatem, præterquam quod à -supradictis rationibus excusatur, nequaquam id vitio arti est, sed laudi; -quandoquidem ars à suo puncto exhibet, proportione positâ, ut rectum, ut -planum, ut concavum, id quod tale non est._ - - - - -An Answer to the Objection made about the Point of Sight in Perspective. - - _Every one does not approve, that in a Perspective of great - Extent one Point of Sight only should be assign’d the whole - Work; as for Example, In the whole Length of the Nave, Cupola, - and Tribune, express’d in the Ninety-third Figure, they will by - no means allow of one single Point, but insist upon several._ - - -I answer, This Objection may be understood two ways; either that one -Point alone is not sufficient for that whole Length, and in this sense -’tis true; for that Space being very long, it ought to be divided into -Parts, and proper Points assign’d to the Tribune, Cupola, and Vault -of the Nave; as is commonly taught, where the Situation is of a great -Length, and not very high. Or it may be understood of any One of the said -Parts, and so is altogether false. _First_, Because in the Vaults of -Halls or Churches painted by the greatest Masters, if they consist of one -Piece only, we find but one Point of Sight assign’d. _Secondly_, Since -Perspective is but a Counterfeiting of the Truth, the Painter is not -oblig’d to make it appear real when seen from _Any_ part, but from _One_ -determinate Point only. _Thirdly_, Because, if in a Vault, for Example, -where you would paint one entire Design of Architecture and Figures, you -assign several Points of Sight, you will find no place whence you may -take a perfect View of the Whole, and at best you can only view each -Part from its proper Point. From all which Reasons I conclude, that the -Introduction of many Points into the same Piece, is more injurious to the -Work, than making use of one only: Wherefore ’tis absolutely necessary in -a regular Situation, and where the Work is all of a piece, so to place -the same, as that the Figures and Architecture may from every part of -the Design have respect thereto. This suppos’d, I confess that I myself -make use of one Point of Sight only, in very large Vaults that consist -of one Design, such as that of the Nave of the Church of S. _Ignatius_. -If therefore through the Irregularity of the Place, the Architecture -appear with some Deformity, and the Figures intermix’d therewith seem any -thing lame and imperfect when view’d out of the proper Point, besides -the Reasons just now given, it’s so far from being a Fault, that I look -upon it as an Excellency in the Work, that when view’d from the Point -determin’d, it appear, with due Proportion, streight, flat, or concave; -when in reality it is not so. - - - - -INDEX. - - - FIG. - - _INSTRUMENTA paranda_, UTENSILS for Drawing. - - _Explicatio linearum plani I. Explication of the Lines of - & horizontis, ac punctorum the Plan and Horizon, and of - oculi & distantiæ_, the Points of the Eye and of - the Distance. - - _Modus delineandi opticè II. The Manner of delineating a - quadratum_, Square in Perspective. - - _Optica delineatio III. The Delineation of an oblong - rectanguli, alterâ parte Square in Perspective. - longioris_, - - _Optica descriptio quadrati IV. The Optical Delineation of a - duplicis_, double Square. - - _Vestigia quadratorum cum V. Plans of Squares with their - elevationibus_, Elevations. - - _Modus opticæ delineationis VI. The Manner of designing in - absque lineis occultis_, Perspective without occult - Lines. - - _Aliud exemplum vestigii VII. Another Example of a - geometrici, cum elevatione Geometrical Plan and Upright - longitudinis_, put into Perspective. - - _Optica projectio stylobatæ_, VIII. The Projection of a Pedestal - in Perspective. - - _Optica delineatio IX. The Architecture of _Vignola_ - Architecturæ Jacobi in Perspective, and first of - Barozzii, & primum de his Pedestal of the _Tuscan_ - stylobata Ordinis Etrusci_, Order. - - _Optica deformatio stylobatæ X. A _Dorick_ Pedestal in - Dorici; ubi de modo vitandi Perspective, with the Manner - confusionem in vestigiis of avoiding Confusion in - delineandis_, designing the Plans. - - _Stylobatæ Ionici XI. The _Ionick_ Pedestal in - deformatio; ubi de vitanda Perspective, with the Manner - confusione in elevationibus_, of avoiding Confusion in - Elevations. - - _Deformatio stylobatæ XII. The _Corinthian_ Pedestal, with - Corinthii, cum duabus pilis_, its Pilasters, in Perspective. - - _Projectio stylobatæ Ordinis XIII. The Projection of a Pedestal - Compositi_, of the _Composite_ Order. - - _Deformatio circulorum_, XIV. Circles in Perspective. - - _Optica delineatio columnæ_, XV. A Column in Perspective. - - _Optica projectio basis XVI. The _Tuscan_ Base in - Etruscæ_, Perspective. - - _Deformatio basis Doricæ_, XVII. The _Dorick_ Base in - Perspective. - - _Optica delineatio basis XVIII. The _Ionick_ Base in - Ionicæ_, Perspective. - - _Optica imminutio basis XIX. The _Corinthian_ Base - Corinthiæ_, in Perspective. - - _Basis Atticurga opticè XX. The _Attick_ Base in - imminuta_, Perspective. - - _Optica imminutio capitelli XXI. The _Tuscan_ Capital in - Etrusci_, Perspective. - - _Optica projectio capitelli XXII. The Projection of a - Dorici_, _Dorick_ Capital in - Perspective. - - _Deformatio capitelli XXIII. The _Ionick_ Capital in - Ionici_, Perspective. - - _Optica projectio capitelli XXIV. The _Corinthian_ Capital in - Corinthii_, Perspective. - - _Optica descriptio capitelli XXV. The _Composite_ Capital in - Compositi_, Perspective. - - _Deformatio coronicis XXVI. The _Tuscan_ Entablature - Etruscæ_, in Perspective. - - _Optica delineatio coronicis XXVII. The _Dorick_ Entablature - Doricæ_, in Perspective. - - _Præparatio figuræ XXVIII. Preparatory to the following - sequentis_, Figure. - - _Optica projectio ædificii XXIX. A Projection of the _Dorick_ - Dorici_, Order in Perspective. - - _Optica projectio ædificii XXX. An _Ionick_ Work in - Ionici; ubi de modo jungendi Perspective, with the Manner - fictum cum vero_, of reconciling the fictitious - to the solid Architecture. - - _Optica projectio coronicis XXXI. The Optick Projection of a - Corinthiæ, cum capitello & _Corinthian_ Cornice, with the - summitate columnæ_, Capital and part of the Column. - - _Delineatio geometrica XXXII. The Geometrical Design of a - coronicis Ordinis Compositi_, Cornice of the _Composite_ - Order. - - _Deformatio coronicis XXXIII. A _Composite_ Cornice in - Compositæ_, Perspective. - - _Præparatio ad figuram XXXIV. Preparatory to the - trigesimamquintam_, Thirty-fifth. - - _Deformatio coronicis XXXV. A Side-View of the - Compositæ ad latus inspectæ_, _Composite_ Cornice in - Perspective. - - _Præparatio ad figuram XXXVI. Preparatory to the - trigesimamseptimam_, Thirty-seventh. - - _Deformatio columnæ Etruscæ_, XXXVII. A _Tuscan_ Column in - Perspective. - - _Præparatio ad figuram XXXVIII. Preparatory to the - trigesimamnonam_, Thirty-ninth. - - _Deformatio ædificii Dorici_, XXXIX. A Piece of _Dorick_ - Architecture in Perspective. - - _Vestigium geometricum XL. The Geometrical Plan of a - ædificii Ordinis Dorici_, Design of the _Dorick_ Order. - - _Elevatio geometrica XLI. The Geometrical Elevation of - ædificii Dorici_, the foregoing Design. - - _Modus vitandi confusionem XLII. The Manner of avoiding - in contractione vestigiorum Confusion in reducing Plans - & elevationum_, and Elevations into - Perspective. - - _Contractio vestigii figuræ XLIII. The Plan of the Fortieth - quadragesimæ_, Figure in Perspective. - - _Contractio elevationis XLIV. The Elevation of the - figuræ quadragesimæprimæ_, Forty-first Figure in - Perspective. - - _Dimidium ædificii Dorici XLV. One half of the _Dorick_ - opticè deformati_, Design in Perspective. - - _Alterum dimidium ejusdem XLVI. The other half of the - ædificii_, same Design. - - _Vestigia ædificii Ionici_, XLVII. The Plan of an _Ionick_ - Building. - - _Elevatio geometrica XLVIII. Geometrical Upright of the - ædificii Ionici_, foregoing _Ionick_ Design. - - _Deformatio elevationis XLIX. The Elevation of the _Ionick_ - ædificii Ionici_, Design in Perspective. - - _Architectura Ionica_, L. A Design of _Ionick_ - Architecture. - - _Ordo Corinthius_, LI. A _Corinthian_ Design in - Perspective. - - _Delineatio columnæ spiralis LII. The Description of a - Ordinis Compositi_, wreath’d Column of the - _Composite_ Order. - - _Ordines Architecturæ LIII. A. The Orders of Architecture - desumpti ex Palladio & taken from _Palladio_ and - Scamozzio_, _Scamozzi_. - - _Modus triplex delineandi LIII. B. Three different ways of - columnas spirales_, delineating wreath’d Columns. - - _Vestigia ædificii Ordinis LIV. The Plan of a Design of the - Corinthii_, _Corinthian_ Order. - - _Elevatio ædificii Ordinis LV. The Geometrical Elevation - Corinthii_, of a _Corinthian_ Work. - - _Deformatio vestigiorum LVI. The Perspective-Plans and - & elevationis ædificii Upright of the _Corinthian_ - Corinthii_, Design foregoing. - - _Adumbratio figuræ LVII. The rough Draught of the - sequentis_, following Figure. - - _Ædificium Ordinis Corinthii LVIII. Part of an Octangular Work - octangulare_, of the _Corinthian_ Order. - - _Vestigia Tabernaculi LIX. The Plans of an Octangular - octangularis_, Tabernacle. - - _Tabernaculum octangulare_, LX. An Octangular Tabernacle in - Perspective. - - _Modus erigendi machinas quæ LXI. The Manner of erecting - constant pluribus ordinibus Machines that consist of - telariorum_, several Ranges of Frames. - - _De reticulandis telariis, LXII. Of making the Net-work on - quæ repræsentent ædificia Frames, for representing - solida_, the Architecture as solid. - - _Vestigia ædificii quadrati_, LXIII. The Plan of a square Design. - - _Ædificium quadratum_, LXIV. A square Design in Perspective. - - _Vestigium ædificii rotundi LXV. The Plan of a Circular Work - opticè imminutum_, in Perspective. - - _Projectio ædificii rotundi_, LXVI. A Circular Design in - Perspective. - - _Vestigium geometricum, ac LXVII. The Geometrical Plan, and - prima præparatio ad figuram first Preparation to the - septuagesimamprimam_, Seventy-first Figure. - - _Elevatio geometrica LXVIII. The Geometrical Elevation of - vestigii præcedentis, & the foregoing Plan, and - secunda præparatio ad second Preparation to the - figuram septuagesimamprimam_, Seventy-first Figure. - - _Deformatio vestigii figuræ LXIX. The Plan of the Sixty-seventh - sexagesimæseptimæ, & Figure in Perspective, and - præparatio tertia ad figuram third Preparation to the - septuagesimamprimam_, Seventy-first Figure. - - _Deformatio elevationis LXX. The Perspective of the - figuræ sexagesimæoctavæ, & Elevation of the Sixty-eighth - præparatio quarta ad figuram Figure, and fourth Preparation - septuagesimamprimam_, to the Seventy-first. - - _Theatrum repræsentans LXXI. A Theater representing the - nuptias Canæ Galilææ, Marriage of _Cana_ in - constructum Romæ anno _Galilee_, erected in the - 1685, in expositione Ven. Jesuits Church at _Rome_, - Sacramenti, in templo 1685, for the Solemnity of - Farnesiano Societatis Jesu_, exposing the Holy Sacrament. - - _De theatris scenicis_, LXXII. Of Scenes for the Stage. - - _Aliud vestigium theatri; LXXIII. Another Plan of a Theater, - ubi de modo inveniendi ejus with the Method of finding - punctum_, the Point of Sight therein. - - _Sectio scenarum theatri_, LXXIV. The Section or Profile of - Scenes for Theaters. - - _Elevatio scenarum coram LXXV. The Elevation of Scenes in - inspectarum; ubi docetur Front, and how the oblique - artificium, ut scenæ obliquæ Scenes are made to appear - appareant rectæ_, direct. - - _Modus delineandi exemplar LXXVI. The Manner of delineating - scenarum_, the Designs of Scenes. - - _Modus reticulandi & LXXVII. The Manner of making the - pingendi scenas theatri_, Net-work or Squares, and - painting the Scenes of - Theaters. - - _De projectionibus LXXVIII. Of horizontal Projections. - horizontalibus_, - - _Projectiones vestigii & LXXIX. The Plan and Elevation of - elevationis mutuli_, a Corbel in Perspective. - - _Horizontalis projectio LXXX. The horizontal Projection - mutuli inumbrati_, of a shaded Corbel. - - _Stylobatæ Corinthii LXXXI. _Corinthian_ Pedestals in - horizontaliter contracti_, an horizontal Perspective. - - _Columna Corinthia LXXXII. A _Corinthian_ Column in - horizontaliter deformata_, horizontal Perspective. - - _Capitella Corinthia LXXXIII. A _Corinthian_ Capital in - horizontaliter contracta_, horizontal Perspective. - - _Coronix Corinthia_, LXXXIV. A _Corinthian_ Cornice. - - _Coronix Corinthia LXXXV. A _Corinthian_ Cornice in - horizontaliter contracta_, horizontal Perspective. - - _Horizontalis projectio LXXXVI. A Column in horizontal - columnæ_, Perspective. - - _Præparatio necessaria ad LXXXVII. The Preparation necessary to - sequentem figuram, & ad the following Figure, and to - projectiones horizontales all other horizontal - in laquearibus vel Perspectives, whether on flat - testudinibus_, or vaulted Ceilings. - - _Horizontalis projectio LXXXVIII. The horizontal Projection - balustiorum figuræ of the Balustrade of the - octogesimæseptimæ, cum Eighty-seventh Figure, view’d - brevi distantia_, at a small Distance. - - _Horizontalis projectio LXXXIX. A horizontal Piece of - Architecturæ in laqueari Architecture in a square - quadrato_, Ceiling. - - _Horizontalis projectio XC. A Cupola in horizontal - tholi_, Perspective. - - _Tholus figuræ nonagesimæ, XCI. The Cupola of Fig. 90, with - cum luminibus & umbris_, its Lights and Shades. - - _Tholus octangularis_, XCII. An Octangular Cupola. - - _Vestigium templi XCIII. The Geometrical Plan of S. - Ludovisiani S. Ignatii _Ignatius_’s Church at _Rome_. - almæ urbis_, - - _Orthographia templi XCIV. The Orthography of S. - Ludovisiani_, _Ignatius_’s Church. - - _Aliæ præparationes ad XCV. Other Preparations to - figuras 98 & 99_, the 98th and 99th Figures. - - _Aliæ præparationes ad XCVI. Other Preparations to - figuras 98 & 99_, the 98th and 99th Figures. - - _Alia præparatio ad figuras XCVII. Another Preparation to the - 98 & 99_, 98th and 99th Figures. - - _Quadrans Architecturæ XCVIII. Fourth-part of the - horizontalis in fornice, Architectonical Design on the - cum luminibus & umbris_, Vault of S. _Ignatius_’s - Church, with its Lights and - Shades. - - _Alter quadrans totius XCIX. Another Quarter of the - operis_, whole Design. - - _Modus reticulationis C. The Method of drawing the - faciendæ in testudinibus_, Net-work on Vaults. - -_FINIS._ - - - - -SUBSCRIBERS. - - - A - - His Grace the DUKE of S^{T}. ALBANS. - _M^{r}. Tho. Acres._ - _Capt. Matthew Adams._ - _Hen. Aldrich, DD. DC.C._ - _M^{r}. Joseph Alleine Writing M^{r}._ - _M^{r}. W^{m}. Allingham, Teacher of Mathemat. Chan̄el-Row-Westm^{r}._ - _James Anderson, Writer to Her Ma^{tys} Signet, Reg. Scot._ - _M^{r}. Robert Andrews, Letter-Founder._ - _Tho. Atkinson, Gent._ - _J. Aislabie, Esq^{r}._ - - B - - _M^{r}. R. Baker, Teacher of Mathemat._ - _M^{r}. Henry Bankes._ - _M^{r}. Matthew Bankes._ - _M^{r}. John Barnes, Bookseller._ - _M^{r}. Chr. Bateman, Bookseller._ - _Allen Bathurst, Esqꝫ._ - _M^{r}. Benj. Beardwell, Printer._ - His Grace the DUKE of BEAUFORT. - The Hon^{ble}. the Lady Mary Bertie. - _M^{r}. Philip Bishop, Bookseller, Exon._ - _M^{r}. Sam^{l}. du Bois._ - _Jo^{n}. Bridgeman, Esqꝫ of Blodwell Salop._ - _James Broughton, of Westm^{r}. Gent._ - _M^{r}. Jo^{n}. Buckler, for the Mathemat. Soc. Jones - Coffee-house Finch-lane._ - _M^{r}. W^{m}. Butcher, Carpenter, Richmond._ - _M^{r}. Jo^{n}. Brown, Cl. of the Works at Winds^{r}._ - _Ferd. Buss, Carp^{r}._ - - C - - _M^{r}. Chr. Cass._ - _John Churchill, Esqꝫ, M^{r}. Carpenter, to Her MA^{TY}._ - _M^{r}. Rob^{t}. Churchill, Mason._ - _M^{r}. Tho. Churchill Bricklayer Westm._ - _Edw^{d}. Coke, Esqꝫ._ - _M^{r}. Collins Mason._ - The R^{t}. Hon^{ble}. The L^{D} CONINGSBY. - _M^{r}. Rich^{d}. Conyers._ - _His Excell. Fr. Cornaro, Venetian Amb._ - _Will. Cowper, Surgeon._ - _John Crauford, Esqꝫ._ - _Tho. Curtis, Joyner._ - - D - - The R^{t}. Hon^{ble}. The EARL of DENBIGH. - _M^{r}. Charles Delafaye._ - _Edmund Dummer, Esqꝫ._ - _M^{r}. John Dowling, Painter._ - - E - - _M^{r}. Talbot Edwards, Engineer to Her MA^{TY}._ - _M^{r}. John Ellis, Com. Brazen-Nose-Coll. Oxon._ - _M^{r}. Emmet._ - _M^{r}. Robert Inglish, Compt^{ll}. of Her MA^{TIES}. Royal - Hosp^{l}. at Chelsea._ - The R^{t}. Hon^{ble}. The EARL of ESSEX. - _M^{r}. John Ettie, of York._ - _M^{r}. Rich^{d}. Evans._ - - F - - _M^{r}. John Farlow, Painter._ - _Matthew Foxall, Gent._ - - G - - _John Gape, Esqꝫ, S^{t}. Albans._ - _Sam^{l}. Gee, Gent._ - His Excell. S^{nr}. Jacob Giraldi K^{t}. Envoy from the Gr. D. - of Toscany. - _M^{r}. Tho. Gittins Bookseller Shrewsbury._ - _Capt. John Goodwyn._ - _M^{r}. John Gough, Agent._ - _W^{m}. le Grand, Esqꝫ._ - _M^{r}. Rich^{d}. Gregory, Carpenter._ - _M^{r}. Jam. Grove, M^{r}. Carpenter._ - _M^{r}. John Grove, Her MA^{ties}. Plaisterer._ - _Rich^{d}. Graham, Esqꝫ._ - - H - - _M^{r}. Charles Hale, Plomber._ - _S^{r}. Tho. Hanmer, Bar^{t}._ - _John Harris, D.D._ - _M^{r}. Tho. Harris, Plate Polisher._ - _M^{r}. N. Hawksmoor, Cl. of Her MA^{TIES} Works._ - _M^{r}. Jacob Henckell._ - _John Henley, Esqꝫ._ - _M^{r}. Rob^{t}. Hester._ - _M^{r}. Tho: Hill._ - _M^{r}. Tho: Highmore, Serjeant-Painter._ - _M^{r}. Cha. Hopson, M^{r}. Joyner._ - _S^{r}. James How, K^{t}._ - _Mathew Humberston, Esqꝫ._ - _S^{r}. George Hungerford, K^{t}. Cadnum Wilts._ - _Sam. Horn, Painter._ - - I - - _M^{r}. John James, of Greenwich._ - _M^{r}. R. Janeway, Printer._ - _M^{r}. John Johnson._ - _M^{r}. Hen. Jones._ - - K - - _M^{r}. Rob^{t}. Knaplock, Bookseller._ - - L - - _M^{r}. Bernard Lens Painter, Drawing-M^{r}. to Christs-Hospitall._ - _M^{r}. Bernard Lens_, } Painters. - _M^{r}. Edw^{d}. Lens_, } - - M - - _M^{r}. Sam. Marriot, Jun^{r}._ - _M^{r}. John Mist, of S^{t}. Ann Westm^{r}._ - _M^{r}. Benj. Motte, Printer._ - _M^{r}. James Moore._ - _M^{r}. Rob^{t}. More, Writing-M^{r}._ - _M^{r}. George Moult, Chymist._ - _Jos. Moyle, Esqꝫ._ - - N - - _W^{m}. Naper, Esq^{r}._ - _David Netto._ - _M^{r}. W^{m}. Newton, Math. M^{r}. to Chr. Hosp^{l}._ - _W^{m}. Nicholas, Esq^{r}._ - _M^{r}. John Nicholson, Bookseller._ - _M^{r}. John Nix._ - _M^{r}. John Norris, of Westm^{r}._ - _M^{r}. John Nutt, Printer._ - - O - - _D^{r}. Adam Oatley, of Pickford, ArchD. of Salop and Hereford._ - _M^{r}. Austin Oldesworth, Stationer._ - _M^{r}. Dan^{l}. Osburn B.D. Exeter Coll._ - His Grace the DUKE of ORMOND. - _S^{r}. James Oxenden, K^{t}. Bart._ - - P - - _Ralph Palmer, Esqꝫ._ - _M^{r}. Barth. Peisley, Oxon._ - _M^{r}. Elias Pen Writing-M^{r}._ - _M^{r}. Tho. Pestel, Jeweller._ - _Clement Petit, Esqꝫ._ - _Madam Dorothea Petit._ - _M^{r}. James Petiver, Pharm. Lond. FRS._ - _M^{r}. Edmund Powel, Printer._ - _M^{r}. John Paine._ - - R - - The R^{t}. Hon^{ble} The LORD RABY. - The R^{t}. Hon^{ble} Richard EARL of RANELAGH. - _Edw. Richards, Esqꝫ, LB. Exeter Coll._ - _Benj. Robinson Sec. to the Dutchess of Bucclough._ - _D^{r}. Tancred Robinson._ - _M^{r}. Rich^{d}. Rogerson, Carpenter._ - _Chr. Rawlinson, Esqꝫ, of Cark-Hall, Lanc._ - - S - - The Right Hon^{ble} James EARL of SALISBURY, Christ Church Oxon. - _M^{r}. John Savage_, A. M. - _Edw. Sayer, Esq^{r}, of Barkhamsteed._ - _M^{r}. Will. Scrimshire._ - The Right Hon^{ble} The EARL of SEAFIELD, Chanc. of Scotland. - D^{r}. Hans Sloane, S.R.S. - _M^{r}. Joseph Smart, Town-Clerks-Office._ - _M^{r}. Ralph Snow, Writing-M^{r}._ - _Sam. Stebbins, Esq^{r}._ - _Rob. Steel, Bookbinder, in little Britain._ - _M^{r}. James Stone, Gent._ - _M^{r}. John Stuart, Stationer._ - _M^{r}. Jacob Sturt, of Woodhouse, Sussex._ - - T - - _M^{r}. John Tallman._ - _M^{r}. John Taylor._ - _M^{r}. Lewis Thomas, Oxon._ - _M^{r}. John Thorpe_, A.M. F.R.S. - _M^{r}. Edw. Thwaites_, A.M. Queens Coll. - _M^{r}. John Tijou._ - _Andr. Tooke_, A.M. _Geom. Prof. Gresham Col._ - _Benj. Tooke, Bookseller._ - _M^{r}. Will. Townsend, Oxon._ - _Lewis Tremayne, Esq^{r}._ - _Capt. Edw. Tuffnall, S^{t}. Marg^{t}. Westm^{r}._ - _M^{r}. John Tuffnall, Joyner, S^{t}. Marg^{t}. Westm^{r}._ - _Cholmondley Turner, Esq^{r}._ - - V - - _J. Vanbrugh, Compt^{ll}. of Her MA^{ties} Works &c._ - - W - - _Sam^{l}. Waters, Gent._ - _M^{r}. Jo^{n}. Wilbraham, Brazen-Nose-Coll._ - _M^{r}. John Wilkinson, of the Excheq^{r} Gent._ - _M^{r}. John White._ - _M^{r}. Sam^{l}. Whitfield._ - _M^{r}. Tho. Whitmore, Painter._ - _M^{r}. John Williams, Printer._ - _M^{r}. Waldive Willington._ - _S^{r}. Francis Windham K^{t}._ - _M^{r}. Henry Wise, M^{r}. Gardener._ - _Nicol Wolstenholme, Esq^{r}._ - S^{r}. Chr. Wren K^{t}. Surv^{r}. Gen^{l}. of Her MA^{TIES} Works. - - - - -Transcriber’s Note - - -The following is a list of changes made to the original text to correct -suspected printing errors: - -Under the heading: - - FIGURA QUARTA ~6~, ~7~, => ~6~, ~7~, ~O~ - FIGURA OCTAVA. ex lilinea => ex linea - The Ninth Figure. yon must => you must - Figura Trigesimaprima. qudratâ => quadratâ - Figura Trigesimaquinta. denineationem => delineationem - The Seventy-second FIGURE. hundred an twenty => hundred and twenty - FIGURA OCTOGESIMA. qnam => quam - FIGURA Nonagesima. centrum => Centrum - Figura Nonagesimaprima. spospondit => spopondit - FIGURA SECUNDA. longitudidinem => longitudinem - FIGURA QUINTA. superoiri => superiori - INDEX. Doric => Dorick (twice, lines XL and XLV) - SUBSCRIBERS. Gr. D. of Tosoany => Gr. D. of Toscany - Respondetur objectioni... punctum aliqualem => punctum aliquam - - - - - -End of the Project Gutenberg EBook of Rules and Examples of Perspective -proper for Painters and Architect, by Andrea Pozzo - -*** END OF THIS PROJECT GUTENBERG EBOOK RULES, EXAMPLES OF PERSPECTIVE *** - -***** This file should be named 56312-0.txt or 56312-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/5/6/3/1/56312/ - -Produced by Chris Curnow and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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