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diff --git a/37103.txt b/37103.txt new file mode 100644 index 0000000..d025d39 --- /dev/null +++ b/37103.txt @@ -0,0 +1,1587 @@ +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 + +*** END OF THIS PROJECT GUTENBERG EBOOK OF THE JUST SHAPING OF LETTERS *** + +***** This file should be named 37103.txt or 37103.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/7/1/0/37103/ + +Produced by Ben Courtney, Jana Srna and the Online +Distributed Proofreading Team at http://www.pgdp.net + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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