is highly probable that the anatomical studies which he was pursuing zvith so much zeal between 1510--16 should have led him to
reconsider the subject of Proportion. Preliminary observations (308. 309).
308.
Every man, at three years old is half the full height he will grow to at last.
309.
If a man 2 braccia high is too small, one of four is too tall, the medium being what is admirable. Between 2 and 4 comes 3; therefore take a man of 3 braccia in height and measure him by the rule I will give you. If you tell me that I may be mistaken, and judge a man to be well proportioned who does not conform to this division, I answer that you must look at many men of 3 braccia, and out of
the larger number who are alike in their limbs choose one of those who are most graceful and take your measurements. The length of the hand is 1/3 of a braccio [8 inches] and this is found 9 times in man. And the face [Footnote 7: The account here given of the braccio is of importance in understanding some of the succeeding chapters. Testa must here be understood to mean the face. The statements in this section are illustrated in part on Pl. XI.] is the same, and from the pit of the throat to the shoulder, and from the shoulder to the nipple, and from one nipple to the other, and from each nipple to the pit of the throat.
Proportions of the head and face (310-318).
310.
The space between the parting of the lips [the mouth] and the base of the nose is one-seventh of the face.
The space from the mouth to the bottom of the chin c d is the fourth part of the face and equal to the width of the mouth.
The space from the chin to the base of the nose e f is the third part of the face and equal to the length of the nose and to the forehead.
The distance from the middle of the nose to the bottom of the chin g h, is half the length of the face.
The distance from the top of the nose, where the eyebrows begin, to the bottom of the chin, i k, is two thirds of the face.
The space from the parting of the lips to the top of the chin l m, that is where the chin ends and passes into the lower lip of the mouth, is the third of the distance from the parting of the lips to the bottom of the chin and is the twelfth part of the face. From the top to the bottom of the chin m n is the sixth part of the face and is the fifty fourth part of a man's height.
From the farthest projection of the chin to the throat o p is equal to the space between the mouth and the bottom of the chin, and a
fourth of the face.
The distance from the top of the throat to the pit of the throat below q r is half the length of the face and the eighteenth part of a
man's height.
From the chin to the back of the neck s t, is the same distance as between the mouth and the roots of the hair, that is three quarters
of the head.
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From the chin to the jaw bone v x is half the head and equal to the thickness of the neck in profile. The thickness of the head from the brow to the nape is once and 3/4 that of the neck.
[Footnote: The drawings to this text, lines 1-10 are on Pl. VII, No. I. The two upper sketches of heads, Pl. VII, No. 2, belong to lines
11-14, and in the original are placed immediately below the sketches reproduced on Pl. VII, No. 1.]
311.
The distance from the attachment of one ear to the other is equal to that from the meeting of the eyebrows to the chin, and in a fine face the width of the mouth is equal to the length from the parting of the lips to the bottom of the chin.
312.
The cut or depression below the lower lip of the mouth is half way between the bottom of the nose and the bottom of the chin.
The face forms a square in itself; that is its width is from the outer corner of one eye to the other, and its height is from the very
top of the nose to the bottom of the lower lip of the mouth; then what remains above and below this square amounts to the height of such another square, a b is equal to the space between c d; d n in the same way to n c, and likewise s r, q p, h k are equal to each other.
It is as far between m and s as from the bottom of the nose to the chin. The ear is exactly as long as the nose. It is as far from x to
j as from the nose to the chin. The parting of the mouth seen in profile slopes to the angle of the jaw. The ear should be as high as from the bottom of the nose to the top of the eye-lid. The space between the eyes is equal to the width of an eye. The ear is over the middle of the neck, when seen in profile. The distance from 4 to 5 is equal to that from s_ to r.
[Footnote: See Pl. VIII, No. I, where the text of lines 3-13 is also given in facsimile.]
313.
(a b) is equal to (c d).
[Footnote: See Pl. VII, No. 3. Reference may also be made here to two pen and ink drawings of heads in profile with figured meas-
urements, of which there is no description in the MS. These are given on Pl. XVII, No. 2.--A head, to the left, with part of the
torso [W. P. 5a], No. 1 on the same plate is from MS. A 2b and in the original occurs on a page with wholly irrelevant text on matters of natural history. M. RAVAISSON in his edition of the Paris MS. A has reproduced this head and discussed it fully [note on page
12]; he has however somewhat altered the original measurements. The complicated calculations which M. RAVAISSON has given appear to me in no way justified. The sketch, as we see it, can hardly have been intended for any thing more than an experimental attempt to ascertain relative proportions. We do not find that Leonardo made use of circular lines in any other study of the proportions of the human head. At the same time we see that the proportions of this sketch are not in accordance with the rules which he usually observed (see for instance No. 310).]
The head a f 1/6 larger than n f.
315.
From the eyebrow to the junction of the lip with the chin, and the angle of the jaw and the upper angle where the ear joins the tem-
ple will be a perfect square. And each side by itself is half the head.
The hollow of the cheek bone occurs half way between the tip of the nose and the top of the jaw bone, which is the lower angle of the setting on of the ear, in the frame here represented.
From the angle of the eye-socket to the ear is as far as the length of the ear, or the third of the face.
[Footnote: See Pl. IX. The text, in the original is written behind the head. The handwriting would seem to indicate a date earlier than
1480. On the same leaf there is a drawing in red chalk of two horsemen of which only a portion of the upper figure is here visible. The whole leaf measures 22 1/2 centimetres wide by 29 long, and is numbered 127 in the top right-hand corner.]
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316.
From a to b--that is to say from the roots of the hair in front to the top of the head--ought to be equal to c d;--that is from the bottom of the nose to the meeting of the lips in the middle of the mouth. From the inner corner of the eye m to the top of the head a is as far as from m down to the chin s. s c f b are all at equal distances from each other.
[Footnote: The drawing in silver-point on bluish tinted paper--Pl. X--which belongs to this chapter has been