Thursday, March 22, 2012

Of the Just Shaping of Letters, by Albrecht Dürer - Full 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:

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 whichhe 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.

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.

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.

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.
C

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