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+Project Gutenberg's Of the Just Shaping of Letters, by Albrecht Dürer
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Of the Just Shaping of Letters
+
+Author: Albrecht Dürer
+
+Translator: R. T. Nichol
+
+Release Date: August 16, 2011 [EBook #37103]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK OF THE JUST SHAPING OF LETTERS ***
+
+
+
+
+Produced by Ben Courtney, Jana Srna and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+
+  [ Transcriber's Note:
+
+    Every effort has been made to replicate this text as faithfully
+    as possible, including inconsistencies in spelling and hyphenation.
+    No changes have been made to the printed text.
+  ]
+
+
+
+
+  OF THE JUST SHAPING OF LETTERS
+
+  BY ALBRECHT DÜRER
+
+  TRANSLATED
+  BY
+  R. T. NICHOL
+
+  FROM THE LATIN TEXT OF
+  THE EDITION OF
+  MDXXXV
+
+
+
+
+  OF THE JUST
+  SHAPING OF
+  LETTERS
+
+  FROM THE APPLIED
+  GEOMETRY OF
+  ALBRECHT
+  DÜRER
+  BOOK
+  JJJ
+
+  DOVER PUBLICATIONS, INC. NEW YORK
+
+
+
+
+ALBRECHT DÜRER TO WILIBALD PIRCKHEIMER HIS PATRON AND VERY GOOD FRIEND
+GREETING:
+
+
+[Illustration]
+
+In our Germany, most excellent Wilibald, are to be found at the present
+day many young men of a happy talent for the Art Pictorial, who without
+any artistic training whatever, but taught only by their daily exercise
+of it, have run riot like an unpruned tree, so that unhesitatingly and
+without compunction they turn out their works, purely according to their
+own judgment. But when great and ingenious artists behold their so inept
+performances, not undeservedly do they ridicule the blindness of such
+men; since sane judgment abhors nothing so much as a picture perpetrated
+with no technical knowledge, although with plenty of care and diligence.
+Now the sole reason why painters of this sort are not aware of their own
+error is that they have not learnt Geometry, without which no one can
+either be or become an absolute artist; but the blame for this should be
+laid upon their masters, who themselves are ignorant of this art. Since
+this is in very truth the foundation of the whole graphic art, it seems
+to me a good thing to set down for studious beginners a few rudiments,
+in which I might, as it were, furnish them with a handle for using the
+compass and the rule, and thence, by seeing Truth itself before their
+eyes, they might become not only zealous of the arts, but even arrive at
+a great and true understanding of them.
+
+Now, although in our own time, and amongst ourselves, the Art Pictorial
+is in ill repute with some, as being held to minister incitement to
+idolatry, yet a Christian man is no more enticed to superstition by
+pictures or images, than is an honest man girt with a sword to highway
+robbery. Certes he would be a witless creature who would willingly adore
+either pictures or images of wood or stone. On the contrary, a picture
+is the rather edifying and agreeable to Christian religion and duty, if
+only it be fairly, artificially, and correctly painted.
+
+In what honour and dignity this art was anciently held amongst the
+Greeks and Romans, the old authors sufficiently testify; though
+afterwards all but lost, while it lay hid for more than a thousand
+years. It has now at length, only within the last two hundred years, by
+some Italians been brought again to light. For it is the easiest thing
+in the world for the Arts to be lost and perish; but only with
+difficulty, and after long time & pains are they resuscitated. Wherefore
+I hope that no wise man will defame this laborious task of mine, since
+with good intent & in behoof of all who love the Liberal Arts have I
+undertaken it: nor for painters alone, but for goldsmiths too, & for
+sculptors, and stonecutters, and woodcarvers, and for all, in short, who
+use compass, and rule, and measuring line--that it may serve to their
+utility.
+
+Nor is anyone compelled whether or no to spend gainful hours on these
+exercises of mine; although I am not ignorant that whoever is well
+exercised in them will thence acquire not only the principles of his own
+art, but by daily practice, an exactitude of judgment, with which he
+will proceed to higher investigations & discover many more things than I
+have here pointed out.
+
+But since, illustrious Sir, it is clearer than light that you are
+yourself, so to speak, an asylum of all the noble Arts, it has been my
+pleasure, out of a singular love I bear towards you, to dedicate to you
+this book; not because I desire to appear therein as rendering you any
+great service, but because thereby you may understand how engaged my
+mind is to you; and since by my work I can confer on you but little
+favour, at least by the exhibition of a ready mind I may repay the
+benefits you shower upon me.
+
+Farewell.
+
+[Illustration]
+
+
+
+
+OF THE JUST SHAPING OF LETTERS
+
+
+
+
+FROM THE APPLIED GEOMETRY OF ALBRECHT DÜRER
+
+BOOK III.
+
+
+Now, since architects, painters & others at times are wont to set an
+inscription on lofty walls, it will make for the merit of the work that
+they form the letters correctly. Accordingly I am minded here to treat
+briefly of this. And first I will give rules for a Latin Alphabet, and
+then for one of our common Text: since it is of these two sorts of
+letters we customarily make use in such work; and first, for the Roman
+letters: Draw for each a square of uniform size, in which the letter is
+to be contained. But when you draw in it the heavier limb of the letter,
+make this of the width of a tenth part of the square, and the lighter a
+third as wide as the heavier: and follow this rule for all letters of
+the Alphabet.
+
+First, make an A after this fashion: Indicate the angles of the square
+by the letters a. b. c. d. (and so do for all the rest of the letters):
+then divide the square by two lines bisecting one another at right
+angles--the vertical e. f. the horizontal g. h.: then, in the lower
+line, take two points, i. and k., distant respectively one-tenth of the
+space c. d. from the points c. and d.: then, from the point i. draw
+upwards to the top of the square the lighter limb; & thence downwards
+the heavier limb, so that the outer edges of both may touch,
+respectively, the points i. and k.: then let a triangle be left between
+the limbs, and a point e. be fixed at top in the middle of the letter,
+and next join both limbs beneath the horizontal line, and let this limb
+be a third as broad as the heavier limb.
+
+Now let the arc of a circle, applied to the top of the outside edge of
+the heavier limb, project beyond the square. Then cut off the top of the
+letter with a serpentine or curving line, so that the concavity decline
+towards the lighter limb, and prolong acutely either limb of the letter
+at the bottom to either side, so as to meet the angles of the square at
+c. and d.: this you shall make with the arc of a circle, whose
+semi-diameter is one-seventh of the side of the square; but the two
+lower curves, mutually opposite, permit to extend so that each is a
+third of the heavier limb, and this you shall obtain by the arc of a
+circle whose diameter is equal to the breadth of the heavier limb.
+
+Moreover, this same letter A you may cut off at top with the side of the
+square, and then produce to a fine point in either direction, as you did
+the feet below, yet so that the longer production shall be to the
+fore-side (namely, the left); but in this case it will be necessary to
+draw in the limb k. a little closer.
+
+Likewise the same A you may draw in yet another manner--that is, pointed
+at top. In that case let the limbs slope towards one another yet more
+closely; then lower the transverse a little and double its width. You
+may also cut off the limb at top bluntly, or sharpen it on the
+fore-side. You ought to make yourself familiar with these three forms,
+or whichever of them pleases you best.
+
+And note likewise that in exactly the same fashion in which this letter
+is acutely prolonged at top & bottom, are the other letters to be so
+prolonged which are drawn with oblique lines, as V, X, Y, although a few
+changes may be necessary, as you shall hear below.
+
+I have here subjoined an engraving of this letter.
+
+[Illustration: A]
+
+
+
+
+OF THE LETTER B.
+
+
+And now you shall draw B in its square thus: First divide the square
+horizontally by the line e. f.; then bisect the lines a. e. and b. f. by
+the line g. h. Next, you must first set properly the broad vertical limb
+of the letter, distant its own breadth from the side a. c. of the square
+a. b. c. d. Then erect the line i. k. on the inner side of the limb
+already drawn, and distant from it one-tenth of a side of the square,
+and let it cut the line g. h. in the point l.
+
+Next, draw strips narrower and horizontal (to be produced hereafter into
+the convex limbs) from the vertical band to meet the vertical line
+i. k.--namely, at top, below the line a. b.; next, above the line e. f.;
+and at bottom, above the line c. d.
+
+Now set a leg of the compass on the point l. and describe a semicircle
+to the right of the transverse strips, so that the extremities of the
+circumference, in the vertical line i. k., below the side a. b., and
+above the line e. f. may coincide with those short transverse lines.
+Then bisect the narrow transverse strip which is above the line e. f. in
+the line i. k. by the point m.; and indicate the breadth of the letter,
+to the right of the semicircle, by the point n. in the line g. h.; and
+afterwards draw from the point m. above the line e. f. in the direction
+of f. a short horizontal line as great as need be: then describe a
+semicircle which shall include this line, and the point n., and, at the
+top, the side a. b.; and through n. let pass a vertical line. These all
+combine to form, below, the concave of the curved limb, and above, its
+convex.
+
+Next, produce the transverse strip above c. d., in the direction of d.,
+as far as required, and mark this q. Then bisect the line m. q. by the
+line o. p., cutting the line n. in the point r.; and next describe a
+semicircle touching the horizontal line e. f., the point r., and the
+position q. Then indicate the breadth of this limb of the letter by the
+point s. to the right of the point r. in the line o. p. and describe a
+semicircle, touching the line m., the point s., and the side of the
+square c. d. There will then remain in the letter three right angles to
+be eliminated: the interior and lower one may be shaped into a curve by
+a circle whose semi-diameter is two-thirds of the breadth of the broad
+limb of the letter, and the exterior ones you shall fine to a point by
+circular lines whose semi-diameter is equal to the breadth of that limb.
+
+
+Another method.
+
+Or you may make your B in this fashion: Let the side a. c. of the square
+be divided into nine equal parts, and cut off the four superior parts by
+the horizontal line e. f. Then erect your vertical limb as described
+above; and the superior curved limb you shall make between a. b. and
+e. f.; the inferior between e. f. and c. d.
+
+Now divide a. b. into nine equal parts, and cut off four parts towards
+b. in the point g.; then divide c. d. into five equal parts, and the
+last, towards d. mark off in the point h. and join g. and h. by the line
+g. h. which should touch on their exterior edges the superior and
+inferior limbs of the letter. Now these limbs must be drawn of a
+particular form; and the compass, in drawing the circular lines, must be
+moved up and down their diagonals: and these two diagonals you shall
+determine in this wise.
+
+Divide a. e. into four parts; the lowest, above e., call i. e.; the
+lowest of the five remaining, above c., call c. k. Then join the points
+i. and b. and k. and f. respectively, by the lines i. b. and k. f. Upon
+these lines move and turn your compass, & in this way you shall describe
+both curved limbs: and they must both be broader towards the top than
+towards the bottom, as follows naturally with the stroke of a pen, and,
+moreover, while approximately round, they are not to be circular;
+therefore you will have to move your compass at need along the
+diagonals, and withal to assist it also with the hand, as I have done in
+the picture on the following page.
+
+[Illustration: B]
+
+
+
+
+OF THE LETTER C.
+
+
+Next you shall make the letter C in its own square thus: Bisect the
+square a. b. c. d. by the horizontal line e. f. and in it let i. be the
+middle point. From this point as the centre, & i. f. or i. e. as the
+radius, describe a circle touching interiorly all four sides of the
+square. Now move the leg of the compass, but without varying its span,
+to a point k. a little to the right of i. in the line e. f., letting the
+space i. k. denote the greatest breadth of the letter you desire; & from
+the centre k. describe another circle which shall cut twice the line
+b. d., and whose circumference to the left will mark the required
+breadth of the letter. Next, draw the vertical line g. h., parallel to
+b. d., distant from b. a tenth part of the line a. b. This will cut off
+for you at top and bottom the letter C as the ancients were accustomed
+to use it. But I would have you cut off the lower limb in the middle
+point between g. h. and b. d.: then make the limbs somewhat finer and
+rounder on the inside towards top and bottom from the point where the
+circles intersect; and for its greater perfection round out the letter,
+above and below, to touch the sides of the square a. b. and c. d. Next,
+low down, where the letter with one foot crosses the line g. h., there,
+under the circular line make the form a little more incurved, yet so
+that with the tip of its end it shall again touch the circular line.
+Similarly, but higher up, make the foot more hollow on the inside than
+the circle left it: and thus two circular lines will give you very
+nearly the whole form of the letter.
+
+
+Another method.
+
+Or, secondly, you may make the letter C thus: Draw in the square a
+diagonal c. b.; set the leg of your compass on its middle point i. and
+with the other leg describe the exterior circle as before, terminating
+it above at the diagonal c. b.; but below, make your circle pass a
+little beyond the former sweep. Then set the leg of your compass, but
+without changing its gauge, as far above i. in the diagonal as the
+letter's greatest width, and describe your inner circle; and, as though
+made with a pen, let the descending stroke be heavier than the
+ascending. The rest you may elaborate with your hand; & let the trimming
+of the ends of the letter, above, slope upwards, & below, downwards,
+exactly as I have here drawn the shapes.
+
+[Illustration: C]
+
+
+
+
+THE LETTER D.
+
+
+The letter D you shall make thus: Divide its square by the perpendicular
+or vertical line g. h. and by the horizontal line e. f. into four small
+squares, and call their point of intersection i.: then draw the broader
+limb of the letter from the side a. b. downwards, to meet the side c. d.
+and at the distance of its own width from a. c.; and produce the limb at
+top and bottom to a sharp point at the angles a. and c. as was shown
+above in B; using the same method in all straight limbs in the remaining
+letters. Next you are to produce from this limb two narrower tracts
+horizontally, and from these are to be described the circular arcs of
+the letter between the line a. b. at top and the line c. d. at bottom,
+and extending as far as the perpendicular g. h.; next, with your compass
+join g. f. h. Then, in the line e. f. lay off a portion equal in breadth
+to the widest limb of the letter, at the point k.; next, set one foot of
+your compass on k. and let the other cut the said line e. f. in l.; let
+this be the immovable leg of your compass, and with the other, beginning
+from k., describe internally, to the narrower transverse limbs, an arc
+which shall touch both, completing your acute angle above, but rounding
+out the lower one by a circular arc of the same diameter as the one by
+which you sharpened your exterior subtending angle.
+
+
+Another method.
+
+You may make the round limb of the same D in another fashion; namely, as
+a pen naturally would, broader above than below. For this, draw the
+diagonal c. b. and describe your exterior arc as before; but to describe
+the interior, in the line c. b. take a point m. lower down than i. and
+distant from it the width of the broader limb, and without altering your
+compass describe an interior line; but where the limb must needs be
+narrower, there you are to accommodate it with your hand, both below and
+above, as in the following cut.
+
+[Illustration: D]
+
+
+
+
+THE LETTER E.
+
+
+The letter E you shall form in its square thus: Draw a transverse line
+e. f. bisecting a. b. and c. d. in e. and f.; then draw the great
+vertical limb of the letter, to the left, as you did for D. Next draw
+also an upper transverse limb of narrower dimensions, parallel to a. b.
+and in length six-tenths minus one-third of one-tenth of the length of
+a. b.; and the end of this bend downwards one-tenth of the length of
+a. b. and use this as the diameter of the circle with which you round
+out the inner angle of this extremity: then draw your narrow middle limb
+parallel to the median line e. f. and above it, so that it may be
+shorter than the upper limb by one-tenth of the length of a. b., but at
+its terminus double as wide; & you are to round it out (in either
+direction) by the arc of a circle whose diameter is one-sixth the length
+of e. f. Now construct your lowest limb upon the line c. d., so that at
+its ultimate angle it may exceed in length the upper limb by one-tenth
+of c. d.; the cusp, however, you are to prolong beyond this part by
+two-thirds of one-tenth part, and erect above it to one-sixth of the
+length of c. d., and round out the same by a circle whose semi-diameter
+is also a sixth of c. d. In like manner the final angle of the letter
+you shall round out by an arc of the same circle by which you rounded
+out the middle transverse limb: the other angles you are to leave acute,
+as in the following cut.
+
+[Illustration: E]
+
+
+
+
+THE LETTER F.
+
+
+The letter F you are to form in the same manner as E; except that you
+shall omit the lower limb altogether, and, in its place, round out the
+letter on both sides below, as you did E on one side only, as I have
+shown you below.
+
+[Illustration: F]
+
+
+
+
+THE LETTER G.
+
+
+Likewise the letter G you are to make as you did C, before described;
+this, however, excepted: that in front (that is, to the left) of the
+line g. h. is to be erected the broad limb of the letter, upwards from
+the curve to the line e. f., and above it is to be rounded to a point,
+on either side, as before was said; but below, both angles are to
+remain.
+
+Or, you shall form G in the following fashion in the said square,
+divided as before: Draw the diagonal c. b. and set your compass with one
+leg on the point i. and with the other describe an arc from e. to the
+middle point c. d. and mark this point l.; in like manner also, describe
+an arc upwards to the line a. b. so as to meet the perpendicular line
+g. h. & mark that point z. Then, in the line g. h., take a point m. so
+that the part m. h. shall be one-tenth of the line g. h.; then, with a
+sweep of your hand join l. & m. with the curved line l. m. Next, you are
+to draw from z. a line upwards, as broad as the standard of the letter,
+but oblique and in direction midway between your circular line & the
+perpendicular g. h. and from the extremity of this line you must draw a
+curved line to meet a. b. at the point where your circular line touches
+it. Next, cut off from the bottom of g. h. a part one-third of its
+length, & indicate this by the point n., & to this height, from the
+level of m. upwards, produce the broad limb of the letter, and let its
+extremities above be finished in either direction, of the same size.
+After this set the leg of your compass on the diagonal c. b. the breadth
+of the standard of the letter above i. & at the distance e. i. describe
+an arc, which above shall touch the exterior boundary a. b. but below
+shall stop short above l.; & from this point you must with your hand
+draw a line to the vertical limb at the height of m.
+
+And the same you shall do above in drawing the narrower limb of the
+letter, as seen in the following diagram.
+
+[Illustration: G]
+
+
+
+
+THE LETTER H.
+
+
+The letter H is to be formed of two broad, great, & vertical limbs of
+the height of the square, in such fashion that their extremities, being
+produced exteriorly, shall touch the four angles of the square, a. c.
+and b. d. respectively. Now in what fashion the projections of the
+broader limbs of letters are to be rounded out at top and bottom and on
+either side, you have been instructed; for in any letter you please, any
+broad and vertical limb is to be depicted at top and bottom thrice as
+broad as at its middle: provided always it is not joined to a narrower
+limb. So when this has been accomplished, then draw your narrower
+transverse limb upon the line e. f. as is shown below.
+
+[Illustration: H]
+
+
+
+
+THE LETTER I.
+
+
+The letter I you are to make of a single broad vertical tract in the
+midst of its square, touching the latter top and bottom; and of this, at
+both ends, and on either side, you are to round out the productions or
+projections as below is shown.
+
+[Illustration: I]
+
+
+
+
+THE LETTER K.
+
+
+Now for K: You are to make the first tract vertical, in the same manner
+as you formerly did for H; then draw another narrower limb from the
+broader and erect one, so that it may, at its lower end, impinge
+obliquely on the transverse line e. f. and above may ascend to the right
+till it meet the line a. b., taking care to make it parallel to the
+diagonal c. b.; and this, at the top, you are to produce in both
+directions so that each production may represent a tenth part of the
+line a. b. The hitherward projection you are to round out with a circle
+of which the diameter must not exceed the breadth of the lesser limb;
+but of the other arc, by means of which you round out the farther
+projection, you shall make the diameter double as great as the diameter
+of the arcs by which you have customarily hollowed out the preceding
+extensions of the broad and vertical limbs. Next, from the narrow limb
+so constructed draw in a downward direction another broad limb, so that
+it too may be parallel to a diagonal of the square; & of this the
+beginning is to be taken from the acute angle which the narrower limb
+makes with the broad vertical limb, and let it be drawn with its
+projection to the angle d., yet in this fashion: take two points this
+side of d. after this manner, so that the first point may be distant
+from d. the tenth part of the line c. d. & the second as far again from
+the first; then let the said tract be drawn within the space which is
+between the two points, but in blind and invisible lines. Afterwards you
+shall add the extension, which you shall make this way: take before f.
+in the line e. f., a point g. no farther distant from f. than the
+breadth of the narrower limb; on this point set one leg of your compass,
+& let the other be extended to the angle d., from which let it be guided
+back along the broad but invisible blind limb: thence will result the
+lower convexity of the tail you seek; but its upper concavity look for
+in this way: divide f. d. in its middle point h.; on this set one leg of
+your compass, and with the other describe an arc passing through d. to
+meet the broad limb.
+
+Or you may make K in this manner: First, let your broader vertical limb,
+and your upper narrow one remain as they have been described, except
+that the interior angle which the narrower limb forms with a. b. shall
+remain acute, but the exterior one shall be rounded out, as has been
+said. Then let there be drawn the lower broad limb, obliquely from the
+angle which is included between e. f. and the vertical limb, and let it
+descend to meet the side c. d. so that between d. and the limb the width
+of the limb be left vacant; and the hither angle is to be left, but the
+farther, towards d., shall be rounded out a little, as shown below.
+
+[Illustration: K]
+
+
+
+
+THE LETTER L.
+
+
+As for the letter L, you shall make it by a combination of parts of two
+of the preceding letters: namely, you shall make the first vertical
+broad limb, as you did a while back in I; and to this join a foot as you
+did at the bottom of E, when you made it. Such is L depicted below.
+
+[Illustration: L]
+
+
+
+
+THE LETTER M.
+
+
+The letter M you shall form in two ways within its square. In the first,
+draw the narrower limb of the letter vertical, to the right of a. c.,
+distant from a. one-tenth of the distance a. b.: draw the other, &
+broader limb, on the near side of b. d., also a tenth part of the whole
+distant from b. & in such fashion that both limbs touch the square at
+top and bottom; then, between the two, bisect the line c. d. in the
+point e. and draw a broad limb from the inner angle of the narrow limb,
+downwards to the point e., & next a narrow one upwards from e. to the
+inner angle of the broader vertical limb; and the inner angles at top
+you must not round out, but leave acute; the exterior angles, however,
+at the top, and both exterior and interior at bottom of both vertical
+limbs, you are to adorn with the customary projections, as you have done
+in the preceding letters. You are to know, too, that when these letters
+are drawn with a pen, they are to be described with a single stroke. But
+for your guidance is this letter, in the manner in which I have
+instructed you, depicted below.
+
+
+Another method.
+
+Another way is thus: Divide the side a. b. of the square into six equal
+parts & mark off the two extreme parts, one at either end, by the points
+f. and g.; then draw the inner and broader limb, with its point at e. as
+above; and to this, in an upward direction, a narrower one, so that
+between f. g. be left a vacant space, and so more readily the letter
+slope forward. Then you are to draw the two lateral and vertical
+limbs--the near and slender, and the farther broad one--at the top,
+indeed, as in the first sketch, but at the bottom produce them to the
+two angles c. and d. and finally add projecting cusps, as you were
+instructed in the first M; but the projection below will pass beyond the
+square at the points c. and d. Or you shall make M at top with acute
+angles, in which case the lateral limbs will slope the more; or shear
+them off obtusely, and in this fashion (whichever pleases you best) make
+them as you see them depicted in the following diagrams.
+
+[Illustration: M]
+
+
+
+
+THE LETTER N.
+
+
+Likewise the letter N you shall make in its square thus: First you are
+to draw two standards vertical and slender, so that at top & bottom they
+may touch the square, & that being produced, the nigh one at the bottom,
+and the farther at the top, they may touch the angles at c. and b. Now
+join these two by a broad oblique limb, running from the angle a. to the
+point e., by which is denoted the remote side of the farther limb, where
+you shall allow the acute angle to remain; but at the top, this limb,
+produced beyond the angle a., you are to round out to a fifth part of
+the length of a. b. This prolongation should incurve below, a fifteenth
+part of the distance a. b. projected on two arcs, the upper one the
+greater, the lower the less. For the lesser arc, therefore, you shall
+take as diameter of its circle, a line the fifth part of the distance
+a. b. and its centre is to be taken outside the square, so that the foot
+of the compass may touch the tip of the extension and the angle a.; then
+extend a little the feet of the compass, and shift its centre until the
+arc touch both the tip of the part produced, & the broad oblique limb,
+in the middle point between the side a. c. & the nearer of the two
+slender vertical limbs.
+
+Or you may make the letter N in such fashion that its upper nigh
+extension shall remain within the square; or you may make from it an
+acute angle as shown overleaf.
+
+[Illustration: N]
+
+
+
+
+THE LETTER O.
+
+
+Now O you shall make this way in its square. Set in the square the
+diameter c. b. and bisect it in the point e., so that e. may form a
+middle point between the two points f. and g. which are to be your two
+centres; and from each let a circle be described touching two sides of
+the square; & where the circles cut one another, there with your hand
+you must shape the slender outline of the letter to a juster proportion,
+as below is shown.
+
+[Illustration: O]
+
+
+
+
+THE LETTER P.
+
+
+P you shall make in its square in this wise. Divide the square
+a. b. c. d. by the median horizontal line e. f.; then divide a. e. &
+b. f. equally by the line g. h. Next draw, first the broad vertical limb
+for this letter P, as you did a short while ago for K, and afterwards
+erect the line i. k. the distance of its own breadth to the right of
+your vertical limb; (here you must ever observe that in a lettered
+square we speak of the angle a. as the "hither" angle, that is, to the
+left; & the angle b. as the "farther" angle, that is, to the right).
+Then where the line i. k. cuts g. h. call the point l., and next draw
+two slender horizontal limbs, the upper below a. b., the lower above
+e. f., from the broad vertical limb as far as the line i. k. Set one leg
+of the compass on the point l., extending the other to the lower side of
+the lower horizontal limb near k.; then describe an arc through the line
+g. h. as far as the other slender horizontal limb of this same P, &
+where it cuts the line g. h. set the point m. Next, on the far side of
+m. measure the width of the large limb of the letter, along the line
+g. h. to the point n. and let your compass be stretched so that with one
+foot it may touch the line a. b. and with the other the point n.; then
+set one foot of the compass on n. & the other on the line g. h. to the
+right, in the point o., in which this foot is to be left standing
+immovable, and with the other is to be described an arc, passing through
+the point n. and touching the lines a. b. and e. f.
+
+Or you may form the loop of this letter in the following manner. Set a
+leg of the compass under the transverse g. h. in the line i. k., in a
+place median between the line e. f. & the lower part of the upper
+transverse of the slender limb, in the point p. and describe an arc as
+before, passing through m. so that the loop will be acute at the bottom,
+and its tip will end in the middle space between the line i. k. and the
+broad vertical limb of the letter.
+
+Or make this same P with a circular sweep, by shifting the compass upon
+the diameter, so that that sweep may be broader at the top (as though
+made with a pen) as will be shown in the diagram on the following page.
+
+[Illustration: P]
+
+
+
+
+THE LETTER Q.
+
+
+Make your Q in its square in the self-same manner as was prescribed for
+O; but add to it its tail thus: Draw a diameter of the square, the line
+a. d., about which, starting from the curved outline, begin to draw a
+long tail, producing it through the angle d. in such fashion that d. may
+be in the middle of the thickest part of the tail; but where the tail
+begins let it be a little narrower than in the angle d., where it should
+attain its real thickness. Then let it be drawn out, beyond the angle d.
+to the length of the entire diameter, and in a downward direction, yet
+so that it curves while it slopes, & that its tip shall not fall lower
+than a third of the side below the lowest side of the square, and shall
+tend, as it nears the point, to grow sharper little by little, and at
+length end in a very fine point indeed.
+
+Or you shall give Q a shorter tail in this fashion, to wit: set your
+compasses to the length of the side c. d. and draw a tail from the bulge
+of the same letter, describing through the point d. its inner arc of the
+same length as c. d., taking care that the tail bend upwards until it
+again reach c. d. produced, in the point h.; then shift your compasses,
+& with the other leg again describe from the bulge of the letter an arc
+below d. & continue it until again it reach h., but in such fashion that
+the tail shall find its greatest thickness at the start, as in the
+following figure is doubly depicted.
+
+[Illustration: Q]
+
+
+
+
+THE LETTER R.
+
+
+Moreover R you must make in its square just as was directed for P; but
+then erect a right line q. r. through the middle point of the square, &
+let it cut the exterior arc of the rounded limb in s., from which point,
+downwards towards the angle d., let there be drawn a broad tract, almost
+equal to that which you made above for the letter K., but this is to be
+somewhat bent in, and so shaped by your hand that its tip, well formed,
+may arrive directly on the angle d.
+
+Or make R in such fashion that its rounded sweep, as though made with a
+pen, shall be above broader, & narrower below. To accomplish this, you
+must shift your compasses on the diameter q. e. & not allow the rounded
+limb to touch the vertical one, as was described in P. Besides, the
+oblique limb is to be deduced from the rounded one with a little more of
+a curve; just as I have drawn overleaf.
+
+[Illustration: R]
+
+
+
+
+THE LETTER S.
+
+
+Next, the letter S you shall make as follows in its square, a. b. c. d.
+First draw the horizontal line e. f. and the median & vertical one g. h.
+and let them bisect one another in the point m. Then choose the main
+thickness of the letter, and set it in the line g. h. so that the point
+m. may divide it, having one-third of the thickness below it; next, set
+the lesser thickness, at the top beneath g., indicating it by the point
+i., and at bottom, above h. in the point k.; and the thickness of the
+letter indicate above by n. and below by l.
+
+Next, set a leg of your compasses on the line g. h. in the mid-point
+between i. and n., and with the other describe a circle passing through
+i. and n.; in like manner, upon the line g. h. set your compasses upon
+the mid-point of g. l. and describe a circle passing through g. & l.
+Then once more set your compass on the same line g. h. in the mid-point
+of n. h. and describe a circle through n. & h.; and lastly, in the
+mid-point of l. k. you must set one leg, & with the other is a circle to
+be described through these same points l. & k.; afterwards cut off by
+vertical section the upper portion of this letter, so that the part thus
+cut off may contain in its extremity the maximum thickness of the letter
+and a third part besides, & also that its tip may project downwards so
+far as to stand midway between the centre of the circle i. n. and the
+side b. d.; in other words, let the tip be distant on the right, from
+the circle i. n. the first third of the interval between the greater and
+lesser circles.
+
+Next cut the lower limb of the letter to the left, by a vertical line
+through the mid-point between the two circles, & in such fashion that
+the part so cut off may be a fourth part wider & higher than the upper,
+and that its tip may rise to the height of the centre of the circle
+n. h.
+
+
+Another method.
+
+Yet another way may you make the letter S. In the square a. b. c. d.
+bisect the horizontal line e. f. in the point m.; then set one leg of
+your compass upon the mid-point between g. and m. & with the other
+describe a segment of a circle in the direction of a. e. passing through
+the points m. and g.; next, set your compass upon the mid-point between
+m. and h. and describe a segment of a circle through m. and h. in the
+direction of f. d. The two arcs will touch above, in front, and below,
+in the rear, the exterior curvatures of this same letter S.
+
+Next, draw through m. the diameter c. b. and at its middle indicate the
+maximum thickness of the letter by the two points p. and q. from which
+let there be drawn two right lines, one up, & one down, to those two
+arcs; & next, from the two points p. & q. draw two curved parallels to
+the same arcs, regulating the distance between them, their elevation &
+depression from the centres of the same circles. Next, indicate below g.
+and above h. the minimum thickness of the letter; and from these points
+you will with your hand fashion the inner shape of the letter, both
+above and below, & produce the limb of S, above towards b. Cut it off so
+that its lower tip may touch the segment, & that the part cut off
+upwards may contain a tenth part of a. b. and that the segment may still
+exceed the part cut off. Then construct a vertical line r. s. to the
+right of e. c. and distant from it a fifth part of c. d.; let it cut the
+diagonal c. b. in t. and to the angle just formed produce the extremity
+of the letter, making the part so cut off a third broader than the upper
+portion. Lastly, you will have to produce the tip ever so little beyond
+t.; as I have briefly indicated.
+
+[Illustration: S]
+
+
+
+
+THE LETTER T.
+
+
+Set the broad limb of T in the midst of its square erect, produced &
+drawn to a point on either side below, just as you did before in the
+letter I; then take two points e. and f., distant respectively one-tenth
+of the whole space from a. and b., and let the transverse limb of the
+letter be drawn below e. f. and of an equal length with it; but the
+projecting extremities of this line are to be cut obliquely, and the
+tips of these projections shall so far extend above the line a. b. to
+the right as below they depend to the left. The oblique lines of these
+projections are to be each a fifth part of the length of a. b.; & the
+angles of these projections you shall round out by means of circles of
+diverse radius--namely, for the lesser angle you are to use a diameter
+only two-thirds of the width of the broader limb; but for the greater
+angle you shall take a diameter equal to the side of a square contained
+between the broad and vertical limb and the intercepted portion of the
+line a. b.
+
+
+Another method.
+
+Or you make T thus in its square: Take your point e. as before, to the
+right of a., and cut your transverse limb diagonally, as before, yet so
+that the projection be dimidiated to the right, and at top the angle
+remain as it falls; and so at the other extremity, only the point f.
+must be moved as near again to b., the cutting line to be a little more
+erect, & the projection formed a trifle broader than at the hither end;
+otherwise shall everything remain as before; as I have delineated for
+you on the opposite page.
+
+[Illustration: T]
+
+
+
+
+THE LETTER V.
+
+
+V you shall thus make in its square: Bisect c. d. in the point e.; then
+set the point f. one-tenth of the whole line a. b. beyond a., and in
+like fashion g. to the hither side of b. Then draw the broad limb of
+your letter downwards from f. to e. and sharpen it; & thence draw
+upwards your slender limb to g.; and at the top produce it in either
+direction, as you did before at the bottom of A; just as you see it
+shown below.
+
+[Illustration: V]
+
+
+
+
+THE LETTER X.
+
+
+X you shall form thus: Draw two vertical lines e. f. and g. h. distant
+respectively one-tenth part of the line a. b. from the sides a. c. and
+b. d. Then draw the two limbs intersecting one another in the form of a
+cross--the broad one so that at top, & with its hither side it shall
+touch e., & at the bottom, and with its farther side h.; but the narrow
+limb so that at top, and with its farther side it may touch g., & at
+bottom, with its hither side f. Then add its projections, touching, at
+top and bottom, the four angles a. b. c. d., & choose a semi-diameter of
+the larger circle of the length of a fifth part of a. b.; & with that
+you shall round out the four greater angles; but for the lesser circle
+you shall take a diameter as long as two-thirds the width of the broader
+limb.
+
+Or you may vary X thus: Let everything be left as before except the
+narrower limb, which at top you shall make more erect by one-half the
+breadth of the wider limb; and so the upper part of the letter shall be
+less and narrower than the lower, and shall have a different aspect, as
+is shown below.
+
+[Illustration: X]
+
+
+
+
+THE LETTER Y.
+
+
+Y you shall achieve in the midst of its square, as far as its lower half
+is concerned, after the instructions before given for I; but its upper
+part you shall divide so that its hither limb shall contain two-thirds,
+and its farther one-third of the broad standard; and let them slope to
+either side so that produced they may touch the two angles a. and b.;
+and the greater circles, by which you are to round out their obtuse or
+greater angles, make of a diameter as great as a containing side of the
+square enclosed between the standard and the sides of the great square,
+as in T was shown; but the diameters of the circles which you apply to
+the lesser angles, make double the width of the broad standard, as
+below.
+
+[Illustration: Y]
+
+
+
+
+THE LETTER Z.
+
+
+Z you shall make thus: Set upon either side, both beneath & beyond the
+angle a., two points e. & f., each at a distance of the tenth part of
+a. b.; so also, set two other points g. and h. both before and above the
+angle d. and with right lines join e. f. and g. h.; then draw your
+narrower transverse limb, beneath a. b. backwards as far as the angle
+b.; from thence draw your broad limb diagonally to c.; and then again a
+narrower one from c. to g.; and with your hand round out the two tips e.
+and h.
+
+Or make Z thus: Divide the square a. b. c. d. by the vertical line e. f.
+and in this reduced space construct the letter as before; but so that
+the two transverse limbs be cut short, above on the nigh side, and below
+on the far, by the vertical lines a. c. and e. f. respectively as below.
+
+[Illustration: Z]
+
+So likewise, in other fashion, can we make all the letters already
+drawn, on a scale of ninths, just as we have now drawn them on a scale
+of tenths; in just the same manner, according to the due proportion of
+each, in its own square, a. b. c. d., dividing them into nine, as just
+now into ten parts; & that this may be the better understood, I have
+chosen to append here letters of such fashion. Also these letters are to
+be made five parts high when written small & rapidly, by hand. In such
+writing the versals are made of the same proportion and form, but
+one-third larger than the ordinary letters of the writing.
+
+  [Illustration:
+  A A A A
+  B B B B
+  C C C C
+  D D D D]
+
+  [Illustration:
+  E E F F
+  G G G H
+  H I I K
+  K K L L]
+
+  [Illustration:
+  M M M
+  M N N
+  N N O O
+  P P P P]
+
+  [Illustration:
+  Q Q Q
+  R R R
+  S S S T
+  T T V V]
+
+  [Illustration:
+  X X X
+  Y Y Z
+  Z Z]
+
+
+
+
+DIRECTIONS FOR THE CONSTRUCTION OF THE TEXT OR QUADRATE LETTERS
+
+
+The letters which are usually called "text," or quadrate, it was
+formerly customary so to write, although they are now imitated by the
+new art, as presently I shall show below. Although the alphabet begins
+with the writing of A, yet shall I (not needlessly) in the first place
+undertake to draw an I; because almost all the other letters are formed
+after this letter, although always something has to be added to it or
+taken away.
+
+First make your I of equal squares, of which three are properly set one
+over the other; and the top of the top one, and the bottom of the bottom
+one, divide in two points, that is to say, into three equal parts: then
+set a square equal to the others in an oblique manner, so that its
+diagonal be vertical, and its angle on the first point of the top
+square. In this way, this oblique square shall extend with its angles
+more to the left than the right. Then produce upwards on either side,
+after the width of the superposed squares, right lines to meet the sides
+of the oblique set square. Next do below precisely as you did above,
+except that you must set the angle of the oblique square on the second
+point, that is, the one farthest to the right in the bottom of the
+lowest square; and let fall your lines on either side upon the
+transposed square: so will I be perfect; only above it draw with a fine
+pen a tiny in-crescent.
+
+So shall you make N from two standards of this same I, set so that their
+angles at top and bottom touch; and in this manner the space between the
+two shall be narrower than the breadth of either: also, you shall no
+longer put little crescents above them; you must make of the same length
+all the short letters throughout the alphabet.
+
+In like manner make M of three standards, just as you made N of two.
+
+R make as I, except only that at top you must set an equal square
+diagonally, to the right, so that angle touch angle. R you may make also
+in this fashion: below leave its foot as before, but above add two
+diagonal squares, which shall touch each other with their angles in the
+middle point of the vertical limb, and then produce upwards both sides
+of the latter to meet the diagonal square.
+
+V is made in three ways. First let it be made simply, as N; only that in
+the farther limb, you shall omit at the top the diagonal square; and
+instead shall draw an oblique line, so that it may make two angles in
+this limb (produced) of which the farther shall be of the same height as
+that of the topmost angle of the diagonal square, & the higher angle of
+the same height as the angle nearest to it in the said square.
+
+The second V, which we use at the beginning of a sentence, make thus:
+Draw the first limb as before for I; only, at the bottom, push the
+diagonal square a little further to the right, so that its hither angle
+does not project beyond the side of the vertical limb, but falls in the
+line of its descent. Then set the second limb to the right of this, and
+cut it off below by an oblique line, drawn from the lowest angle upwards
+to the right, as far as the middle point of the lowest of the three
+superposed squares.
+
+Next make W (i. e., double V) just as you made V-simplex; only you shall
+set before it the standard limb of I.
+
+B make as the second V-simplex; but in the first upright omit the
+diagonal square at the top, and set upon the three original squares
+three others similar, but the seventh one you shall cut off diagonally
+from its lower hither angle.
+
+Likewise when your B so made is turned upside down, then it will be a Q.
+
+X you shall construct from I. Append from top angle to the right a
+diagonally set square, as you did before in R; and at the bottom draw an
+acute tail to the left from the diagonal, and at the middle of the
+vertical limb describe a transverse, in such way that the former is cut
+before and aft by the latter's diagonal; let the hither and lower angle
+be terminated as far in front of the upright as would measure one-half
+of the cutting diagonal, which at top shall just touch the upright; but
+to the right let the transverse at top project to a point just below the
+angle of the oblique square; from thence downwards let it be cut off by
+an oblique line parallel to the anterior diagonal.
+
+C you shall construct from I after this fashion: Remove the top diagonal
+square, & let lines be produced on either side to the proper height of
+the letter, and cut off the hither angle by a diagonal; then draw at top
+a broad transverse, projecting beyond the vertical to the right the
+width of the latter, and cut this off by a diagonal in such a way that
+it project below only half as far as above.
+
+The vertical standard of E you shall make as for C; but from above let
+there descend to the right a broad limb from the diagonal bisecting the
+right angles of one square, and one-third again as long as broad; and
+let there be drawn from its lower angle a small diagonal line to the
+vertical limb.
+
+T shall be made like C, except that at top something is added to its
+diagonal, so that its tip converges to a fine point, and the like to the
+left on the hither side of the broad standard, just as at the top: and
+because of this is T at top more elegant than C, and has not the same
+incurved appearance.
+
+L you are to make below like I; only six squares are to be set on end;
+then cut off the hither side of the seventh by a diagonal, and so the
+apex of the letter shall remain to the right.
+
+The letter S you shall make as L; except that at top to the right must
+be drawn a broad limb of the length of the diagonal, which afterwards
+you are to cut off by a line parallel to the diagonal.
+
+F you shall make as S, just adding to it a transverse limb at the height
+of the shorter letters and double as long as broad, so that the point on
+the hither side & below shall project as far as half the limb's breadth,
+so that the two diagonal abscissions may be equidistant from one
+another.
+
+The near limb of the letter H make like L, and to it join by its top, in
+the proper place, the farther made like I; but below, for the diagonal
+square, substitute a fourth square in line with the others, and the
+fifth and lowest cut off on the far side by its diagonal.
+
+Of K make the near limb like L; and to the right of it append a diagonal
+square, from the lowest angle of which let a line be obliquely produced
+to meet the said vertical limb; and next from this line let a broad limb
+be obliquely drawn, and this, at the bottom, you are to cut off by a
+diagonal, in such fashion that the space below, between the two tips
+shall not be more than the diagonal of a single square.
+
+D in its lower half make like B; but at top let the anterior limb ascend
+upwards to the maximum height of the letters, and then cut off the
+hither angle by its diagonal; next superpose to the same height half a
+square upon the other three squares of the farther limb, & once more do
+here as you did below, and let this broken limb rest on the angle of the
+near limb, and let it extend beyond it as far as the end of the upright
+near limb; and so will it all but contain three conjunct squares; for
+when it meets the near vertical limb, that fraction is to be cut off at
+right angles.
+
+O you are to make below as D, and also the same at the top as the
+bottom, only, as it were, turning it upside down.
+
+The anterior limb of P make like L inverted; but the posterior like the
+standard of I: at bottom, however, you are not to add an oblique square,
+but amputate the limb diagonally, & draw at the bottom a broad
+transverse limb, which likewise is to be cut off diagonally, so that the
+lower point shall project to the left, a distance of half the breadth of
+the limb.
+
+Likewise A in the lower half you are to make like N; but of its anterior
+vertical limb, you are to cut off the hither angle of the middle square
+by its diagonal; of the posterior, however, allow three squares to
+remain superposed, and incline the top part (the fourth square) rather
+to the left, so that if at this side is joined to it the half of a
+square, then it shall attain the height of the letter; and cut off the
+square obliquely, yet so that the lower point shall project farther than
+the upper; then describe to the left a circle, sweeping downwards, so
+that its contents shall embrace the farthest limit of the anterior limb.
+
+Z is made in threefold fashion. First set a diagonal square which shall
+touch the height of the letter; then add another like it, on the right,
+joining their sides, & let these form a quadrangle sloping downwards on
+the right: next set a diagonal square in straight line under the top
+square, and distant from the lower one the length of its diameter: then
+draw a diagonal line between the near angles of these two squares, or
+make a rounded limb to reach the lower square; but from the said lowest
+square of all you shall draw downwards and to the right, by the aid of
+divers circles, a round extension, whose bottom shall mark the length of
+the letter; and let its tip, sharp and tenuous, verge to the left. Or
+construct Z of three oblique limbs, one above the other, & to connect
+them draw the diagonal, which shall slope upwards to the right.
+
+Another Z you may make in this way: Let three diagonal squares be set
+atop of one another; and let the lowest have a rounded extension, as in
+the first Z.
+
+The first limb of G make below like I, and add at the bottom another
+diagonal square, joining the two by their angles; but at top produce the
+farther tip of this limb upwards to the height of the letter, & from
+this point draw a diagonal downward to the left, as far as the hither
+angle of the first right square of the three set one on other. Next draw
+the farther vertical standard entire, of the same length as the hither
+standard, and at the bottom draw a diagonal from the angle of the lowest
+oblique square to touch the tip of the angle of the farther limb, & on
+the inner side produce downwards the side of the limb, to meet the tip
+of the said diagonal; to this also, by one line, join the lowest of the
+hither squares. Now draw at top a transverse limb of the customary
+breadth, from the back of the nearer vertical limb, passing through the
+farther one, and reaching as far beyond this as its breadth; & this
+limb, finally, you shall cut off by an oblique line parallel to that of
+the near limb.
+
+Y you shall make as N, only at bottom must be omitted the farther
+diagonal square, & in its place is to be set a right square under the
+other three superposed squares; then split the fifth square by a
+diagonal, so that the tip shall be in front; from which let there be
+produced a diagonal line, equal in length to a single side of the
+square.
+
+Curved, or short S, you shall make on this wise. At the middle height of
+the letter, let there be set, close to one another, their angles
+touching, two oblique squares; from the near square draw a broad
+vertical limb to the height of the letter; and in the same fashion, from
+the farther square let one fall downwards--just as you constructed I top
+& bottom. Next cut off both these limbs, one at top and one at bottom,
+by diagonals, in such fashion that the sharp tips of both may be on the
+side near the middle. Then let there be drawn two broad limbs--namely,
+from the upper, to the right, and downwards; and in like manner, from
+the lower, upwards, and to the left; of the breadth of the limb, above
+and below, but let them be produced no further than the breadth of the
+distance between the limbs: then draw a diagonal downwards, from right
+to left, which shall cut off both oblique limbs. To it also you must
+produce the sides of the squares set in the midst.
+
+So, accordingly, have I set them down--in skeleton in rotation, and in
+proper order in black. This (as I said above) is the antique form of the
+letters; but in these days there is used a more elegant text, and a
+diagonal square is substituted in the middle place for a right square,
+so that the lines of the letters are not so much curved; and there are
+made certain limbs adjoined and cleft; and there are set one on another
+three squares & a half; and spaces are left between two limbs as great
+as their width. Letters of this sort also have I set forth on the third
+page following; as also capital letters, which are called "versals,"
+because they are customarily set at the beginning of a verse; and these
+ought to be made one-third higher than the remaining shorter letters in
+writing.
+
+  [Illustration:
+  i n m r r u v
+  w b q x c e t l
+  s f h k d o p
+  a z z z g y s]
+
+  [Illustration:
+  a b c d e f g h
+  i k l m n o p
+  q r r s s t u v
+  w x y z z z]
+
+  [Illustration:
+  A B C D E F G H
+  I K L M N O P R
+  S T V X Y Z Q *
+  a b c d e f g h
+  i k l m n o p q
+  r s s t u v w x
+  y z]
+
+Here ends this little Book.
+
+
+
+
+
+
+End of Project Gutenberg's Of the Just Shaping of Letters, by Albrecht Dürer
+
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+
+Project Gutenberg's Of the Just Shaping of Letters, by Albrecht Dürer
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+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Of the Just Shaping of Letters
+
+Author: Albrecht Dürer
+
+Translator: R. T. Nichol
+
+Release Date: August 16, 2011 [EBook #37103]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK OF THE JUST SHAPING OF LETTERS ***
+
+
+
+
+Produced by Ben Courtney, Jana Srna and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+
+</pre>
+
+
+
+<div id="tnote">
+<p class="center"><b>Transcriber's Note:</b></p>
+
+<p>Every effort has been made to replicate this text as faithfully
+as possible, including inconsistencies in spelling and hyphenation.
+No changes have been made to the printed text.</p>
+</div>
+
+<p class="center page-break" style="line-height: 1.4em;">OF THE JUST SHAPING OF LETTERS<br/>
+BY ALBRECHT DÃœRER<br/>
+TRANSLATED<br/>
+BY<br/>
+R.&nbsp;T. NICHOL<br/>
+FROM THE LATIN TEXT OF<br/>
+THE EDITION OF<br/>
+MDXXXV<br/>
+*</p>
+
+<div class="figcenter page-break" style="width: 391px;">
+<img id="coverpage" src="images/title-page.jpg" width="391" height="588" alt=""/>
+</div>
+
+<h1>OF THE JUST<br/>
+SHAPING OF<br/>
+LETTERS</h1>
+
+<p class="center">FROM THE APPLIED<br/>
+GEOMETRY OF<br/>
+ALBRECHT<br/>
+DÃœRER<br/>
+BOOK<br/>
+JJJ</p>
+
+<p class="center" style="margin-top: 3em;">DOVER PUBLICATIONS, INC. · NEW YORK</p>
+
+<h2><a class="pagenum" name="Page_1" title="1"> </a>ALBRECHT DÃœRER TO WILIBALD PIRCKHEIMER<br/> HIS PATRON AND VERY GOOD FRIEND<br/> GREETING:</h2>
+
+<div class="figcenter" style="width: 231px;">
+<img src="images/i005.png" width="231" height="286" alt=""/>
+</div>
+
+<p class="drop-cap"><span class="upper-case">In</span> our Germany, most excellent Wilibald, are to be found at the
+present day many young men of a happy talent for the Art Pictorial,
+who without any artistic training whatever, but taught only
+by their daily exercise of it, have run riot like an unpruned tree, so that
+unhesitatingly and without compunction they turn out their works,
+purely according to their own judgment. But when great and ingenious
+artists behold their so inept performances, not undeservedly do
+they ridicule the blindness of such men; since sane judgment abhors
+nothing so much as a picture perpetrated with no technical knowledge,
+although with plenty of care and diligence. Now the sole reason why
+<a class="pagenum" name="Page_2" title="2"> </a>
+painters of this sort are not aware of their own error is that they have
+not learnt Geometry, without which no one can either be or become
+an absolute artist; but the blame for this should be laid upon their
+masters, who themselves are ignorant of this art. Since this is in very
+truth the foundation of the whole graphic art, it seems to me a good
+thing to set down for studious beginners a few rudiments, in which I
+might, as it were, furnish them with a handle for using the compass
+and the rule, and thence, by seeing Truth itself before their eyes, they
+might become not only zealous of the arts, but even arrive at a great
+and true understanding of them.</p>
+
+<p>Now, although in our own time, and amongst ourselves, the Art
+Pictorial is in ill repute with some, as being held to minister incitement
+to idolatry, yet a Christian man is no more enticed to superstition
+by pictures or images, than is an honest man girt with a sword to highway
+robbery. Certes he would be a witless creature who would willingly
+adore either pictures or images of wood or stone. On the contrary, a
+picture is the rather edifying and agreeable to Christian religion and
+duty, if only it be fairly, artificially, and correctly painted.</p>
+
+<p>In what honour and dignity this art was anciently held amongst
+the Greeks and Romans, the old authors sufficiently testify; though
+afterwards all but lost, while it lay hid for more than a thousand years.
+It has now at length, only within the last two hundred years, by some
+Italians been brought again to light. For it is the easiest thing in the
+world for the Arts to be lost and perish; but only with difficulty, and
+after long time &amp; pains are they resuscitated. Wherefore I hope that
+no wise man will defame this laborious task of mine, since with good
+intent &amp; in behoof of all who love the Liberal Arts have I undertaken
+it: nor for painters alone, but for goldsmiths too, &amp; for sculptors, and
+stonecutters, and woodcarvers, and for all, in short, who use compass,
+and rule, and measuring line&mdash;that it may serve to their utility.</p>
+
+<p>Nor is anyone compelled whether or no to spend gainful hours on
+these exercises of mine; although I am not ignorant that whoever is
+well exercised in them will thence acquire not only the principles of
+his own art, but by daily practice, an exactitude of judgment, with which
+he will proceed to higher investigations &amp; discover many more things
+than I have here pointed out.</p>
+
+<p>But since, illustrious Sir, it is clearer than light that you are yourself,
+<a class="pagenum" name="Page_3" title="3"> </a>
+so to speak, an asylum of all the noble Arts, it has been my pleasure, out
+of a singular love I bear towards you, to dedicate to you this book; not
+because I desire to appear therein as rendering you any great service,
+but because thereby you may understand how engaged my mind
+is to you; and since by my work I can confer on you but
+little favour, at least by the exhibition of a ready
+mind I may repay the benefits
+you shower upon
+me.</p>
+
+<p class="center">Farewell.</p>
+
+<div class="figcenter" style="width: 349px;"><a class="pagenum" name="Page_4" title="4"> </a>
+<img src="images/i008.png" width="349" height="376" alt=""/>
+</div>
+
+<h2><a class="pagenum" name="Page_5" title="5"> </a>OF THE JUST SHAPING OF LETTERS</h2>
+
+<p class="center" style="font-size: large; line-height: 1.4em;">FROM THE APPLIED GEOMETRY<br/>
+OF ALBRECHT DÃœRER<br/>
+BOOK III.</p>
+
+<div><img class="large-cap" src="images/i009.png" width="121" height="125" alt=""/></div>
+
+<p class="large-cap"><span class="upper-case">Now</span>, since architects, painters &amp; others at
+times are wont to set an inscription on lofty
+walls, it will make for the merit of the work
+that they form the letters correctly. Accordingly
+I am minded here to treat briefly of
+this. And first I will give rules for a Latin
+Alphabet, and then for one of our common
+Text: since it is of these two sorts of letters
+we customarily make use in such work; and
+first, for the Roman letters: Draw for each a square of uniform size,
+in which the letter is to be contained. But when you draw in it the
+heavier limb of the letter, make this of the width of a tenth part of
+the square, and the lighter a third as wide as the heavier: and follow
+this rule for all letters of the Alphabet.</p>
+
+<p><a name="Letter_A">First, make an A after this fashion:</a> Indicate the angles of the square
+by the letters a.&nbsp;b.&nbsp;c.&nbsp;d. (and so do for all the rest of the letters): then
+divide the square by two lines bisecting one another at right angles&mdash;the
+vertical e.&nbsp;f. the horizontal g.&nbsp;h.: then, in the lower line, take two
+points, i. and k., distant respectively one-tenth of the space c.&nbsp;d. from
+the points c. and d.: then, from the point i. draw upwards to the top
+of the square the lighter limb; &amp; thence downwards the heavier limb,
+so that the outer edges of both may touch, respectively, the points i.
+and k.: then let a triangle be left between the limbs, and a point e. be
+fixed at top in the middle of the letter, and next join both limbs
+beneath the horizontal line, and let this limb be a third as broad as the
+heavier limb.</p>
+
+<p>Now let the arc of a circle, applied to the top of the outside edge of
+the heavier limb, project beyond the square. Then cut off the top of
+<a class="pagenum" name="Page_6" title="6"> </a>
+the letter with a serpentine or curving line, so that the concavity decline
+towards the lighter limb, and prolong acutely either limb of the
+letter at the bottom to either side, so as to meet the angles of the square
+at c. and d.: this you shall make with the arc of a circle, whose semi-diameter
+is one-seventh of the side of the square; but the two lower
+curves, mutually opposite, permit to extend so that each is a third of
+the heavier limb, and this you shall obtain by the arc of a circle whose
+diameter is equal to the breadth of the heavier limb.</p>
+
+<p>Moreover, this same letter A you may cut off at top with the side
+of the square, and then produce to a fine point in either direction, as
+you did the feet below, yet so that the longer production shall be to
+the fore-side (namely, the left); but in this case it will be necessary to
+draw in the limb k. a little closer.</p>
+
+<p>Likewise the same A you may draw in yet another manner&mdash;that is,
+pointed at top. In that case let the limbs slope towards one another yet
+more closely; then lower the transverse a little and double its width.
+You may also cut off the limb at top bluntly, or sharpen it on the fore-side.
+You ought to make yourself familiar with these three forms, or
+whichever of them pleases you best.</p>
+
+<p>And note likewise that in exactly the same fashion in which this
+letter is acutely prolonged at top &amp; bottom, are the other letters to be
+so prolonged which are drawn with oblique lines, as V, X, Y, although
+a few changes may be necessary, as you shall hear below.</p>
+
+<p>I have here subjoined an engraving of this letter.</p>
+
+<div class="figcenter" style="width: 290px;">
+<img src="images/i010.png" width="290" height="133" alt="A"/><br/>
+<a class="pagenum" name="Page_7" title="7"> </a><img src="images/i011.png" width="283" height="115" alt=""/>
+</div>
+
+<h2><a name="Letter_B">OF THE LETTER B.</a></h2>
+
+<p>And now you shall draw B in its square thus: First divide the square
+horizontally by the line e.&nbsp;f.; then bisect the lines a.&nbsp;e. and b.&nbsp;f. by the
+line g.&nbsp;h. Next, you must first set properly the broad vertical limb of
+the letter, distant its own breadth from the side a.&nbsp;c. of the square a.&nbsp;b.&nbsp;c.&nbsp;d.
+Then erect the line i.&nbsp;k. on the inner side of the limb already drawn,
+and distant from it one-tenth of a side of the square, and let it cut the
+line g.&nbsp;h. in the point l.</p>
+
+<p>Next, draw strips narrower and horizontal (to be produced hereafter
+into the convex limbs) from the vertical band to meet the vertical
+line i.&nbsp;k.&mdash;namely, at top, below the line a.&nbsp;b.; next, above the line e.&nbsp;f.;
+and at bottom, above the line c.&nbsp;d.</p>
+
+<p>Now set a leg of the compass on the point l. and describe a semicircle
+to the right of the transverse strips, so that the extremities of the
+circumference, in the vertical line i.&nbsp;k., below the side a.&nbsp;b., and above
+the line e.&nbsp;f. may coincide with those short transverse lines. Then bisect
+the narrow transverse strip which is above the line e.&nbsp;f. in the line i.&nbsp;k. by
+the point m.; and indicate the breadth of the letter, to the right of the
+semicircle, by the point n. in the line g.&nbsp;h.; and afterwards draw from
+the point m. above the line e.&nbsp;f. in the direction of f. a short horizontal
+line as great as need be: then describe a semicircle which shall include
+this line, and the point n., and, at the top, the side a.&nbsp;b.; and through n.
+let pass a vertical line. These all combine to form, below, the concave
+of the curved limb, and above, its convex.</p>
+
+<p>Next, produce the transverse strip above c.&nbsp;d., in the direction of d.,
+<a class="pagenum" name="Page_8" title="8"> </a>
+as far as required, and mark this q. Then bisect the line m.&nbsp;q. by the
+line o.&nbsp;p., cutting the line n. in the point r.; and next describe a semicircle
+touching the horizontal line e.&nbsp;f., the point r., and the position
+q. Then indicate the breadth of this limb of the letter by the point s.
+to the right of the point r. in the line o.&nbsp;p. and describe a semicircle,
+touching the line m., the point s., and the side of the square c.&nbsp;d. There
+will then remain in the letter three right angles to be eliminated: the
+interior and lower one may be shaped into a curve by a circle whose
+semi-diameter is two-thirds of the breadth of the broad limb of the
+letter, and the exterior ones you shall fine to a point by circular lines
+whose semi-diameter is equal to the breadth of that limb.</p>
+
+<h3>Another method.</h3>
+
+<p>Or you may make your B in this fashion: Let the side a.&nbsp;c. of the
+square be divided into nine equal parts, and cut off the four superior
+parts by the horizontal line e.&nbsp;f. Then erect your vertical limb as
+described above; and the superior curved limb you shall make between
+a.&nbsp;b. and e.&nbsp;f.; the inferior between e.&nbsp;f. and c.&nbsp;d.</p>
+
+<p>Now divide a.&nbsp;b. into nine equal parts, and cut off four parts towards
+b. in the point g.; then divide c.&nbsp;d. into five equal parts, and the last,
+towards d. mark off in the point h. and join g. and h. by the line g.&nbsp;h.
+which should touch on their exterior edges the superior and inferior
+limbs of the letter. Now these limbs must be drawn of a particular form;
+and the compass, in drawing the circular lines, must be moved up and
+down their diagonals: and these two diagonals you shall determine in
+this wise.</p>
+
+<p>Divide a.&nbsp;e. into four parts; the lowest, above e., call i.&nbsp;e.; the lowest of
+the five remaining, above c., call c.&nbsp;k. Then join the points i. and b. and
+k. and f. respectively, by the lines i.&nbsp;b. and k.&nbsp;f. Upon these lines move
+and turn your compass, &amp; in this way you shall describe both curved
+limbs: and they must both be broader towards the top than towards
+the bottom, as follows naturally with the stroke of a pen, and, moreover,
+while approximately round, they are not to be circular; therefore
+you will have to move your compass at need along the diagonals, and
+withal to assist it also with the hand, as I have done in the picture on
+the following page.</p>
+
+<div class="figcenter" style="width: 289px;"><a class="pagenum" name="Page_9" title="9"> </a>
+<img src="images/i013.png" width="289" height="256" alt="B"/>
+</div>
+
+<h2><a name="Letter_C">OF THE LETTER C.</a></h2>
+
+<p>Next you shall make the letter C in its own square thus: Bisect the
+square a.&nbsp;b.&nbsp;c.&nbsp;d. by the horizontal line e.&nbsp;f. and in it let i. be the middle
+point. From this point as the centre, &amp; i.&nbsp;f. or i.&nbsp;e. as the radius, describe
+a circle touching interiorly all four sides of the square. Now move the
+leg of the compass, but without varying its span, to a point k. a little to
+the right of i. in the line e.&nbsp;f., letting the space i.&nbsp;k. denote the greatest
+breadth of the letter you desire; &amp; from the centre k. describe another
+circle which shall cut twice the line b.&nbsp;d., and whose circumference to
+the left will mark the required breadth of the letter. Next, draw the
+vertical line g.&nbsp;h., parallel to b.&nbsp;d., distant from b. a tenth part of the line
+a.&nbsp;b. This will cut off for you at top and bottom the letter C as the ancients
+were accustomed to use it. But I would have you cut off the lower
+limb in the middle point between g.&nbsp;h. and b.&nbsp;d.: then make the limbs
+somewhat finer and rounder on the inside towards top and bottom
+from the point where the circles intersect; and for its greater perfection
+<a class="pagenum" name="Page_10" title="10"> </a>
+round out the letter, above and below, to touch the sides of the square
+a.&nbsp;b. and c.&nbsp;d. Next, low down, where the letter with one foot crosses
+the line g.&nbsp;h., there, under the circular line make the form a little more
+incurved, yet so that with the tip of its end it shall again touch the circular
+line. Similarly, but higher up, make the foot more hollow on the
+inside than the circle left it: and thus two circular lines will give you
+very nearly the whole form of the letter.</p>
+
+<h3>Another method.</h3>
+
+<p>Or, secondly, you may make the letter C thus: Draw in the square
+a diagonal c.&nbsp;b.; set the leg of your compass on its middle point i. and
+with the other leg describe the exterior circle as before, terminating it
+above at the diagonal c.&nbsp;b.; but below, make your circle pass a little beyond
+the former sweep. Then set the leg of your compass, but without
+changing its gauge, as far above i. in the diagonal as the letter's greatest
+width, and describe your inner circle; and, as though made with a pen,
+let the descending stroke be heavier than the ascending. The rest you
+may elaborate with your hand; &amp; let the trimming of the ends of the
+letter, above, slope upwards, &amp; below, downwards, exactly as I have here
+drawn the shapes.</p>
+
+<div class="figcenter" style="width: 288px;">
+<img src="images/i014.png" width="288" height="249" alt="C"/>
+</div>
+
+<h2><a class="pagenum" name="Page_11" title="11"> </a><a name="Letter_D">THE LETTER D.</a></h2>
+
+<p>The letter D you shall make thus: Divide its square by the perpendicular
+or vertical line g.&nbsp;h. and by the horizontal line e.&nbsp;f. into four
+small squares, and call their point of intersection i.: then draw the
+broader limb of the letter from the side a.&nbsp;b. downwards, to meet the
+side c.&nbsp;d. and at the distance of its own width from a.&nbsp;c.; and produce
+the limb at top and bottom to a sharp point at the angles a. and c. as
+was shown above in <a href="#Letter_B">B</a>; using the same method in all straight limbs in
+the remaining letters. Next you are to produce from this limb two
+narrower tracts horizontally, and from these are to be described the
+circular arcs of the letter between the line a.&nbsp;b. at top and the line c.&nbsp;d.
+at bottom, and extending as far as the perpendicular g.&nbsp;h.; next, with
+your compass join g.&nbsp;f.&nbsp;h. Then, in the line e.&nbsp;f. lay off a portion equal
+in breadth to the widest limb of the letter, at the point k.; next, set one
+foot of your compass on k. and let the other cut the said line e.&nbsp;f. in l.;
+let this be the immovable leg of your compass, and with the other, beginning
+from k., describe internally, to the narrower transverse limbs,
+an arc which shall touch both, completing your acute angle above, but
+rounding out the lower one by a circular arc of the same diameter as
+the one by which you sharpened your exterior subtending angle.</p>
+
+<h3>Another method.</h3>
+
+<p>You may make the round limb of the same D in another fashion;
+namely, as a pen naturally would, broader above than below. For this,
+draw the diagonal c.&nbsp;b. and describe your exterior arc as before; but to
+describe the interior, in the line c.&nbsp;b. take a point m. lower down than
+i. and distant from it the width of the broader limb, and without altering
+your compass describe an interior line; but where the limb must
+needs be narrower, there you are to accommodate it with your hand,
+both below and above, as in the following cut.</p>
+
+<div class="figcenter" style="width: 267px;">
+<img src="images/i015.png" width="267" height="135" alt="D"/><br/>
+<a class="pagenum" name="Page_12" title="12"> </a><img src="images/i016.png" width="255" height="112" alt=""/>
+</div>
+
+<h2><a name="Letter_E">THE LETTER E.</a></h2>
+
+<p>The letter E you shall form in its square thus: Draw a transverse
+line e.&nbsp;f. bisecting a.&nbsp;b. and c.&nbsp;d. in e. and f.; then draw the great vertical
+limb of the letter, to the left, as you did for <a href="#Letter_D">D</a>. Next draw also
+an upper transverse limb of narrower dimensions, parallel to a.&nbsp;b. and
+in length six-tenths minus one-third of one-tenth of the length of a.&nbsp;b.;
+and the end of this bend downwards one-tenth of the length of a.&nbsp;b.
+and use this as the diameter of the circle with which you round out
+the inner angle of this extremity: then draw your narrow middle limb
+parallel to the median line e.&nbsp;f. and above it, so that it may be shorter
+than the upper limb by one-tenth of the length of a.&nbsp;b., but at its terminus
+double as wide; &amp; you are to round it out (in either direction)
+by the arc of a circle whose diameter is one-sixth the length of e.&nbsp;f.
+Now construct your lowest limb upon the line c.&nbsp;d., so that at its ultimate
+angle it may exceed in length the upper limb by one-tenth of
+c.&nbsp;d.; the cusp, however, you are to prolong beyond this part by
+two-thirds
+of one-tenth part, and erect above it to one-sixth of the length
+of c.&nbsp;d., and round out the same by a circle whose semi-diameter is also
+a sixth of c.&nbsp;d. In like manner the final angle of the letter you shall
+round out by an arc of the same circle by which you rounded out the
+middle transverse limb: the other angles you are to leave acute, as in
+the following cut.</p>
+
+<div class="figcenter" style="width: 257px;"><a class="pagenum" name="Page_13" title="13"> </a>
+<img src="images/i017a.png" width="257" height="128" alt="E"/>
+</div>
+
+<h2><a name="Letter_F">THE LETTER F.</a></h2>
+
+<p>The letter F you are to form in the same manner as <a href="#Letter_E">E</a>; except that
+you shall omit the lower limb altogether, and, in its place, round out
+the letter on both sides below, as you did E on one side only, as I have
+shown you below.</p>
+
+<div class="figcenter" style="width: 249px;">
+<img src="images/i017b.png" width="249" height="126" alt="F"/>
+</div>
+
+<h2><a name="Letter_G">THE LETTER G.</a></h2>
+
+<p>Likewise the letter G you are to make as you did <a href="#Letter_C">C</a>, before described;
+this, however, excepted: that in front (that is, to the left) of the line g.&nbsp;h.
+is to be erected the broad limb of the letter, upwards from the curve
+to the line e.&nbsp;f., and above it is to be rounded to a point, on either side,
+as before was said; but below, both angles are to remain.</p>
+
+<p>Or, you shall form G in the following fashion in the said square,
+divided as before: Draw the diagonal c.&nbsp;b. and set your compass with
+one leg on the point i. and with the other describe an arc from e. to the
+middle point c.&nbsp;d. and mark this point l.; in like manner also, describe
+<a class="pagenum" name="Page_14" title="14"> </a>
+an arc upwards to the line a.&nbsp;b. so as to meet the perpendicular line
+g.&nbsp;h. &amp; mark that point z. Then, in the line g.&nbsp;h., take a point m. so that
+the part m.&nbsp;h. shall be one-tenth of the line g.&nbsp;h.; then, with a sweep of
+your hand join l. &amp; m. with the curved line l.&nbsp;m. Next, you are to draw
+from z. a line upwards, as broad as the standard of the letter, but oblique
+and in direction midway between your circular line &amp; the perpendicular
+g.&nbsp;h. and from the extremity of this line you must draw a curved
+line to meet a.&nbsp;b. at the point where your circular line touches it. Next,
+cut off from the bottom of g.&nbsp;h. a part one-third of its length, &amp; indicate
+this by the point n., &amp; to this height, from the level of m. upwards,
+produce the broad limb of the letter, and let its extremities above be
+finished in either direction, of the same size. After this set the leg of
+your compass on the diagonal c.&nbsp;b. the breadth of the standard of the
+letter above i. &amp; at the distance e.&nbsp;i. describe an arc, which above shall
+touch the exterior boundary a.&nbsp;b. but below shall stop short above l.;
+&amp; from this point you must with your hand draw a line to the vertical
+limb at the height of m.</p>
+
+<p>And the same you shall do above in drawing the narrower limb of
+the letter, as seen in the following diagram.</p>
+
+<div class="figcenter" style="width: 271px;">
+<img src="images/i018.png" width="271" height="248" alt="G"/>
+</div>
+
+<h2><a class="pagenum" name="Page_15" title="15"> </a><a name="Letter_H">THE LETTER H.</a></h2>
+
+<p>The letter H is to be formed of two broad, great, &amp; vertical limbs of
+the height of the square, in such fashion that their extremities, being
+produced exteriorly, shall touch the four angles of the square, a.&nbsp;c. and
+b.&nbsp;d. respectively. Now in what fashion the projections of the broader
+limbs of letters are to be rounded out at top and bottom and on either
+side, you have been instructed; for in any letter you please, any broad
+and vertical limb is to be depicted at top and bottom thrice as broad as
+at its middle: provided always it is not joined to a narrower limb. So
+when this has been accomplished, then draw your narrower transverse
+limb upon the line e.&nbsp;f. as is shown below.</p>
+
+<div class="figcenter" style="width: 272px;">
+<img src="images/i019a.png" width="272" height="124" alt="H"/>
+</div>
+
+<h2><a name="Letter_I">THE LETTER I.</a></h2>
+
+<p>The letter I you are to make of a single broad vertical tract in the
+midst of its square, touching the latter top and bottom; and of this, at
+both ends, and on either side, you are to round out the productions or
+projections as below is shown.</p>
+
+<div class="figcenter" style="width: 237px;">
+<img src="images/i019b.png" width="237" height="123" alt="I"/>
+</div>
+
+<h2><a class="pagenum" name="Page_16" title="16"> </a><a name="Letter_K">THE LETTER K.</a></h2>
+
+<p>Now for K: You are to make the first tract vertical, in the same manner
+as you formerly did for <a href="#Letter_H">H</a>; then draw another narrower limb from
+the broader and erect one, so that it may, at its lower end, impinge
+obliquely on the transverse line e.&nbsp;f. and above may ascend to the right
+till it meet the line a.&nbsp;b., taking care to make it parallel to the diagonal
+c.&nbsp;b.; and this, at the top, you are to produce in both directions so that
+each production may represent a tenth part of the line a.&nbsp;b. The hitherward
+projection you are to round out with a circle of which the diameter
+must not exceed the breadth of the lesser limb; but of the other
+arc, by means of which you round out the farther projection, you shall
+make the diameter double as great as the diameter of the arcs by which
+you have customarily hollowed out the preceding extensions of the
+broad and vertical limbs. Next, from the narrow limb so constructed
+draw in a downward direction another broad limb, so that it too may
+be parallel to a diagonal of the square; &amp; of this the beginning is to be
+taken from the acute angle which the narrower limb makes with the
+broad vertical limb, and let it be drawn with its projection to the angle
+d., yet in this fashion: take two points this side of d. after this manner,
+so that the first point may be distant from d. the tenth part of the line
+c.&nbsp;d. &amp; the second as far again from the first; then let the said tract be
+drawn within the space which is between the two points, but in blind
+and invisible lines. Afterwards you shall add the extension, which you
+shall make this way: take before f. in the line e.&nbsp;f., a point g. no farther
+distant from f. than the breadth of the narrower limb; on this point
+set one leg of your compass, &amp; let the other be extended to the angle d.,
+from which let it be guided back along the broad but invisible blind
+limb: thence will result the lower convexity of the tail you seek; but
+its upper concavity look for in this way: divide f.&nbsp;d. in its middle point
+h.; on this set one leg of your compass, and with the other describe an
+arc passing through d. to meet the broad limb.</p>
+
+<p>Or you may make K in this manner: First, let your broader vertical
+limb, and your upper narrow one remain as they have been described,
+except that the interior angle which the narrower limb forms with a.&nbsp;b.
+shall remain acute, but the exterior one shall be rounded out, as has
+<a class="pagenum" name="Page_17" title="17"> </a>
+been said. Then let there be drawn the lower broad limb, obliquely
+from the angle which is included between e.&nbsp;f. and the vertical limb,
+and let it descend to meet the side c.&nbsp;d. so that between d. and the limb
+the width of the limb be left vacant; and the hither angle is to be left,
+but the farther, towards d., shall be rounded out a little, as shown below.</p>
+
+<div class="figcenter" style="width: 353px;">
+<img src="images/i021a.png" width="353" height="128" alt="K"/>
+</div>
+
+<h2><a name="Letter_L">THE LETTER L.</a></h2>
+
+<p>As for the letter L, you shall make it by a combination of parts of
+two of the preceding letters: namely, you shall make the first vertical
+broad limb, as you did a while back in <a href="#Letter_I">I</a>; and to this join a foot as you
+did at the bottom of <a href="#Letter_E">E</a>, when you made it. Such is L depicted below.</p>
+
+<div class="figcenter" style="width: 265px;">
+<img src="images/i021b.png" width="265" height="124" alt="L"/>
+</div>
+
+<h2><a name="Letter_M">THE LETTER M.</a></h2>
+
+<p>The letter M you shall form in two ways within its square. In the
+first, draw the narrower limb of the letter vertical, to the right of a.&nbsp;c.,
+distant from a. one-tenth of the distance a.&nbsp;b.: draw the other, &amp; broader
+limb, on the near side of b.&nbsp;d., also a tenth part of the whole distant
+<a class="pagenum" name="Page_18" title="18"> </a>
+from b. &amp; in such fashion that both limbs touch the square at top and
+bottom; then, between the two, bisect the line c.&nbsp;d. in the point e. and
+draw a broad limb from the inner angle of the narrow limb, downwards
+to the point e., &amp; next a narrow one upwards from e. to the inner angle
+of the broader vertical limb; and the inner angles at top you must not
+round out, but leave acute; the exterior angles, however, at the top, and
+both exterior and interior at bottom of both vertical limbs, you are to
+adorn with the customary projections, as you have done in the preceding
+letters. You are to know, too, that when these letters are drawn with
+a pen, they are to be described with a single stroke. But for your guidance
+is this letter, in the manner in which I have instructed you, depicted
+below.</p>
+
+<h3>Another method.</h3>
+
+<p>Another way is thus: Divide the side a.&nbsp;b. of the square into six equal
+parts &amp; mark off the two extreme parts, one at either end, by the points
+f. and g.; then draw the inner and broader limb, with its point at e. as
+above; and to this, in an upward direction, a narrower one, so that between
+f.&nbsp;g. be left a vacant space, and so more readily the letter slope
+forward. Then you are to draw the two lateral and vertical limbs&mdash;the
+near and slender, and the farther broad one&mdash;at the top, indeed, as in
+the first sketch, but at the bottom produce them to the two angles c.
+and d. and finally add projecting cusps, as you were instructed in the
+first M; but the projection below will pass beyond the square at the
+points c. and d. Or you shall make M at top with acute angles, in which
+case the lateral limbs will slope the more; or shear them off obtusely,
+and in this fashion (whichever pleases you best) make them as you see
+them depicted in the following diagrams.</p>
+
+<div class="figcenter" style="width: 365px;">
+<img src="images/i022.png" width="273" height="135" alt="M"/><br/>
+<a class="pagenum" name="Page_19" title="19"> </a><img src="images/i023.png" width="365" height="111" alt=""/>
+</div>
+
+<h2><a name="Letter_N">THE LETTER N.</a></h2>
+
+<p>Likewise the letter N you shall make in its square thus: First you
+are to draw two standards vertical and slender, so that at top &amp; bottom
+they may touch the square, &amp; that being produced, the nigh one at the
+bottom, and the farther at the top, they may touch the angles at c. and
+b. Now join these two by a broad oblique limb, running from the angle
+a. to the point e., by which is denoted the remote side of the farther
+limb, where you shall allow the acute angle to remain; but at the top,
+this limb, produced beyond the angle a., you are to round out to a fifth
+part of the length of a.&nbsp;b. This prolongation should incurve below, a
+fifteenth part of the distance a.&nbsp;b. projected on two arcs, the upper one
+the greater, the lower the less. For the lesser arc, therefore, you shall
+take as diameter of its circle, a line the fifth part of the distance a.&nbsp;b.
+and its centre is to be taken outside the square, so that the foot of the
+compass may touch the tip of the extension and the angle a.; then extend
+a little the feet of the compass, and shift its centre until the arc
+touch both the tip of the part produced, &amp; the broad oblique limb, in
+the middle point between the side a.&nbsp;c. &amp; the nearer of the two slender
+vertical limbs.</p>
+
+<p>Or you may make the letter N in such fashion that its upper nigh
+extension shall remain within the square; or you may make from it an
+acute angle as shown overleaf.</p>
+
+<div class="figcenter" style="width: 284px;"><a class="pagenum" name="Page_20" title="20"> </a>
+<img src="images/i024a.png" width="284" height="252" alt="N"/>
+</div>
+
+<h2><a name="Letter_O">THE LETTER O.</a></h2>
+
+<p>Now O you shall make this way in its square. Set in the square the
+diameter c.&nbsp;b. and bisect it in the point e., so that e. may form a middle
+point between the two points f. and g. which are to be your two centres;
+and from each let a circle be described touching two sides of the
+square; &amp; where the circles cut one another, there with your hand you
+must shape the slender outline of the letter to a juster proportion, as
+below is shown.</p>
+
+<div class="figcenter" style="width: 258px;">
+<img src="images/i024b.png" width="258" height="124" alt="O"/>
+</div>
+
+<h2><a class="pagenum" name="Page_21" title="21"> </a><a name="Letter_P">THE LETTER P.</a></h2>
+
+<p>P you shall make in its square in this wise. Divide the square a.&nbsp;b.&nbsp;c.&nbsp;d.
+by the median horizontal line e.&nbsp;f.; then divide a.&nbsp;e. &amp; b.&nbsp;f. equally
+by the line g.&nbsp;h. Next draw, first the broad vertical limb for this letter
+P, as you did a short while ago for <a href="#Letter_K">K</a>, and afterwards erect the line i.&nbsp;k.
+the distance of its own breadth to the right of your vertical limb; (here
+you must ever observe that in a lettered square we speak of the angle a.
+as the &ldquo;hither&rdquo; angle, that is, to the left; &amp; the angle b. as the &ldquo;farther&rdquo;
+angle, that is, to the right). Then where the line i.&nbsp;k. cuts g.&nbsp;h. call the
+point l., and next draw two slender horizontal limbs, the upper below
+a.&nbsp;b., the lower above e.&nbsp;f., from the broad vertical limb as far as the line
+i.&nbsp;k. Set one leg of the compass on the point l., extending the other to
+the lower side of the lower horizontal limb near k.; then describe an
+arc through the line g.&nbsp;h. as far as the other slender horizontal limb of
+this same P, &amp; where it cuts the line g.&nbsp;h. set the point m. Next, on the
+far side of m. measure the width of the large limb of the letter, along
+the line g.&nbsp;h. to the point n. and let your compass be stretched so that
+with one foot it may touch the line a.&nbsp;b. and with the other the point
+n.; then set one foot of the compass on n. &amp; the other on the line g.&nbsp;h.
+to the right, in the point o., in which this foot is to be left standing immovable,
+and with the other is to be described an arc, passing through
+the point n. and touching the lines a.&nbsp;b. and e.&nbsp;f.</p>
+
+<p>Or you may form the loop of this letter in the following manner.
+Set a leg of the compass under the transverse g.&nbsp;h. in the line i.&nbsp;k., in a
+place median between the line e.&nbsp;f. &amp; the lower part of the upper transverse
+of the slender limb, in the point p. and describe an arc as before,
+passing through m. so that the loop will be acute at the bottom, and
+its tip will end in the middle space between the line i.&nbsp;k. and the broad
+vertical limb of the letter.</p>
+
+<p>Or make this same P with a circular sweep, by shifting the compass
+upon the diameter, so that that sweep may be broader at the top (as
+though made with a pen) as will be shown in the diagram on the following
+page.</p>
+
+<div class="figcenter" style="width: 252px;"><a class="pagenum" name="Page_22" title="22"> </a>
+<img src="images/i026.png" width="252" height="125" alt="P"/>
+</div>
+
+<h2><a name="Letter_Q">THE LETTER Q.</a></h2>
+
+<p>Make your Q in its square in the self-same manner as was prescribed
+for <a href="#Letter_O">O</a>; but add to it its tail thus: Draw a diameter of the square,
+the line a.&nbsp;d., about which, starting from the curved outline, begin to
+draw a long tail, producing it through the angle d. in such fashion that
+d. may be in the middle of the thickest part of the tail; but where the
+tail begins let it be a little narrower than in the angle d., where it should
+attain its real thickness. Then let it be drawn out, beyond the angle d.
+to the length of the entire diameter, and in a downward direction, yet
+so that it curves while it slopes, &amp; that its tip shall not fall lower than
+a third of the side below the lowest side of the square, and shall tend,
+as it nears the point, to grow sharper little by little, and at length end
+in a very fine point indeed.</p>
+
+<p>Or you shall give Q a shorter tail in this fashion, to wit: set your
+compasses to the length of the side c.&nbsp;d. and draw a tail from the bulge
+of the same letter, describing through the point d. its inner arc of the
+same length as c.&nbsp;d., taking care that the tail bend upwards until it again
+reach c.&nbsp;d. produced, in the point h.; then shift your compasses, &amp; with
+the other leg again describe from the bulge of the letter an arc below
+d. &amp; continue it until again it reach h., but in such fashion that the tail
+shall find its greatest thickness at the start, as in the following figure
+is doubly depicted.</p>
+
+<div class="figcenter" style="width: 333px;"><a class="pagenum" name="Page_23" title="23"> </a>
+<img src="images/i027.png" width="333" height="305" alt="Q"/>
+</div>
+
+<h2><a name="Letter_R">THE LETTER R.</a></h2>
+
+<p>Moreover R you must make in its square just as was directed for <a href="#Letter_P">P</a>;
+but then erect a right line q.&nbsp;r. through the middle point of the square,
+&amp; let it cut the exterior arc of the rounded limb in s., from which point,
+downwards towards the angle d., let there be drawn a broad tract, almost
+equal to that which you made above for the letter <a href="#Letter_K">K.</a>, but this is to be
+somewhat bent in, and so shaped by your hand that its tip, well formed,
+may arrive directly on the angle d.</p>
+
+<p>Or make R in such fashion that its rounded sweep, as though made
+with a pen, shall be above broader, &amp; narrower below. To accomplish
+this, you must shift your compasses on the diameter q.&nbsp;e. &amp; not allow
+the rounded limb to touch the vertical one, as was described in <a href="#Letter_P">P</a>. Besides,
+the oblique limb is to be deduced from the rounded one with a
+little more of a curve; just as I have drawn overleaf.</p>
+
+<div class="figcenter" style="width: 352px;"><a class="pagenum" name="Page_24" title="24"> </a>
+<img src="images/i028.png" width="352" height="131" alt="R"/>
+</div>
+
+<h2><a name="Letter_S">THE LETTER S.</a></h2>
+
+<p>Next, the letter S you shall make as follows in its square, a.&nbsp;b.&nbsp;c.&nbsp;d.
+First draw the horizontal line e.&nbsp;f. and the median &amp; vertical one g.&nbsp;h.
+and let them bisect one another in the point m. Then choose the main
+thickness of the letter, and set it in the line g.&nbsp;h. so that the point m.
+may divide it, having one-third of the thickness below it; next, set the
+lesser thickness, at the top beneath g., indicating it by the point i., and
+at bottom, above h. in the point k.; and the thickness of the letter indicate
+above by n. and below by l.</p>
+
+<p>Next, set a leg of your compasses on the line g.&nbsp;h. in the mid-point
+between i. and n., and with the other describe a circle passing through
+i. and n.; in like manner, upon the line g.&nbsp;h. set your compasses upon
+the mid-point of g.&nbsp;l. and describe a circle passing through g. &amp; l. Then
+once more set your compass on the same line g.&nbsp;h. in the mid-point of
+n.&nbsp;h. and describe a circle through n. &amp; h.; and lastly, in the mid-point
+of l.&nbsp;k. you must set one leg, &amp; with the other is a circle to be described
+through these same points l. &amp; k.; afterwards cut off by vertical section
+the upper portion of this letter, so that the part thus cut off may contain
+in its extremity the maximum thickness of the letter and a third
+part besides, &amp; also that its tip may project downwards so far as to stand
+midway between the centre of the circle i.&nbsp;n. and the side b.&nbsp;d.; in other
+words, let the tip be distant on the right, from the circle i.&nbsp;n. the first
+third of the interval between the greater and lesser circles.</p>
+
+<p>Next cut the lower limb of the letter to the left, by a vertical line
+through the mid-point between the two circles, &amp; in such fashion that
+<a class="pagenum" name="Page_25" title="25"> </a>
+the part so cut off may be a fourth part wider &amp; higher than the upper,
+and that its tip may rise to the height of the centre of the circle n.&nbsp;h.</p>
+
+<h3>Another method.</h3>
+
+<p>Yet another way may you make the letter S. In the square a.&nbsp;b.&nbsp;c.&nbsp;d.
+bisect the horizontal line e.&nbsp;f. in the point m.; then set one leg of your
+compass upon the mid-point between g. and m. &amp; with the other describe
+a segment of a circle in the direction of a.&nbsp;e. passing through the
+points m. and g.; next, set your compass upon the mid-point between
+m. and h. and describe a segment of a circle through m. and h. in the
+direction of f.&nbsp;d. The two arcs will touch above, in front, and below, in
+the rear, the exterior curvatures of this same letter S.</p>
+
+<p>Next, draw through m. the diameter c.&nbsp;b. and at its middle indicate
+the maximum thickness of the letter by the two points p. and q. from
+which let there be drawn two right lines, one up, &amp; one down, to those
+two arcs; &amp; next, from the two points p. &amp; q. draw two curved parallels
+to the same arcs, regulating the distance between them, their elevation
+&amp; depression from the centres of the same circles. Next, indicate below
+g. and above h. the minimum thickness of the letter; and from these
+points you will with your hand fashion the inner shape of the letter,
+both above and below, &amp; produce the limb of S, above towards b. Cut
+it off so that its lower tip may touch the segment, &amp; that the part cut
+off upwards may contain a tenth part of a.&nbsp;b. and that the segment may
+still exceed the part cut off. Then construct a vertical line r.&nbsp;s. to the
+right of e.&nbsp;c. and distant from it a fifth part of c.&nbsp;d.; let it cut the diagonal
+c.&nbsp;b. in t. and to the angle just formed produce the extremity of
+the letter, making the part so cut off a third broader than the upper portion.
+Lastly, you will have to produce the tip ever so little beyond t.; as
+I have briefly indicated.</p>
+
+<div class="figcenter" style="width: 263px;">
+<img src="images/i029.png" width="263" height="136" alt="S"/><br/>
+<a class="pagenum" name="Page_26" title="26"> </a><img src="images/i030.png" width="215" height="111" alt=""/>
+</div>
+
+<h2><a name="Letter_T">THE LETTER T.</a></h2>
+
+<p>Set the broad limb of T in the midst of its square erect, produced &amp;
+drawn to a point on either side below, just as you did before in the letter
+<a href="#Letter_I">I</a>; then take two points e. and f., distant respectively one-tenth of the
+whole space from a. and b., and let the transverse limb of the letter be
+drawn below e.&nbsp;f. and of an equal length with it; but the projecting extremities
+of this line are to be cut obliquely, and the tips of these projections
+shall so far extend above the line a.&nbsp;b. to the right as below they
+depend to the left. The oblique lines of these projections are to be each
+a fifth part of the length of a.&nbsp;b.; &amp; the angles of these projections you
+shall round out by means of circles of diverse radius&mdash;namely, for the
+lesser angle you are to use a diameter only two-thirds of the width of
+the broader limb; but for the greater angle you shall take a diameter
+equal to the side of a square contained between the broad and vertical
+limb and the intercepted portion of the line a.&nbsp;b.</p>
+
+<h3>Another method.</h3>
+
+<p>Or you make T thus in its square: Take your point e. as before, to
+the right of a., and cut your transverse limb diagonally, as before, yet
+so that the projection be dimidiated to the right, and at top the angle
+remain as it falls; and so at the other extremity, only the point f. must
+be moved as near again to b., the cutting line to be a little more erect,
+&amp; the projection formed a trifle broader than at the hither end; otherwise
+shall everything remain as before; as I have delineated for you on
+the opposite page.</p>
+
+<div class="figcenter" style="width: 343px;"><a class="pagenum" name="Page_27" title="27"> </a>
+<img src="images/i031a.png" width="343" height="146" alt="T"/>
+</div>
+
+<h2><a name="Letter_V">THE LETTER V.</a></h2>
+
+<p>V you shall thus make in its square: Bisect c.&nbsp;d. in the point e.; then
+set the point f. one-tenth of the whole line a.&nbsp;b. beyond a., and in like
+fashion g. to the hither side of b. Then draw the broad limb of your
+letter downwards from f. to e. and sharpen it; &amp; thence draw upwards
+your slender limb to g.; and at the top produce it in either direction,
+as you did before at the bottom of <a href="#Letter_A">A</a>; just as you see it shown below.</p>
+
+<div class="figcenter" style="width: 256px;">
+<img src="images/i031b.png" width="256" height="132" alt="V"/>
+</div>
+
+<h2><a name="Letter_X">THE LETTER X.</a></h2>
+
+<p>X you shall form thus: Draw two vertical lines e.&nbsp;f. and g.&nbsp;h. distant
+respectively one-tenth part of the line a.&nbsp;b. from the sides a.&nbsp;c. and b.&nbsp;d.
+Then draw the two limbs intersecting one another in the form of a
+cross&mdash;the broad one so that at top, &amp; with its hither side it shall touch
+e., &amp; at the bottom, and with its farther side h.; but the narrow limb so
+that at top, and with its farther side it may touch g., &amp; at bottom, with
+its hither side f. Then add its projections, touching, at top and bottom,
+the four angles a.&nbsp;b.&nbsp;c.&nbsp;d., &amp; choose a semi-diameter of the larger circle
+<a class="pagenum" name="Page_28" title="28"> </a>
+of the length of a fifth part of a.&nbsp;b.; &amp; with that you shall round out the
+four greater angles; but for the lesser circle you shall take a diameter
+as long as two-thirds the width of the broader limb.</p>
+
+<p>Or you may vary X thus: Let everything be left as before except the
+narrower limb, which at top you shall make more erect by one-half the
+breadth of the wider limb; and so the upper part of the letter shall be
+less and narrower than the lower, and shall have a different aspect, as
+is shown below.</p>
+
+<div class="figcenter" style="width: 354px;">
+<img src="images/i032a.png" width="354" height="143" alt="X"/>
+</div>
+
+<h2><a name="Letter_Y">THE LETTER Y.</a></h2>
+
+<p>Y you shall achieve in the midst of its square, as far as its lower half
+is concerned, after the instructions before given for <a href="#Letter_I">I</a>; but its upper part
+you shall divide so that its hither limb shall contain two-thirds, and its
+farther one-third of the broad standard; and let them slope to either
+side so that produced they may touch the two angles a. and b.; and the
+greater circles, by which you are to round out their obtuse or greater
+angles, make of a diameter as great as a containing side of the square
+enclosed between the standard and the sides of the great square, as in
+<a href="#Letter_T">T</a> was shown; but the diameters of the circles which you apply to the
+lesser angles, make double the width of the broad standard, as below.</p>
+
+<div class="figcenter" style="width: 278px;">
+<img src="images/i032b.png" width="278" height="131" alt="Y"/>
+</div>
+
+<h2><a class="pagenum" name="Page_29" title="29"> </a><a name="Letter_Z">THE LETTER Z.</a></h2>
+
+<p>Z you shall make thus: Set upon either side, both beneath &amp; beyond
+the angle a., two points e. &amp; f., each at a distance of the tenth part of a.&nbsp;b.;
+so also, set two other points g. and h. both before and above the angle d.
+and with right lines join e.&nbsp;f. and g.&nbsp;h.; then draw your narrower transverse
+limb, beneath a.&nbsp;b. backwards as far as the angle b.; from thence
+draw your broad limb diagonally to c.; and then again a narrower one
+from c. to g.; and with your hand round out the two tips e. and h.</p>
+
+<p>Or make Z thus: Divide the square a.&nbsp;b.&nbsp;c.&nbsp;d. by the vertical line e.&nbsp;f.
+and in this reduced space construct the letter as before; but so that the
+two transverse limbs be cut short, above on the nigh side, and below on
+the far, by the vertical lines a.&nbsp;c. and e.&nbsp;f. respectively as below.</p>
+
+<div class="figcenter" style="width: 281px;">
+<img src="images/i033.png" width="281" height="249" alt="Z"/>
+</div>
+
+<p>So likewise, in other fashion, can we make all the letters already
+drawn, on a scale of ninths, just as we have now drawn them on a scale
+of tenths; in just the same manner, according to the due proportion of
+each, in its own square, a.&nbsp;b.&nbsp;c.&nbsp;d., dividing them into nine, as just now
+into ten parts; &amp; that this may be the better understood, I have chosen
+to append here letters of such fashion. Also these letters are to be made
+five parts high when written small &amp; rapidly, by hand. In such writing
+the versals are made of the same proportion and form, but one-third
+larger than the ordinary letters of the writing.</p>
+
+<div class="figcenter page-break" style="width: 412px;"><a class="pagenum" name="Page_30" title="30"> </a>
+<img src="images/i034.png" width="412" height="565" alt="A to D"/>
+</div>
+
+<div class="figcenter" style="width: 417px;"><a class="pagenum" name="Page_31" title="31"> </a>
+<img src="images/i035.png" width="417" height="557" alt="E to L"/>
+</div>
+
+<div class="figcenter" style="width: 408px;"><a class="pagenum" name="Page_32" title="32"> </a>
+<img src="images/i036.png" width="408" height="556" alt="M to P"/>
+</div>
+
+<div class="figcenter" style="width: 408px;"><a class="pagenum" name="Page_33" title="33"> </a>
+<img src="images/i037.png" width="408" height="553" alt="Q to V"/>
+</div>
+
+<div class="figcenter" style="width: 330px;"><a class="pagenum" name="Page_34" title="34"> </a>
+<img src="images/i038.png" width="330" height="378" alt="X to Z"/>
+</div>
+
+<h2><a class="pagenum" name="Page_35" title="35"> </a>DIRECTIONS FOR THE CONSTRUCTION OF THE TEXT OR QUADRATE LETTERS</h2>
+
+<p class="drop-cap"><span class="upper-case">The</span> letters which are usually called &ldquo;text,&rdquo; or quadrate, it was formerly
+customary so to write, although they are now imitated by
+the new art, as presently I shall show below. Although the alphabet
+begins with the writing of A, yet shall I (not needlessly) in the first
+place undertake to draw an I; because almost all the other letters are
+formed after this letter, although always something has to be added to
+it or taken away.</p>
+
+<p>First make your I of equal squares, of which three are properly set
+one over the other; and the top of the top one, and the bottom of the
+bottom one, divide in two points, that is to say, into three equal parts:
+then set a square equal to the others in an oblique manner, so that its
+diagonal be vertical, and its angle on the first point of the top square. In
+this way, this oblique square shall extend with its angles more to the left
+than the right. Then produce upwards on either side, after the width
+of the superposed squares, right lines to meet the sides of the oblique
+set square. Next do below precisely as you did above, except that you
+must set the angle of the oblique square on the second point, that is, the
+one farthest to the right in the bottom of the lowest square; and let fall
+your lines on either side upon the transposed square: so will I be perfect;
+only above it draw with a fine pen a tiny in-crescent.</p>
+
+<p>So shall you make N from two standards of this same I, set so that
+their angles at top and bottom touch; and in this manner the space between
+the two shall be narrower than the breadth of either: also, you
+shall no longer put little crescents above them; you must make of the
+same length all the short letters throughout the alphabet.</p>
+
+<p>In like manner make M of three standards, just as you made N of
+two.</p>
+
+<p>R make as I, except only that at top you must set an equal square
+diagonally, to the right, so that angle touch angle. R you may make also
+in this fashion: below leave its foot as before, but above add two diagonal
+squares, which shall touch each other with their angles in the
+<a class="pagenum" name="Page_36" title="36"> </a>
+middle point of the vertical limb, and then produce upwards both sides
+of the latter to meet the diagonal square.</p>
+
+<p>V is made in three ways. First let it be made simply, as N; only that
+in the farther limb, you shall omit at the top the diagonal square; and
+instead shall draw an oblique line, so that it may make two angles in
+this limb (produced) of which the farther shall be of the same height
+as that of the topmost angle of the diagonal square, &amp; the higher angle
+of the same height as the angle nearest to it in the said square.</p>
+
+<p>The second V, which we use at the beginning of a sentence, make
+thus: Draw the first limb as before for I; only, at the bottom, push the
+diagonal square a little further to the right, so that its hither angle does
+not project beyond the side of the vertical limb, but falls in the line of
+its descent. Then set the second limb to the right of this, and cut it off
+below by an oblique line, drawn from the lowest angle upwards to the
+right, as far as the middle point of the lowest of the three superposed
+squares.</p>
+
+<p>Next make W (i.&nbsp;e., double V) just as you made V-simplex; only you
+shall set before it the standard limb of I.</p>
+
+<p>B make as the second V-simplex; but in the first upright omit the
+diagonal square at the top, and set upon the three original squares three
+others similar, but the seventh one you shall cut off diagonally from its
+lower hither angle.</p>
+
+<p>Likewise when your B so made is turned upside down, then it will be
+a Q.</p>
+
+<p>X you shall construct from I. Append from top angle to the right a
+diagonally set square, as you did before in R; and at the bottom draw
+an acute tail to the left from the diagonal, and at the middle of the vertical
+limb describe a transverse, in such way that the former is cut before
+and aft by the latter's diagonal; let the hither and lower angle be terminated
+as far in front of the upright as would measure one-half of the
+cutting diagonal, which at top shall just touch the upright; but to the
+right let the transverse at top project to a point just below the angle of
+the oblique square; from thence downwards let it be cut off by an oblique
+line parallel to the anterior diagonal.</p>
+
+<p>C you shall construct from I after this fashion: Remove the top diagonal
+square, &amp; let lines be produced on either side to the proper height
+of the letter, and cut off the hither angle by a diagonal; then draw at
+<a class="pagenum" name="Page_37" title="37"> </a>
+top a broad transverse, projecting beyond the vertical to the right the
+width of the latter, and cut this off by a diagonal in such a way that it
+project below only half as far as above.</p>
+
+<p>The vertical standard of E you shall make as for C; but from above
+let there descend to the right a broad limb from the diagonal bisecting
+the right angles of one square, and one-third again as long as broad; and
+let there be drawn from its lower angle a small diagonal line to the vertical
+limb.</p>
+
+<p>T shall be made like C, except that at top something is added to its
+diagonal, so that its tip converges to a fine point, and the like to the left
+on the hither side of the broad standard, just as at the top: and because
+of this is T at top more elegant than C, and has not the same incurved
+appearance.</p>
+
+<p>L you are to make below like I; only six squares are to be set on end;
+then cut off the hither side of the seventh by a diagonal, and so the apex
+of the letter shall remain to the right.</p>
+
+<p>The letter S you shall make as L; except that at top to the right must
+be drawn a broad limb of the length of the diagonal, which afterwards
+you are to cut off by a line parallel to the diagonal.</p>
+
+<p>F you shall make as S, just adding to it a transverse limb at the height
+of the shorter letters and double as long as broad, so that the point on
+the hither side &amp; below shall project as far as half the limb's breadth, so
+that the two diagonal abscissions may be equidistant from one another.</p>
+
+<p>The near limb of the letter H make like L, and to it join by its top, in
+the proper place, the farther made like I; but below, for the diagonal
+square, substitute a fourth square in line with the others, and the fifth
+and lowest cut off on the far side by its diagonal.</p>
+
+<p>Of K make the near limb like L; and to the right of it append a diagonal
+square, from the lowest angle of which let a line be obliquely
+produced to meet the said vertical limb; and next from this line let a
+broad limb be obliquely drawn, and this, at the bottom, you are to cut
+off by a diagonal, in such fashion that the space below, between the two
+tips shall not be more than the diagonal of a single square.</p>
+
+<p>D in its lower half make like B; but at top let the anterior limb
+ascend upwards to the maximum height of the letters, and then cut off
+the hither angle by its diagonal; next superpose to the same height half
+a square upon the other three squares of the farther limb, &amp; once more
+<a class="pagenum" name="Page_38" title="38"> </a>
+do here as you did below, and let this broken limb rest on the angle of
+the near limb, and let it extend beyond it as far as the end of the upright
+near limb; and so will it all but contain three conjunct squares;
+for when it meets the near vertical limb, that fraction is to be cut off
+at right angles.</p>
+
+<p>O you are to make below as D, and also the same at the top as the
+bottom, only, as it were, turning it upside down.</p>
+
+<p>The anterior limb of P make like L inverted; but the posterior like
+the standard of I: at bottom, however, you are not to add an oblique
+square, but amputate the limb diagonally, &amp; draw at the bottom a broad
+transverse limb, which likewise is to be cut off diagonally, so that the
+lower point shall project to the left, a distance of half the breadth of
+the limb.</p>
+
+<p>Likewise A in the lower half you are to make like N; but of its anterior
+vertical limb, you are to cut off the hither angle of the middle
+square by its diagonal; of the posterior, however, allow three squares to
+remain superposed, and incline the top part (the fourth square) rather
+to the left, so that if at this side is joined to it the half of a square, then
+it shall attain the height of the letter; and cut off the square obliquely,
+yet so that the lower point shall project farther than the upper; then
+describe to the left a circle, sweeping downwards, so that its contents
+shall embrace the farthest limit of the anterior limb.</p>
+
+<p>Z is made in threefold fashion. First set a diagonal square which
+shall touch the height of the letter; then add another like it, on the
+right, joining their sides, &amp; let these form a quadrangle sloping downwards
+on the right: next set a diagonal square in straight line under the
+top square, and distant from the lower one the length of its diameter:
+then draw a diagonal line between the near angles of these two squares,
+or make a rounded limb to reach the lower square; but from the said
+lowest square of all you shall draw downwards and to the right, by the
+aid of divers circles, a round extension, whose bottom shall mark the
+length of the letter; and let its tip, sharp and tenuous, verge to the left.
+Or construct Z of three oblique limbs, one above the other, &amp; to connect
+them draw the diagonal, which shall slope upwards to the right.</p>
+
+<p>Another Z you may make in this way: Let three diagonal squares
+be set atop of one another; and let the lowest have a rounded extension,
+as in the first Z.</p>
+
+<p><a class="pagenum" name="Page_39" title="39"> </a>The first limb of G make below like I, and add at the bottom another
+diagonal square, joining the two by their angles; but at top produce the
+farther tip of this limb upwards to the height of the letter, &amp; from this
+point draw a diagonal downward to the left, as far as the hither angle of
+the first right square of the three set one on other. Next draw the farther
+vertical standard entire, of the same length as the hither standard, and
+at the bottom draw a diagonal from the angle of the lowest oblique
+square to touch the tip of the angle of the farther limb, &amp; on the inner
+side produce downwards the side of the limb, to meet the tip of the said
+diagonal; to this also, by one line, join the lowest of the hither squares.
+Now draw at top a transverse limb of the customary breadth, from the
+back of the nearer vertical limb, passing through the farther one, and
+reaching as far beyond this as its breadth; &amp; this limb, finally, you shall
+cut off by an oblique line parallel to that of the near limb.</p>
+
+<p>Y you shall make as N, only at bottom must be omitted the farther
+diagonal square, &amp; in its place is to be set a right square under the other
+three superposed squares; then split the fifth square by a diagonal, so
+that the tip shall be in front; from which let there be produced a diagonal
+line, equal in length to a single side of the square.</p>
+
+<p>Curved, or short S, you shall make on this wise. At the middle height
+of the letter, let there be set, close to one another, their angles touching,
+two oblique squares; from the near square draw a broad vertical limb
+to the height of the letter; and in the same fashion, from the farther
+square let one fall downwards&mdash;just as you constructed I top &amp; bottom.
+Next cut off both these limbs, one at top and one at bottom, by diagonals,
+in such fashion that the sharp tips of both may be on the side
+near the middle. Then let there be drawn two broad limbs&mdash;namely,
+from the upper, to the right, and downwards; and in like manner, from
+the lower, upwards, and to the left; of the breadth of the limb, above
+and below, but let them be produced no further than the breadth of
+the distance between the limbs: then draw a diagonal downwards, from
+right to left, which shall cut off both oblique limbs. To it also you must
+produce the sides of the squares set in the midst.</p>
+
+<p>So, accordingly, have I set them down&mdash;in skeleton in rotation, and
+in proper order in black. This (as I said above) is the antique form of
+the letters; but in these days there is used a more elegant text, and a
+diagonal square is substituted in the middle place for a right square, so
+<a class="pagenum" name="Page_40" title="40"> </a>
+that the lines of the letters are not so much curved; and there are made
+certain limbs adjoined and cleft; and there are set one on another three
+squares &amp; a half; and spaces are left between two limbs as great as their
+width. Letters of this sort also have I set forth on the third page following;
+as also capital letters, which are called &ldquo;versals,&rdquo; because
+they are customarily set at the beginning of a verse;
+and these ought to be made one-third
+higher than the remaining
+shorter letters in
+writing.</p>
+
+<div class="figcenter page-break" style="width: 398px;"><a class="pagenum" name="Page_41" title="41"> </a>
+<img src="images/i045.png" width="398" height="552" alt="Antique form of the letters in skeleton"/>
+</div>
+
+<div class="figcenter page-break" style="width: 409px;"><a class="pagenum" name="Page_42" title="42"> </a>
+<img src="images/i046.png" width="409" height="600" alt="Antique form of the letters in black"/>
+</div>
+
+<div class="figcenter page-break" style="width: 387px;"><a class="pagenum" name="Page_43" title="43"> </a>
+<img src="images/i047.png" width="387" height="436" alt="More elegant form of the letters, including versals"/>
+</div>
+
+<p class="center page-break-after">Here ends this little Book.</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's Of the Just Shaping of Letters, by Albrecht Dürer
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+Project Gutenberg's Of the Just Shaping of Letters, by Albrecht Duerer
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Of the Just Shaping of Letters
+
+Author: Albrecht Duerer
+
+Translator: R. T. Nichol
+
+Release Date: August 16, 2011 [EBook #37103]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK OF THE JUST SHAPING OF LETTERS ***
+
+
+
+
+Produced by Ben Courtney, Jana Srna and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+
+  [ Transcriber's Note:
+
+    Every effort has been made to replicate this text as faithfully
+    as possible, including inconsistencies in spelling and hyphenation.
+    No changes have been made to the printed text.
+  ]
+
+
+
+
+  OF THE JUST SHAPING OF LETTERS
+
+  BY ALBRECHT DUeRER
+
+  TRANSLATED
+  BY
+  R. T. NICHOL
+
+  FROM THE LATIN TEXT OF
+  THE EDITION OF
+  MDXXXV
+
+
+
+
+  OF THE JUST
+  SHAPING OF
+  LETTERS
+
+  FROM THE APPLIED
+  GEOMETRY OF
+  ALBRECHT
+  DUeRER
+  BOOK
+  JJJ
+
+  DOVER PUBLICATIONS, INC. NEW YORK
+
+
+
+
+ALBRECHT DUeRER TO WILIBALD PIRCKHEIMER HIS PATRON AND VERY GOOD FRIEND
+GREETING:
+
+
+[Illustration]
+
+In our Germany, most excellent Wilibald, are to be found at the present
+day many young men of a happy talent for the Art Pictorial, who without
+any artistic training whatever, but taught only by their daily exercise
+of it, have run riot like an unpruned tree, so that unhesitatingly and
+without compunction they turn out their works, purely according to their
+own judgment. But when great and ingenious artists behold their so inept
+performances, not undeservedly do they ridicule the blindness of such
+men; since sane judgment abhors nothing so much as a picture perpetrated
+with no technical knowledge, although with plenty of care and diligence.
+Now the sole reason why painters of this sort are not aware of their own
+error is that they have not learnt Geometry, without which no one can
+either be or become an absolute artist; but the blame for this should be
+laid upon their masters, who themselves are ignorant of this art. Since
+this is in very truth the foundation of the whole graphic art, it seems
+to me a good thing to set down for studious beginners a few rudiments,
+in which I might, as it were, furnish them with a handle for using the
+compass and the rule, and thence, by seeing Truth itself before their
+eyes, they might become not only zealous of the arts, but even arrive at
+a great and true understanding of them.
+
+Now, although in our own time, and amongst ourselves, the Art Pictorial
+is in ill repute with some, as being held to minister incitement to
+idolatry, yet a Christian man is no more enticed to superstition by
+pictures or images, than is an honest man girt with a sword to highway
+robbery. Certes he would be a witless creature who would willingly adore
+either pictures or images of wood or stone. On the contrary, a picture
+is the rather edifying and agreeable to Christian religion and duty, if
+only it be fairly, artificially, and correctly painted.
+
+In what honour and dignity this art was anciently held amongst the
+Greeks and Romans, the old authors sufficiently testify; though
+afterwards all but lost, while it lay hid for more than a thousand
+years. It has now at length, only within the last two hundred years, by
+some Italians been brought again to light. For it is the easiest thing
+in the world for the Arts to be lost and perish; but only with
+difficulty, and after long time & pains are they resuscitated. Wherefore
+I hope that no wise man will defame this laborious task of mine, since
+with good intent & in behoof of all who love the Liberal Arts have I
+undertaken it: nor for painters alone, but for goldsmiths too, & for
+sculptors, and stonecutters, and woodcarvers, and for all, in short, who
+use compass, and rule, and measuring line--that it may serve to their
+utility.
+
+Nor is anyone compelled whether or no to spend gainful hours on these
+exercises of mine; although I am not ignorant that whoever is well
+exercised in them will thence acquire not only the principles of his own
+art, but by daily practice, an exactitude of judgment, with which he
+will proceed to higher investigations & discover many more things than I
+have here pointed out.
+
+But since, illustrious Sir, it is clearer than light that you are
+yourself, so to speak, an asylum of all the noble Arts, it has been my
+pleasure, out of a singular love I bear towards you, to dedicate to you
+this book; not because I desire to appear therein as rendering you any
+great service, but because thereby you may understand how engaged my
+mind is to you; and since by my work I can confer on you but little
+favour, at least by the exhibition of a ready mind I may repay the
+benefits you shower upon me.
+
+Farewell.
+
+[Illustration]
+
+
+
+
+OF THE JUST SHAPING OF LETTERS
+
+
+
+
+FROM THE APPLIED GEOMETRY OF ALBRECHT DUeRER
+
+BOOK III.
+
+
+Now, since architects, painters & others at times are wont to set an
+inscription on lofty walls, it will make for the merit of the work that
+they form the letters correctly. Accordingly I am minded here to treat
+briefly of this. And first I will give rules for a Latin Alphabet, and
+then for one of our common Text: since it is of these two sorts of
+letters we customarily make use in such work; and first, for the Roman
+letters: Draw for each a square of uniform size, in which the letter is
+to be contained. But when you draw in it the heavier limb of the letter,
+make this of the width of a tenth part of the square, and the lighter a
+third as wide as the heavier: and follow this rule for all letters of
+the Alphabet.
+
+First, make an A after this fashion: Indicate the angles of the square
+by the letters a. b. c. d. (and so do for all the rest of the letters):
+then divide the square by two lines bisecting one another at right
+angles--the vertical e. f. the horizontal g. h.: then, in the lower
+line, take two points, i. and k., distant respectively one-tenth of the
+space c. d. from the points c. and d.: then, from the point i. draw
+upwards to the top of the square the lighter limb; & thence downwards
+the heavier limb, so that the outer edges of both may touch,
+respectively, the points i. and k.: then let a triangle be left between
+the limbs, and a point e. be fixed at top in the middle of the letter,
+and next join both limbs beneath the horizontal line, and let this limb
+be a third as broad as the heavier limb.
+
+Now let the arc of a circle, applied to the top of the outside edge of
+the heavier limb, project beyond the square. Then cut off the top of the
+letter with a serpentine or curving line, so that the concavity decline
+towards the lighter limb, and prolong acutely either limb of the letter
+at the bottom to either side, so as to meet the angles of the square at
+c. and d.: this you shall make with the arc of a circle, whose
+semi-diameter is one-seventh of the side of the square; but the two
+lower curves, mutually opposite, permit to extend so that each is a
+third of the heavier limb, and this you shall obtain by the arc of a
+circle whose diameter is equal to the breadth of the heavier limb.
+
+Moreover, this same letter A you may cut off at top with the side of the
+square, and then produce to a fine point in either direction, as you did
+the feet below, yet so that the longer production shall be to the
+fore-side (namely, the left); but in this case it will be necessary to
+draw in the limb k. a little closer.
+
+Likewise the same A you may draw in yet another manner--that is, pointed
+at top. In that case let the limbs slope towards one another yet more
+closely; then lower the transverse a little and double its width. You
+may also cut off the limb at top bluntly, or sharpen it on the
+fore-side. You ought to make yourself familiar with these three forms,
+or whichever of them pleases you best.
+
+And note likewise that in exactly the same fashion in which this letter
+is acutely prolonged at top & bottom, are the other letters to be so
+prolonged which are drawn with oblique lines, as V, X, Y, although a few
+changes may be necessary, as you shall hear below.
+
+I have here subjoined an engraving of this letter.
+
+[Illustration: A]
+
+
+
+
+OF THE LETTER B.
+
+
+And now you shall draw B in its square thus: First divide the square
+horizontally by the line e. f.; then bisect the lines a. e. and b. f. by
+the line g. h. Next, you must first set properly the broad vertical limb
+of the letter, distant its own breadth from the side a. c. of the square
+a. b. c. d. Then erect the line i. k. on the inner side of the limb
+already drawn, and distant from it one-tenth of a side of the square,
+and let it cut the line g. h. in the point l.
+
+Next, draw strips narrower and horizontal (to be produced hereafter into
+the convex limbs) from the vertical band to meet the vertical line
+i. k.--namely, at top, below the line a. b.; next, above the line e. f.;
+and at bottom, above the line c. d.
+
+Now set a leg of the compass on the point l. and describe a semicircle
+to the right of the transverse strips, so that the extremities of the
+circumference, in the vertical line i. k., below the side a. b., and
+above the line e. f. may coincide with those short transverse lines.
+Then bisect the narrow transverse strip which is above the line e. f. in
+the line i. k. by the point m.; and indicate the breadth of the letter,
+to the right of the semicircle, by the point n. in the line g. h.; and
+afterwards draw from the point m. above the line e. f. in the direction
+of f. a short horizontal line as great as need be: then describe a
+semicircle which shall include this line, and the point n., and, at the
+top, the side a. b.; and through n. let pass a vertical line. These all
+combine to form, below, the concave of the curved limb, and above, its
+convex.
+
+Next, produce the transverse strip above c. d., in the direction of d.,
+as far as required, and mark this q. Then bisect the line m. q. by the
+line o. p., cutting the line n. in the point r.; and next describe a
+semicircle touching the horizontal line e. f., the point r., and the
+position q. Then indicate the breadth of this limb of the letter by the
+point s. to the right of the point r. in the line o. p. and describe a
+semicircle, touching the line m., the point s., and the side of the
+square c. d. There will then remain in the letter three right angles to
+be eliminated: the interior and lower one may be shaped into a curve by
+a circle whose semi-diameter is two-thirds of the breadth of the broad
+limb of the letter, and the exterior ones you shall fine to a point by
+circular lines whose semi-diameter is equal to the breadth of that limb.
+
+
+Another method.
+
+Or you may make your B in this fashion: Let the side a. c. of the square
+be divided into nine equal parts, and cut off the four superior parts by
+the horizontal line e. f. Then erect your vertical limb as described
+above; and the superior curved limb you shall make between a. b. and
+e. f.; the inferior between e. f. and c. d.
+
+Now divide a. b. into nine equal parts, and cut off four parts towards
+b. in the point g.; then divide c. d. into five equal parts, and the
+last, towards d. mark off in the point h. and join g. and h. by the line
+g. h. which should touch on their exterior edges the superior and
+inferior limbs of the letter. Now these limbs must be drawn of a
+particular form; and the compass, in drawing the circular lines, must be
+moved up and down their diagonals: and these two diagonals you shall
+determine in this wise.
+
+Divide a. e. into four parts; the lowest, above e., call i. e.; the
+lowest of the five remaining, above c., call c. k. Then join the points
+i. and b. and k. and f. respectively, by the lines i. b. and k. f. Upon
+these lines move and turn your compass, & in this way you shall describe
+both curved limbs: and they must both be broader towards the top than
+towards the bottom, as follows naturally with the stroke of a pen, and,
+moreover, while approximately round, they are not to be circular;
+therefore you will have to move your compass at need along the
+diagonals, and withal to assist it also with the hand, as I have done in
+the picture on the following page.
+
+[Illustration: B]
+
+
+
+
+OF THE LETTER C.
+
+
+Next you shall make the letter C in its own square thus: Bisect the
+square a. b. c. d. by the horizontal line e. f. and in it let i. be the
+middle point. From this point as the centre, & i. f. or i. e. as the
+radius, describe a circle touching interiorly all four sides of the
+square. Now move the leg of the compass, but without varying its span,
+to a point k. a little to the right of i. in the line e. f., letting the
+space i. k. denote the greatest breadth of the letter you desire; & from
+the centre k. describe another circle which shall cut twice the line
+b. d., and whose circumference to the left will mark the required
+breadth of the letter. Next, draw the vertical line g. h., parallel to
+b. d., distant from b. a tenth part of the line a. b. This will cut off
+for you at top and bottom the letter C as the ancients were accustomed
+to use it. But I would have you cut off the lower limb in the middle
+point between g. h. and b. d.: then make the limbs somewhat finer and
+rounder on the inside towards top and bottom from the point where the
+circles intersect; and for its greater perfection round out the letter,
+above and below, to touch the sides of the square a. b. and c. d. Next,
+low down, where the letter with one foot crosses the line g. h., there,
+under the circular line make the form a little more incurved, yet so
+that with the tip of its end it shall again touch the circular line.
+Similarly, but higher up, make the foot more hollow on the inside than
+the circle left it: and thus two circular lines will give you very
+nearly the whole form of the letter.
+
+
+Another method.
+
+Or, secondly, you may make the letter C thus: Draw in the square a
+diagonal c. b.; set the leg of your compass on its middle point i. and
+with the other leg describe the exterior circle as before, terminating
+it above at the diagonal c. b.; but below, make your circle pass a
+little beyond the former sweep. Then set the leg of your compass, but
+without changing its gauge, as far above i. in the diagonal as the
+letter's greatest width, and describe your inner circle; and, as though
+made with a pen, let the descending stroke be heavier than the
+ascending. The rest you may elaborate with your hand; & let the trimming
+of the ends of the letter, above, slope upwards, & below, downwards,
+exactly as I have here drawn the shapes.
+
+[Illustration: C]
+
+
+
+
+THE LETTER D.
+
+
+The letter D you shall make thus: Divide its square by the perpendicular
+or vertical line g. h. and by the horizontal line e. f. into four small
+squares, and call their point of intersection i.: then draw the broader
+limb of the letter from the side a. b. downwards, to meet the side c. d.
+and at the distance of its own width from a. c.; and produce the limb at
+top and bottom to a sharp point at the angles a. and c. as was shown
+above in B; using the same method in all straight limbs in the remaining
+letters. Next you are to produce from this limb two narrower tracts
+horizontally, and from these are to be described the circular arcs of
+the letter between the line a. b. at top and the line c. d. at bottom,
+and extending as far as the perpendicular g. h.; next, with your compass
+join g. f. h. Then, in the line e. f. lay off a portion equal in breadth
+to the widest limb of the letter, at the point k.; next, set one foot of
+your compass on k. and let the other cut the said line e. f. in l.; let
+this be the immovable leg of your compass, and with the other, beginning
+from k., describe internally, to the narrower transverse limbs, an arc
+which shall touch both, completing your acute angle above, but rounding
+out the lower one by a circular arc of the same diameter as the one by
+which you sharpened your exterior subtending angle.
+
+
+Another method.
+
+You may make the round limb of the same D in another fashion; namely, as
+a pen naturally would, broader above than below. For this, draw the
+diagonal c. b. and describe your exterior arc as before; but to describe
+the interior, in the line c. b. take a point m. lower down than i. and
+distant from it the width of the broader limb, and without altering your
+compass describe an interior line; but where the limb must needs be
+narrower, there you are to accommodate it with your hand, both below and
+above, as in the following cut.
+
+[Illustration: D]
+
+
+
+
+THE LETTER E.
+
+
+The letter E you shall form in its square thus: Draw a transverse line
+e. f. bisecting a. b. and c. d. in e. and f.; then draw the great
+vertical limb of the letter, to the left, as you did for D. Next draw
+also an upper transverse limb of narrower dimensions, parallel to a. b.
+and in length six-tenths minus one-third of one-tenth of the length of
+a. b.; and the end of this bend downwards one-tenth of the length of
+a. b. and use this as the diameter of the circle with which you round
+out the inner angle of this extremity: then draw your narrow middle limb
+parallel to the median line e. f. and above it, so that it may be
+shorter than the upper limb by one-tenth of the length of a. b., but at
+its terminus double as wide; & you are to round it out (in either
+direction) by the arc of a circle whose diameter is one-sixth the length
+of e. f. Now construct your lowest limb upon the line c. d., so that at
+its ultimate angle it may exceed in length the upper limb by one-tenth
+of c. d.; the cusp, however, you are to prolong beyond this part by
+two-thirds of one-tenth part, and erect above it to one-sixth of the
+length of c. d., and round out the same by a circle whose semi-diameter
+is also a sixth of c. d. In like manner the final angle of the letter
+you shall round out by an arc of the same circle by which you rounded
+out the middle transverse limb: the other angles you are to leave acute,
+as in the following cut.
+
+[Illustration: E]
+
+
+
+
+THE LETTER F.
+
+
+The letter F you are to form in the same manner as E; except that you
+shall omit the lower limb altogether, and, in its place, round out the
+letter on both sides below, as you did E on one side only, as I have
+shown you below.
+
+[Illustration: F]
+
+
+
+
+THE LETTER G.
+
+
+Likewise the letter G you are to make as you did C, before described;
+this, however, excepted: that in front (that is, to the left) of the
+line g. h. is to be erected the broad limb of the letter, upwards from
+the curve to the line e. f., and above it is to be rounded to a point,
+on either side, as before was said; but below, both angles are to
+remain.
+
+Or, you shall form G in the following fashion in the said square,
+divided as before: Draw the diagonal c. b. and set your compass with one
+leg on the point i. and with the other describe an arc from e. to the
+middle point c. d. and mark this point l.; in like manner also, describe
+an arc upwards to the line a. b. so as to meet the perpendicular line
+g. h. & mark that point z. Then, in the line g. h., take a point m. so
+that the part m. h. shall be one-tenth of the line g. h.; then, with a
+sweep of your hand join l. & m. with the curved line l. m. Next, you are
+to draw from z. a line upwards, as broad as the standard of the letter,
+but oblique and in direction midway between your circular line & the
+perpendicular g. h. and from the extremity of this line you must draw a
+curved line to meet a. b. at the point where your circular line touches
+it. Next, cut off from the bottom of g. h. a part one-third of its
+length, & indicate this by the point n., & to this height, from the
+level of m. upwards, produce the broad limb of the letter, and let its
+extremities above be finished in either direction, of the same size.
+After this set the leg of your compass on the diagonal c. b. the breadth
+of the standard of the letter above i. & at the distance e. i. describe
+an arc, which above shall touch the exterior boundary a. b. but below
+shall stop short above l.; & from this point you must with your hand
+draw a line to the vertical limb at the height of m.
+
+And the same you shall do above in drawing the narrower limb of the
+letter, as seen in the following diagram.
+
+[Illustration: G]
+
+
+
+
+THE LETTER H.
+
+
+The letter H is to be formed of two broad, great, & vertical limbs of
+the height of the square, in such fashion that their extremities, being
+produced exteriorly, shall touch the four angles of the square, a. c.
+and b. d. respectively. Now in what fashion the projections of the
+broader limbs of letters are to be rounded out at top and bottom and on
+either side, you have been instructed; for in any letter you please, any
+broad and vertical limb is to be depicted at top and bottom thrice as
+broad as at its middle: provided always it is not joined to a narrower
+limb. So when this has been accomplished, then draw your narrower
+transverse limb upon the line e. f. as is shown below.
+
+[Illustration: H]
+
+
+
+
+THE LETTER I.
+
+
+The letter I you are to make of a single broad vertical tract in the
+midst of its square, touching the latter top and bottom; and of this, at
+both ends, and on either side, you are to round out the productions or
+projections as below is shown.
+
+[Illustration: I]
+
+
+
+
+THE LETTER K.
+
+
+Now for K: You are to make the first tract vertical, in the same manner
+as you formerly did for H; then draw another narrower limb from the
+broader and erect one, so that it may, at its lower end, impinge
+obliquely on the transverse line e. f. and above may ascend to the right
+till it meet the line a. b., taking care to make it parallel to the
+diagonal c. b.; and this, at the top, you are to produce in both
+directions so that each production may represent a tenth part of the
+line a. b. The hitherward projection you are to round out with a circle
+of which the diameter must not exceed the breadth of the lesser limb;
+but of the other arc, by means of which you round out the farther
+projection, you shall make the diameter double as great as the diameter
+of the arcs by which you have customarily hollowed out the preceding
+extensions of the broad and vertical limbs. Next, from the narrow limb
+so constructed draw in a downward direction another broad limb, so that
+it too may be parallel to a diagonal of the square; & of this the
+beginning is to be taken from the acute angle which the narrower limb
+makes with the broad vertical limb, and let it be drawn with its
+projection to the angle d., yet in this fashion: take two points this
+side of d. after this manner, so that the first point may be distant
+from d. the tenth part of the line c. d. & the second as far again from
+the first; then let the said tract be drawn within the space which is
+between the two points, but in blind and invisible lines. Afterwards you
+shall add the extension, which you shall make this way: take before f.
+in the line e. f., a point g. no farther distant from f. than the
+breadth of the narrower limb; on this point set one leg of your compass,
+& let the other be extended to the angle d., from which let it be guided
+back along the broad but invisible blind limb: thence will result the
+lower convexity of the tail you seek; but its upper concavity look for
+in this way: divide f. d. in its middle point h.; on this set one leg of
+your compass, and with the other describe an arc passing through d. to
+meet the broad limb.
+
+Or you may make K in this manner: First, let your broader vertical limb,
+and your upper narrow one remain as they have been described, except
+that the interior angle which the narrower limb forms with a. b. shall
+remain acute, but the exterior one shall be rounded out, as has been
+said. Then let there be drawn the lower broad limb, obliquely from the
+angle which is included between e. f. and the vertical limb, and let it
+descend to meet the side c. d. so that between d. and the limb the width
+of the limb be left vacant; and the hither angle is to be left, but the
+farther, towards d., shall be rounded out a little, as shown below.
+
+[Illustration: K]
+
+
+
+
+THE LETTER L.
+
+
+As for the letter L, you shall make it by a combination of parts of two
+of the preceding letters: namely, you shall make the first vertical
+broad limb, as you did a while back in I; and to this join a foot as you
+did at the bottom of E, when you made it. Such is L depicted below.
+
+[Illustration: L]
+
+
+
+
+THE LETTER M.
+
+
+The letter M you shall form in two ways within its square. In the first,
+draw the narrower limb of the letter vertical, to the right of a. c.,
+distant from a. one-tenth of the distance a. b.: draw the other, &
+broader limb, on the near side of b. d., also a tenth part of the whole
+distant from b. & in such fashion that both limbs touch the square at
+top and bottom; then, between the two, bisect the line c. d. in the
+point e. and draw a broad limb from the inner angle of the narrow limb,
+downwards to the point e., & next a narrow one upwards from e. to the
+inner angle of the broader vertical limb; and the inner angles at top
+you must not round out, but leave acute; the exterior angles, however,
+at the top, and both exterior and interior at bottom of both vertical
+limbs, you are to adorn with the customary projections, as you have done
+in the preceding letters. You are to know, too, that when these letters
+are drawn with a pen, they are to be described with a single stroke. But
+for your guidance is this letter, in the manner in which I have
+instructed you, depicted below.
+
+
+Another method.
+
+Another way is thus: Divide the side a. b. of the square into six equal
+parts & mark off the two extreme parts, one at either end, by the points
+f. and g.; then draw the inner and broader limb, with its point at e. as
+above; and to this, in an upward direction, a narrower one, so that
+between f. g. be left a vacant space, and so more readily the letter
+slope forward. Then you are to draw the two lateral and vertical
+limbs--the near and slender, and the farther broad one--at the top,
+indeed, as in the first sketch, but at the bottom produce them to the
+two angles c. and d. and finally add projecting cusps, as you were
+instructed in the first M; but the projection below will pass beyond the
+square at the points c. and d. Or you shall make M at top with acute
+angles, in which case the lateral limbs will slope the more; or shear
+them off obtusely, and in this fashion (whichever pleases you best) make
+them as you see them depicted in the following diagrams.
+
+[Illustration: M]
+
+
+
+
+THE LETTER N.
+
+
+Likewise the letter N you shall make in its square thus: First you are
+to draw two standards vertical and slender, so that at top & bottom they
+may touch the square, & that being produced, the nigh one at the bottom,
+and the farther at the top, they may touch the angles at c. and b. Now
+join these two by a broad oblique limb, running from the angle a. to the
+point e., by which is denoted the remote side of the farther limb, where
+you shall allow the acute angle to remain; but at the top, this limb,
+produced beyond the angle a., you are to round out to a fifth part of
+the length of a. b. This prolongation should incurve below, a fifteenth
+part of the distance a. b. projected on two arcs, the upper one the
+greater, the lower the less. For the lesser arc, therefore, you shall
+take as diameter of its circle, a line the fifth part of the distance
+a. b. and its centre is to be taken outside the square, so that the foot
+of the compass may touch the tip of the extension and the angle a.; then
+extend a little the feet of the compass, and shift its centre until the
+arc touch both the tip of the part produced, & the broad oblique limb,
+in the middle point between the side a. c. & the nearer of the two
+slender vertical limbs.
+
+Or you may make the letter N in such fashion that its upper nigh
+extension shall remain within the square; or you may make from it an
+acute angle as shown overleaf.
+
+[Illustration: N]
+
+
+
+
+THE LETTER O.
+
+
+Now O you shall make this way in its square. Set in the square the
+diameter c. b. and bisect it in the point e., so that e. may form a
+middle point between the two points f. and g. which are to be your two
+centres; and from each let a circle be described touching two sides of
+the square; & where the circles cut one another, there with your hand
+you must shape the slender outline of the letter to a juster proportion,
+as below is shown.
+
+[Illustration: O]
+
+
+
+
+THE LETTER P.
+
+
+P you shall make in its square in this wise. Divide the square
+a. b. c. d. by the median horizontal line e. f.; then divide a. e. &
+b. f. equally by the line g. h. Next draw, first the broad vertical limb
+for this letter P, as you did a short while ago for K, and afterwards
+erect the line i. k. the distance of its own breadth to the right of
+your vertical limb; (here you must ever observe that in a lettered
+square we speak of the angle a. as the "hither" angle, that is, to the
+left; & the angle b. as the "farther" angle, that is, to the right).
+Then where the line i. k. cuts g. h. call the point l., and next draw
+two slender horizontal limbs, the upper below a. b., the lower above
+e. f., from the broad vertical limb as far as the line i. k. Set one leg
+of the compass on the point l., extending the other to the lower side of
+the lower horizontal limb near k.; then describe an arc through the line
+g. h. as far as the other slender horizontal limb of this same P, &
+where it cuts the line g. h. set the point m. Next, on the far side of
+m. measure the width of the large limb of the letter, along the line
+g. h. to the point n. and let your compass be stretched so that with one
+foot it may touch the line a. b. and with the other the point n.; then
+set one foot of the compass on n. & the other on the line g. h. to the
+right, in the point o., in which this foot is to be left standing
+immovable, and with the other is to be described an arc, passing through
+the point n. and touching the lines a. b. and e. f.
+
+Or you may form the loop of this letter in the following manner. Set a
+leg of the compass under the transverse g. h. in the line i. k., in a
+place median between the line e. f. & the lower part of the upper
+transverse of the slender limb, in the point p. and describe an arc as
+before, passing through m. so that the loop will be acute at the bottom,
+and its tip will end in the middle space between the line i. k. and the
+broad vertical limb of the letter.
+
+Or make this same P with a circular sweep, by shifting the compass upon
+the diameter, so that that sweep may be broader at the top (as though
+made with a pen) as will be shown in the diagram on the following page.
+
+[Illustration: P]
+
+
+
+
+THE LETTER Q.
+
+
+Make your Q in its square in the self-same manner as was prescribed for
+O; but add to it its tail thus: Draw a diameter of the square, the line
+a. d., about which, starting from the curved outline, begin to draw a
+long tail, producing it through the angle d. in such fashion that d. may
+be in the middle of the thickest part of the tail; but where the tail
+begins let it be a little narrower than in the angle d., where it should
+attain its real thickness. Then let it be drawn out, beyond the angle d.
+to the length of the entire diameter, and in a downward direction, yet
+so that it curves while it slopes, & that its tip shall not fall lower
+than a third of the side below the lowest side of the square, and shall
+tend, as it nears the point, to grow sharper little by little, and at
+length end in a very fine point indeed.
+
+Or you shall give Q a shorter tail in this fashion, to wit: set your
+compasses to the length of the side c. d. and draw a tail from the bulge
+of the same letter, describing through the point d. its inner arc of the
+same length as c. d., taking care that the tail bend upwards until it
+again reach c. d. produced, in the point h.; then shift your compasses,
+& with the other leg again describe from the bulge of the letter an arc
+below d. & continue it until again it reach h., but in such fashion that
+the tail shall find its greatest thickness at the start, as in the
+following figure is doubly depicted.
+
+[Illustration: Q]
+
+
+
+
+THE LETTER R.
+
+
+Moreover R you must make in its square just as was directed for P; but
+then erect a right line q. r. through the middle point of the square, &
+let it cut the exterior arc of the rounded limb in s., from which point,
+downwards towards the angle d., let there be drawn a broad tract, almost
+equal to that which you made above for the letter K., but this is to be
+somewhat bent in, and so shaped by your hand that its tip, well formed,
+may arrive directly on the angle d.
+
+Or make R in such fashion that its rounded sweep, as though made with a
+pen, shall be above broader, & narrower below. To accomplish this, you
+must shift your compasses on the diameter q. e. & not allow the rounded
+limb to touch the vertical one, as was described in P. Besides, the
+oblique limb is to be deduced from the rounded one with a little more of
+a curve; just as I have drawn overleaf.
+
+[Illustration: R]
+
+
+
+
+THE LETTER S.
+
+
+Next, the letter S you shall make as follows in its square, a. b. c. d.
+First draw the horizontal line e. f. and the median & vertical one g. h.
+and let them bisect one another in the point m. Then choose the main
+thickness of the letter, and set it in the line g. h. so that the point
+m. may divide it, having one-third of the thickness below it; next, set
+the lesser thickness, at the top beneath g., indicating it by the point
+i., and at bottom, above h. in the point k.; and the thickness of the
+letter indicate above by n. and below by l.
+
+Next, set a leg of your compasses on the line g. h. in the mid-point
+between i. and n., and with the other describe a circle passing through
+i. and n.; in like manner, upon the line g. h. set your compasses upon
+the mid-point of g. l. and describe a circle passing through g. & l.
+Then once more set your compass on the same line g. h. in the mid-point
+of n. h. and describe a circle through n. & h.; and lastly, in the
+mid-point of l. k. you must set one leg, & with the other is a circle to
+be described through these same points l. & k.; afterwards cut off by
+vertical section the upper portion of this letter, so that the part thus
+cut off may contain in its extremity the maximum thickness of the letter
+and a third part besides, & also that its tip may project downwards so
+far as to stand midway between the centre of the circle i. n. and the
+side b. d.; in other words, let the tip be distant on the right, from
+the circle i. n. the first third of the interval between the greater and
+lesser circles.
+
+Next cut the lower limb of the letter to the left, by a vertical line
+through the mid-point between the two circles, & in such fashion that
+the part so cut off may be a fourth part wider & higher than the upper,
+and that its tip may rise to the height of the centre of the circle
+n. h.
+
+
+Another method.
+
+Yet another way may you make the letter S. In the square a. b. c. d.
+bisect the horizontal line e. f. in the point m.; then set one leg of
+your compass upon the mid-point between g. and m. & with the other
+describe a segment of a circle in the direction of a. e. passing through
+the points m. and g.; next, set your compass upon the mid-point between
+m. and h. and describe a segment of a circle through m. and h. in the
+direction of f. d. The two arcs will touch above, in front, and below,
+in the rear, the exterior curvatures of this same letter S.
+
+Next, draw through m. the diameter c. b. and at its middle indicate the
+maximum thickness of the letter by the two points p. and q. from which
+let there be drawn two right lines, one up, & one down, to those two
+arcs; & next, from the two points p. & q. draw two curved parallels to
+the same arcs, regulating the distance between them, their elevation &
+depression from the centres of the same circles. Next, indicate below g.
+and above h. the minimum thickness of the letter; and from these points
+you will with your hand fashion the inner shape of the letter, both
+above and below, & produce the limb of S, above towards b. Cut it off so
+that its lower tip may touch the segment, & that the part cut off
+upwards may contain a tenth part of a. b. and that the segment may still
+exceed the part cut off. Then construct a vertical line r. s. to the
+right of e. c. and distant from it a fifth part of c. d.; let it cut the
+diagonal c. b. in t. and to the angle just formed produce the extremity
+of the letter, making the part so cut off a third broader than the upper
+portion. Lastly, you will have to produce the tip ever so little beyond
+t.; as I have briefly indicated.
+
+[Illustration: S]
+
+
+
+
+THE LETTER T.
+
+
+Set the broad limb of T in the midst of its square erect, produced &
+drawn to a point on either side below, just as you did before in the
+letter I; then take two points e. and f., distant respectively one-tenth
+of the whole space from a. and b., and let the transverse limb of the
+letter be drawn below e. f. and of an equal length with it; but the
+projecting extremities of this line are to be cut obliquely, and the
+tips of these projections shall so far extend above the line a. b. to
+the right as below they depend to the left. The oblique lines of these
+projections are to be each a fifth part of the length of a. b.; & the
+angles of these projections you shall round out by means of circles of
+diverse radius--namely, for the lesser angle you are to use a diameter
+only two-thirds of the width of the broader limb; but for the greater
+angle you shall take a diameter equal to the side of a square contained
+between the broad and vertical limb and the intercepted portion of the
+line a. b.
+
+
+Another method.
+
+Or you make T thus in its square: Take your point e. as before, to the
+right of a., and cut your transverse limb diagonally, as before, yet so
+that the projection be dimidiated to the right, and at top the angle
+remain as it falls; and so at the other extremity, only the point f.
+must be moved as near again to b., the cutting line to be a little more
+erect, & the projection formed a trifle broader than at the hither end;
+otherwise shall everything remain as before; as I have delineated for
+you on the opposite page.
+
+[Illustration: T]
+
+
+
+
+THE LETTER V.
+
+
+V you shall thus make in its square: Bisect c. d. in the point e.; then
+set the point f. one-tenth of the whole line a. b. beyond a., and in
+like fashion g. to the hither side of b. Then draw the broad limb of
+your letter downwards from f. to e. and sharpen it; & thence draw
+upwards your slender limb to g.; and at the top produce it in either
+direction, as you did before at the bottom of A; just as you see it
+shown below.
+
+[Illustration: V]
+
+
+
+
+THE LETTER X.
+
+
+X you shall form thus: Draw two vertical lines e. f. and g. h. distant
+respectively one-tenth part of the line a. b. from the sides a. c. and
+b. d. Then draw the two limbs intersecting one another in the form of a
+cross--the broad one so that at top, & with its hither side it shall
+touch e., & at the bottom, and with its farther side h.; but the narrow
+limb so that at top, and with its farther side it may touch g., & at
+bottom, with its hither side f. Then add its projections, touching, at
+top and bottom, the four angles a. b. c. d., & choose a semi-diameter of
+the larger circle of the length of a fifth part of a. b.; & with that
+you shall round out the four greater angles; but for the lesser circle
+you shall take a diameter as long as two-thirds the width of the broader
+limb.
+
+Or you may vary X thus: Let everything be left as before except the
+narrower limb, which at top you shall make more erect by one-half the
+breadth of the wider limb; and so the upper part of the letter shall be
+less and narrower than the lower, and shall have a different aspect, as
+is shown below.
+
+[Illustration: X]
+
+
+
+
+THE LETTER Y.
+
+
+Y you shall achieve in the midst of its square, as far as its lower half
+is concerned, after the instructions before given for I; but its upper
+part you shall divide so that its hither limb shall contain two-thirds,
+and its farther one-third of the broad standard; and let them slope to
+either side so that produced they may touch the two angles a. and b.;
+and the greater circles, by which you are to round out their obtuse or
+greater angles, make of a diameter as great as a containing side of the
+square enclosed between the standard and the sides of the great square,
+as in T was shown; but the diameters of the circles which you apply to
+the lesser angles, make double the width of the broad standard, as
+below.
+
+[Illustration: Y]
+
+
+
+
+THE LETTER Z.
+
+
+Z you shall make thus: Set upon either side, both beneath & beyond the
+angle a., two points e. & f., each at a distance of the tenth part of
+a. b.; so also, set two other points g. and h. both before and above the
+angle d. and with right lines join e. f. and g. h.; then draw your
+narrower transverse limb, beneath a. b. backwards as far as the angle
+b.; from thence draw your broad limb diagonally to c.; and then again a
+narrower one from c. to g.; and with your hand round out the two tips e.
+and h.
+
+Or make Z thus: Divide the square a. b. c. d. by the vertical line e. f.
+and in this reduced space construct the letter as before; but so that
+the two transverse limbs be cut short, above on the nigh side, and below
+on the far, by the vertical lines a. c. and e. f. respectively as below.
+
+[Illustration: Z]
+
+So likewise, in other fashion, can we make all the letters already
+drawn, on a scale of ninths, just as we have now drawn them on a scale
+of tenths; in just the same manner, according to the due proportion of
+each, in its own square, a. b. c. d., dividing them into nine, as just
+now into ten parts; & that this may be the better understood, I have
+chosen to append here letters of such fashion. Also these letters are to
+be made five parts high when written small & rapidly, by hand. In such
+writing the versals are made of the same proportion and form, but
+one-third larger than the ordinary letters of the writing.
+
+  [Illustration:
+  A A A A
+  B B B B
+  C C C C
+  D D D D]
+
+  [Illustration:
+  E E F F
+  G G G H
+  H I I K
+  K K L L]
+
+  [Illustration:
+  M M M
+  M N N
+  N N O O
+  P P P P]
+
+  [Illustration:
+  Q Q Q
+  R R R
+  S S S T
+  T T V V]
+
+  [Illustration:
+  X X X
+  Y Y Z
+  Z Z]
+
+
+
+
+DIRECTIONS FOR THE CONSTRUCTION OF THE TEXT OR QUADRATE LETTERS
+
+
+The letters which are usually called "text," or quadrate, it was
+formerly customary so to write, although they are now imitated by the
+new art, as presently I shall show below. Although the alphabet begins
+with the writing of A, yet shall I (not needlessly) in the first place
+undertake to draw an I; because almost all the other letters are formed
+after this letter, although always something has to be added to it or
+taken away.
+
+First make your I of equal squares, of which three are properly set one
+over the other; and the top of the top one, and the bottom of the bottom
+one, divide in two points, that is to say, into three equal parts: then
+set a square equal to the others in an oblique manner, so that its
+diagonal be vertical, and its angle on the first point of the top
+square. In this way, this oblique square shall extend with its angles
+more to the left than the right. Then produce upwards on either side,
+after the width of the superposed squares, right lines to meet the sides
+of the oblique set square. Next do below precisely as you did above,
+except that you must set the angle of the oblique square on the second
+point, that is, the one farthest to the right in the bottom of the
+lowest square; and let fall your lines on either side upon the
+transposed square: so will I be perfect; only above it draw with a fine
+pen a tiny in-crescent.
+
+So shall you make N from two standards of this same I, set so that their
+angles at top and bottom touch; and in this manner the space between the
+two shall be narrower than the breadth of either: also, you shall no
+longer put little crescents above them; you must make of the same length
+all the short letters throughout the alphabet.
+
+In like manner make M of three standards, just as you made N of two.
+
+R make as I, except only that at top you must set an equal square
+diagonally, to the right, so that angle touch angle. R you may make also
+in this fashion: below leave its foot as before, but above add two
+diagonal squares, which shall touch each other with their angles in the
+middle point of the vertical limb, and then produce upwards both sides
+of the latter to meet the diagonal square.
+
+V is made in three ways. First let it be made simply, as N; only that in
+the farther limb, you shall omit at the top the diagonal square; and
+instead shall draw an oblique line, so that it may make two angles in
+this limb (produced) of which the farther shall be of the same height as
+that of the topmost angle of the diagonal square, & the higher angle of
+the same height as the angle nearest to it in the said square.
+
+The second V, which we use at the beginning of a sentence, make thus:
+Draw the first limb as before for I; only, at the bottom, push the
+diagonal square a little further to the right, so that its hither angle
+does not project beyond the side of the vertical limb, but falls in the
+line of its descent. Then set the second limb to the right of this, and
+cut it off below by an oblique line, drawn from the lowest angle upwards
+to the right, as far as the middle point of the lowest of the three
+superposed squares.
+
+Next make W (i. e., double V) just as you made V-simplex; only you shall
+set before it the standard limb of I.
+
+B make as the second V-simplex; but in the first upright omit the
+diagonal square at the top, and set upon the three original squares
+three others similar, but the seventh one you shall cut off diagonally
+from its lower hither angle.
+
+Likewise when your B so made is turned upside down, then it will be a Q.
+
+X you shall construct from I. Append from top angle to the right a
+diagonally set square, as you did before in R; and at the bottom draw an
+acute tail to the left from the diagonal, and at the middle of the
+vertical limb describe a transverse, in such way that the former is cut
+before and aft by the latter's diagonal; let the hither and lower angle
+be terminated as far in front of the upright as would measure one-half
+of the cutting diagonal, which at top shall just touch the upright; but
+to the right let the transverse at top project to a point just below the
+angle of the oblique square; from thence downwards let it be cut off by
+an oblique line parallel to the anterior diagonal.
+
+C you shall construct from I after this fashion: Remove the top diagonal
+square, & let lines be produced on either side to the proper height of
+the letter, and cut off the hither angle by a diagonal; then draw at top
+a broad transverse, projecting beyond the vertical to the right the
+width of the latter, and cut this off by a diagonal in such a way that
+it project below only half as far as above.
+
+The vertical standard of E you shall make as for C; but from above let
+there descend to the right a broad limb from the diagonal bisecting the
+right angles of one square, and one-third again as long as broad; and
+let there be drawn from its lower angle a small diagonal line to the
+vertical limb.
+
+T shall be made like C, except that at top something is added to its
+diagonal, so that its tip converges to a fine point, and the like to the
+left on the hither side of the broad standard, just as at the top: and
+because of this is T at top more elegant than C, and has not the same
+incurved appearance.
+
+L you are to make below like I; only six squares are to be set on end;
+then cut off the hither side of the seventh by a diagonal, and so the
+apex of the letter shall remain to the right.
+
+The letter S you shall make as L; except that at top to the right must
+be drawn a broad limb of the length of the diagonal, which afterwards
+you are to cut off by a line parallel to the diagonal.
+
+F you shall make as S, just adding to it a transverse limb at the height
+of the shorter letters and double as long as broad, so that the point on
+the hither side & below shall project as far as half the limb's breadth,
+so that the two diagonal abscissions may be equidistant from one
+another.
+
+The near limb of the letter H make like L, and to it join by its top, in
+the proper place, the farther made like I; but below, for the diagonal
+square, substitute a fourth square in line with the others, and the
+fifth and lowest cut off on the far side by its diagonal.
+
+Of K make the near limb like L; and to the right of it append a diagonal
+square, from the lowest angle of which let a line be obliquely produced
+to meet the said vertical limb; and next from this line let a broad limb
+be obliquely drawn, and this, at the bottom, you are to cut off by a
+diagonal, in such fashion that the space below, between the two tips
+shall not be more than the diagonal of a single square.
+
+D in its lower half make like B; but at top let the anterior limb ascend
+upwards to the maximum height of the letters, and then cut off the
+hither angle by its diagonal; next superpose to the same height half a
+square upon the other three squares of the farther limb, & once more do
+here as you did below, and let this broken limb rest on the angle of the
+near limb, and let it extend beyond it as far as the end of the upright
+near limb; and so will it all but contain three conjunct squares; for
+when it meets the near vertical limb, that fraction is to be cut off at
+right angles.
+
+O you are to make below as D, and also the same at the top as the
+bottom, only, as it were, turning it upside down.
+
+The anterior limb of P make like L inverted; but the posterior like the
+standard of I: at bottom, however, you are not to add an oblique square,
+but amputate the limb diagonally, & draw at the bottom a broad
+transverse limb, which likewise is to be cut off diagonally, so that the
+lower point shall project to the left, a distance of half the breadth of
+the limb.
+
+Likewise A in the lower half you are to make like N; but of its anterior
+vertical limb, you are to cut off the hither angle of the middle square
+by its diagonal; of the posterior, however, allow three squares to
+remain superposed, and incline the top part (the fourth square) rather
+to the left, so that if at this side is joined to it the half of a
+square, then it shall attain the height of the letter; and cut off the
+square obliquely, yet so that the lower point shall project farther than
+the upper; then describe to the left a circle, sweeping downwards, so
+that its contents shall embrace the farthest limit of the anterior limb.
+
+Z is made in threefold fashion. First set a diagonal square which shall
+touch the height of the letter; then add another like it, on the right,
+joining their sides, & let these form a quadrangle sloping downwards on
+the right: next set a diagonal square in straight line under the top
+square, and distant from the lower one the length of its diameter: then
+draw a diagonal line between the near angles of these two squares, or
+make a rounded limb to reach the lower square; but from the said lowest
+square of all you shall draw downwards and to the right, by the aid of
+divers circles, a round extension, whose bottom shall mark the length of
+the letter; and let its tip, sharp and tenuous, verge to the left. Or
+construct Z of three oblique limbs, one above the other, & to connect
+them draw the diagonal, which shall slope upwards to the right.
+
+Another Z you may make in this way: Let three diagonal squares be set
+atop of one another; and let the lowest have a rounded extension, as in
+the first Z.
+
+The first limb of G make below like I, and add at the bottom another
+diagonal square, joining the two by their angles; but at top produce the
+farther tip of this limb upwards to the height of the letter, & from
+this point draw a diagonal downward to the left, as far as the hither
+angle of the first right square of the three set one on other. Next draw
+the farther vertical standard entire, of the same length as the hither
+standard, and at the bottom draw a diagonal from the angle of the lowest
+oblique square to touch the tip of the angle of the farther limb, & on
+the inner side produce downwards the side of the limb, to meet the tip
+of the said diagonal; to this also, by one line, join the lowest of the
+hither squares. Now draw at top a transverse limb of the customary
+breadth, from the back of the nearer vertical limb, passing through the
+farther one, and reaching as far beyond this as its breadth; & this
+limb, finally, you shall cut off by an oblique line parallel to that of
+the near limb.
+
+Y you shall make as N, only at bottom must be omitted the farther
+diagonal square, & in its place is to be set a right square under the
+other three superposed squares; then split the fifth square by a
+diagonal, so that the tip shall be in front; from which let there be
+produced a diagonal line, equal in length to a single side of the
+square.
+
+Curved, or short S, you shall make on this wise. At the middle height of
+the letter, let there be set, close to one another, their angles
+touching, two oblique squares; from the near square draw a broad
+vertical limb to the height of the letter; and in the same fashion, from
+the farther square let one fall downwards--just as you constructed I top
+& bottom. Next cut off both these limbs, one at top and one at bottom,
+by diagonals, in such fashion that the sharp tips of both may be on the
+side near the middle. Then let there be drawn two broad limbs--namely,
+from the upper, to the right, and downwards; and in like manner, from
+the lower, upwards, and to the left; of the breadth of the limb, above
+and below, but let them be produced no further than the breadth of the
+distance between the limbs: then draw a diagonal downwards, from right
+to left, which shall cut off both oblique limbs. To it also you must
+produce the sides of the squares set in the midst.
+
+So, accordingly, have I set them down--in skeleton in rotation, and in
+proper order in black. This (as I said above) is the antique form of the
+letters; but in these days there is used a more elegant text, and a
+diagonal square is substituted in the middle place for a right square,
+so that the lines of the letters are not so much curved; and there are
+made certain limbs adjoined and cleft; and there are set one on another
+three squares & a half; and spaces are left between two limbs as great
+as their width. Letters of this sort also have I set forth on the third
+page following; as also capital letters, which are called "versals,"
+because they are customarily set at the beginning of a verse; and these
+ought to be made one-third higher than the remaining shorter letters in
+writing.
+
+  [Illustration:
+  i n m r r u v
+  w b q x c e t l
+  s f h k d o p
+  a z z z g y s]
+
+  [Illustration:
+  a b c d e f g h
+  i k l m n o p
+  q r r s s t u v
+  w x y z z z]
+
+  [Illustration:
+  A B C D E F G H
+  I K L M N O P R
+  S T V X Y Z Q *
+  a b c d e f g h
+  i k l m n o p q
+  r s s t u v w x
+  y z]
+
+Here ends this little Book.
+
+
+
+
+
+
+End of Project Gutenberg's Of the Just Shaping of Letters, by Albrecht Duerer
+
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