Leonardo da Vinci - the anatomist (1930) 9
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McMurrich JP. Leonardo da Vinci - the anatomist. (1930) Carnegie institution of Washington, Williams & Wilkins Company, Baltimore.
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Leonardo da Vinci - The Anatomist
Chapter IX Leonardo’s Canon of Proportions
It was Leonardo the artist rather than Leonardo the anatomist who was dominant in an endeavor to formulate a canon of proportions for the human body. An anatomist in determining the relative proportions of different parts of the body would be seeking for the structural and physiological adaptations underlying these proportions, and of this there is nothing in Leonardo’s treatment of the subject; the artist, on the other hand, would be working more empirically, seeking merely to establish a standard for the more accurate portrayal of the human form. This was evidently Leonardo’s purpose, and, furthermore, as will be shown later, he evidently approached the study of proportions purely from the standpoint of the artist.
Cantor in his lectures on the history of mathematics 1 states that Giotto had written on the proportions of the body and that such studies had also been ascribed to Piero della Francesca and to Ghirlandajo, but there is no evidence that Leonardo was influenced by any of these. He was, however, indebted to the Roman writer Vitruvius, 2 who, in the reign of Augustus, wrote a treatise on architecture in which he advocated the observance of a definite symmetry in the various parts of an architectural design, and advanced in support of this idea the fact that such symmetry occurred in natural objects. As proof of this he gives the proportional lengths of several parts of the human body, pointing out, for example, that the length of the body is eight times the height of the head from the point of the chin to the vertex and six times the length of the foot. He says —
“Therefore if it is agreed . . . that a correlation of proportional parts may be found between the individual members and the whole aspect of the body, it follows that we should admire those who, building temples to the immortal Gods, have so ordered the parts of their work that, individually and in general, their distribution is made harmonious in proportions and symmetries.”
An edition of the De architecturd was published in Rome in 1486 and another in Florence in 1494 and either of these may have been consulted by Leonardo. He undoubtedly knew of the work of Vitruvius, for there is a memorandum that he had borrowed a copy of it and there is a folio in the Royal Gallery at Venice with drawings by Leonardo, showing the figure of a man inscribed within a square and also within a circle (fig. 13). These figures are evidently illustrations of two of Vitruvius’ proportions, namely, that in which he states that in a man standing erect with the arms stretched horizontally, the distance between the tips of the fingers will be equal to the height of the body and the figure may therefore be inscribed in a square, and, secondly, if a man lie supine with arms and legs abducted, a circle drawn with the umbilicus as a center will touch the tips of the fingers and toes. Memoranda accompanying the figures mention other proportions recognized by Vitruvius, and it is further noteworthy that the figures were reproduced in an edition of the De architecture,, edited by Jocundum and published in Venice in 1511, as well as in some later editions.
1 Cantor, Vorlcsungcn fiber Gcschichte der Mn.lhemn.tik , Bd. II, Leipzig, 1900.
1 Marcus Vitruvius Pollio, Dc Architecturd, Ed. by A. Choisy, 4 vols., Paris, 1909.
Fg. 13. Figure of a man inscribed in a circle and in a square. Royal Academy, Venice (Anderson).
It is possible that Leonardo may have begun his studies of proportions early in his career, while he was still a pupil of Verrocchio ; it is even possible that he had studied a Vitruvian manuscript prior to his exodus to Milan in 1483, for in his letter to Ludovico Sforza, he boasts of his skill as an architect. But these are mere conjectures; it is more likely that he seriously took up the study of proportions only after he had taken residence in Milan and after the establishment of his friendship with Luca Pacioli. The association with Pacioli has already been mentioned (p. 56), but it may be recalled that in 1497 Pacioli had written his De divina proportione in which he advocates the use of the “divine proportion” in architectural designs, and also, like Vitruvius, considers certain proportions of the human body and, further, the symmetries of the five regular solids. These last and their modifications are illustrated by numerous figures that were drawn by Leonardo and, further, the book contains two outline drawings of heads, through which lines are drawn indicating their symmetry and the proportions of their parts. These also may reasonably be attributed to Leonardo and further evidence of his collaboration has been found in the picture in the book of an arch on the bases of which there are on one side the letters MA and on the other LV; these have been interpreted as MAgister Leonardus Vincius but, as Solmi (1919) has pointed out, may be as well interpreted as MAgister LUca. However, even without this third item, the evidence that Leonardo collaborated with Fra Luca in the De divina proportione is sufficiently authentic and is the first definite indication that he had become interested in the study of bodily proportions.
The book though written in 1497 was not published until 1509, a delay which may have been partly caused by Leonardo’s dilatoriness in his artistic work, but more probably by the exodus of the two friends from Milan in 1500, shortly after the city had been taken by the French. It does not seem improbable that the illustrations were completed in Florence during the residence there of Pacioli and Leonardo after their visit to Venice, when, as is known from a reply to an inquiry of Isabella Gonzaga, Leonardo was too much interested in mathematical studies to find time for his art. But, be that as it may, the book was not published until after Leonardo had returned to Milan in 1506 and had become the guest of the Melzi in their villa at Vaprio.
Leonardo's memoranda concerning proportions are scattered through his various manuscripts, but several folios of QVI are almost exclusively devoted to such memoranda, arranged in a more or less tabular form. At the time these folios were written he must have been actively engaged in the study of proportions, and if an approximate date could be assigned to them it would indicate whether his special interest in this line of studies antedated his association with Pacioli. Fortunately there is a clue to their date. Folios QVI, 10 and 11, both of which are devoted to lists of proportions, have the heading el treqo, which Professor Lesca has plausibly interpreted as meaning that the measurements recorded were made on a man from Trezzo, that is to say from the village of Trezzo sul’ Adda, not far from Vaprio, and well known to Leonardo in connection with his plans for the extension of the Martesan canal to Lake Como. If this identification is correct the folios were probably written during the early months of 1507, when Leonardo was residing at Vaprio, or later in that year, or during 1508 when he was busy with his plans for the canal.
The probabilities then are in favor of the view that the stimulus to intensive study of the bodily proportions came from Pacioli. He had cited a number of them, largely those of Vitruvius, in his book and Leonardo had drawn figures to illustrate those of the head. It seems likely that it was this task, undertaken to oblige a friend, that aroused Leonardo to a more thorough and extensive study of proportions. It is noteworthy, however, that the proportions given by Pacioli do not all correspond with those in Leonardo’s notes. Thus, both authors divide the distance from the roots of the hair to the chin into three equal parts by tw r o horizontal lines (fig. 14), one passing through the eyebrows and the root of the nose and the other through the low r er edge of the nasal septum (these arc Vitruvian proportions), and the low T er of these thirds is again divided by horizontal lines passing through the mouth and through the labiomental groove between the mouth and the chin; while the other two thirds are each divided into only two equal parts. But Pacioli added another principle, which is showm in the illustration, but is not made use of by Leonardo. It is to the effect that if lines are drawn from the external occipital protuberance to the extremities of a line touching the forehead and lips and representing the length of the face, the result will be an equilateral triangle. It is strange that Leonardo, after having drawn a figure illustrating this proportion, should make no mention of it in his notes; indeed he very rarely uses angles or triangles (fig. 16), his measurements being mostly linear, vertical, transverse, or occasionally sagittal.
Fig. 14. Figure illustrating proportions of the head. (QVI, 1.) Fig. 15. Figure showing lines of measurement used in determining proportions of leg. (QVI, llv.)
Fig. 15. Figures illustrating proportions of the face and eye. A drawing in the Royal Palace, Turin (Anderson).
Again, Pacioli in his description of the man inscribed in a circle, states that the circle not only touches the tips of the fingers and toes, but also the top of the head, erroneously modifying the statement of Vitruvius, which may be translated —
“If a man is placed supine with his hands and feet spread out and his umbilicus is taken as a center of a circle, by describing the circle the digits of both hands and feet are touched by the line.”
Leonardo, in his notes on the folio bearing his illustrations of the man inscribed in a circle and in a square, specifies more clearly than Vitruvius the position of the limbs necessary in order that they may touch the circle. He says — “If you open the legs so as to reduce your stature by one-fourteenth, know that the center of the extremities of the opened limbs will be the umbilicus and the area between the legs will be an equilateral triangle.”
This note was probably written in 1509 or 1510, since the accompanying drawings were published in the Vitruvius of 1511; if before that date, surely Leonardo would have noticed and corrected his friend’s error.
It would seem then that when Leonardo drew the illustrations for the De divind proportione he was merely illustrating Pacioli’s views; he had not yet seriously undertaken the study of the proportions of the parts of the body, but when he did so later he went into the question far more thoroughly than Pacioli had done and found it necessary to differ in some respects from the proportions laid down by that author. Thus Pacioli, as has been stated, divided the distance from the edge of the nasal septum to the chin into three equal parts, and since that distance equalled one-third the height of the face, each of the parts would equal one-ninth that height. Leonardo, however, in QVI, states that the distance from the mouth to below the chin equals one-fourth the height of the face (QVI, 4 and 9) and that the distance from the mouth to the labiomental groove, i.e. the height of the lower lip, is one-third that distance and therefore one-twelfth the height of the face instead of one-ninth. If then the distance from the nasal septum to below the chin is one-third the length of the face, the height of the upper lip must also be one-twelfth that length. In other words, the distance from the labiomental groove to below the chin is twice the height of either lip, instead of equal to it as Pacioli would have it, and is therefore one-sixth the length of the face (QVI, 4) instead of oneninth. In passing it may be noted that on that very same QVI, 4 Leonardo also states that the height of the upper lip is one-seventh the length of the face, a proportion irreconcilable with those given above. Is it a variation or an error, for Leonardo sometimes nodded?
Leonardo’s proportions have been thoroughly collated and classified by Professor Favaro (1917), who, to coordinate them, chooses the height of the lip as a modulus, this being one-twelfth the length of the face. The distance from the roots of the hair to the vertex is onesixth greater than the length of the face (QVI, llv) and since the height of the head, from the vertex to below the chin, is one-eighth the total height of the body (QVI, 10), the modulus is one one-hundred-andtwelfth of the total height. Leonardo, however, makes use of no definite unit of proportion or modulus, but expresses his proportions sometimes in terms of the total length, sometimes in terms of the length of the face and, more frequently, in those of the height of the head. In the case of the limbs the length of one part may be expressed in terms of another, as for example, in the statement that the length of the arm from the shoulder to the tip of the middle finger is equal to the length of four hands (QVI, 12), or that the distance from the anterior superior spine of the ilium to the ground is equal to the length of four feet (QV, 4). A good example of his method is shown in figure 15. Llere the leg is shown in side view, crossed by lines lettered and representing diameters at various levels. The accompanying text states that the knee is halfway between the anterior superior spine of the ilium and the sole of the foot; the diameter through the buttocks is equal to one-eighth of that distance and to the distance from the anterior superior iliac spine to the gluteal fold; the diameter of the calf is onequarter the distance from the knee to the sole; the diameter of the leg a little above the malleoli is one-sixth the knee-sole distance; and so on. Occasionally the lengths of the parts of one limb are expressed in terms of the parts of the other, as when the distance from the shoulder joint to the flexed elbow and from this to the tip of the thumb are each made to equal the distance from the middle of the knee to the ankle joint (T.P, cl67.).
And so Leonardo proceeds from region to region, head, neck, trunk, limbs, determining the distance from point to point and comparing it with some other known distance, and, considering the multiplicity of the proportions recorded by him and the variability that occurs in the various parts of the body, it is a wonder that there are not more discrepancies to be found in his statements. Some do occur, for, as pointed out by Favaro, the distance between the vertex of the head and the upper border of the forehead is in QVI, 1 made equal to the length of the upper lip; in one of the Venetian folios it is given the value of one-fifth the height of the head, as is also the distance from the lip fissure to below the chin, which according to the QVI proportions would make it three times the height of the upper lip. And again from the statement on QVI, llv, that the length of the head is one-sixth greater than the height of the face, one would conclude that the forehead-vertex height was twice the height of the upper lip. These discrepancies are partly due to the fact that in the Venetian folio fifths were the units into which the height of the head was divided, while in QVI the length of the face was divided into sixths, and partly, perhaps, to a recognition of the variability of the height of the forehead and of the vaulting of the skull.
The obvious object in formulating a canon of proportions is the determination of what may be regarded as the dimensions of a standard or typical member of a given race of the genus Homo. But no individual of that race will conform to the standard in every particular, there will always be variations or departures from it. Leonardo was too good an artist, too sure in his perception of relative dimensions, too keen an observer to fail to appreciate these individual variations; in fact an examination of his own drawings and writings will show that he did appreciate them. And he says—
“If nature had only one set standard for the proportions of the various parts, the faces of all men would resemble one another to such an extent that it would not be possible to distinguish one from another; but she has varied the five parts of the face (this is the Vitruvian division) in such a manner that although she has made an almost universal standard as to their size, she has not observed it in the various conditions to such an extent as to prevent one from being clearly distinguished from another.’’ (CA, 119v.)
And in another passage (G 5v) he condemns those “who study only the measurements and proportions of the nude figure and do not seek for its variety.” It is possible, accordingly, that some of the discrepancies to be found in his proportions may be due, as has already been suggested, to his recognition of variations. Indeed, in one case, that of the foot, he is willing to modify the actual proportion in order to satisfy an ideal standard of beauty. In one passage the length of the foot is said to equal the height of the head (QVI, 5) and the height of the head is taken as one-eighth the total height (QVI, 10), but in another statement the foot length is said to be one-fourth the distance from the anterior superior spine of the ilium to the ground (QV, 4), a proportion which would make it one-seventh the total height. This is greater than the QVI, 5 proportion, but less than that given by Vitruvius, who makes the foot enter only six times into the total height. Comparing his proportion of one-seventh to the Vitruvian one-sixth, Leonardo expresses his preference for the one-seventh, because such feet have a tendency toward the small side and the beauty of the leg lies in a small rather than a large foot. Favaro (1917) in his resume of Leonardo’s proportions expresses them in centimeters on the assumption that the total height is 168 cm. (5 ft. 7.2 in.). On this basis the length of the foot, according to the three proportions mentioned would be 21 cm. (8.4 in.), 24 cm. (9.6 in.) and 28 cm. (11.2 in.).
Leonardo gives no data as to the proportions of the female form; those recorded refer almost exclusively to the adult male body in the erect position and in such a posture that the ear orifice, the tip of the shoulder and the great trochanter are cut by the same frontal plane (QVI, 11). A few statements are made, however, as to proportions in other postures (fig. 17). Thus it is stated that a kneeling man loses one-third of his height and that in that position the umbilicus is the mid-point of the height (QVI, 8), whereas in the erect position the mid-point is at the symphysis pubis (root of the penis). In the sitting posture the distance from the seat to the vertex (sitting height) is made equal to half the total height plus the length of the scrotum (QVI, 8). Certain proportions of the limbs when in a condition of flexion are also recorded.
.Ynd, finally, there are a few scattered statements as to the proportions of a child. It is noted that with a child’s head in profile a circle may be described, with its center at the ear opening, to cut the middle of the forehead and touch the tip of the nose, the tip of the chin and the prominence of the larynx, all these points being therefore equidistant from the ear opening (A, 2v). The umbilicus is foimd to be the midpoint of both the length and breadth of the child’s body (QIII, 8v), a condition which is correlated with the importance of the umbilical vein during fetal life. An appreciation of the greater relative size of the child’s head is indicated by the statements that while in the adult the width across the shoulders was equal to the height of two heads (QVI, 8), in the child it is equivalent to only one head (Ash, 2Sv). A few data regarding the proportions of the limbs of the child are also given (TP, 167 and 169), but they do not differ essentially from those of the adult.
Fig. 17. Proportions of the human body in standing, kneeling and sitting postures. (QVI, 8.)
l ie. I. J lip Iiotip man from t I ip I’riifling Five-Figure Series ( 1158 ). From SudhofT, Studien, Heft 1 , pi. 14 , 1007 .
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Reference: McMurrich JP. Leonardo da Vinci - the anatomist. (1930) Carnegie institution of Washington, Williams & Wilkins Company, Baltimore.
Cite this page: Hill, M.A. (2024, April 20) Embryology Leonardo da Vinci - the anatomist (1930) 9. Retrieved from https://embryology.med.unsw.edu.au/embryology/index.php/Leonardo_da_Vinci_-_the_anatomist_(1930)_9
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