Dr. Kim H. Veltman
Leonardo da Vinci: Studies of the Human Body and Principles of Anatomy
In some ways Leonardo da Vinci (1452-1519) appears to be very traditional. He studies ancient sources such as Plato and Aristotle. It is likely that he may have studied Galen. He studies mediaeval sources such as Albert the Great and the anatomist Mondino de'Luzzi. This tradition leads him to compare the microcosm of the body and the macrocosm of the world. These analogies extend to comparisons between arteries in the body and underground rivers in the earth; the flow of blood to the head, with circulation of water to the summits of mountains; or blood when a vein bursts in the nose and water rushing out of a burst vein of the earth. His interest in such analogies is evident in the Ms A. (1492) and continues through the Codex Leicester (or Hammer) (c.1505-1510). There is some evidence that he rejects these analogies in the final years of his life (1514-1519), and this has led scholars such as Kemp to assess Leonardo's originality in terms of his courage to abandon these traditional analogies.
For Leonardo, however, these microcosm-macrocosm analogies are more than outmoded comparisons belonging to a pre scientific age. They lead him to compare his study of the body and Ptolemy's study of the earth, and consequently to use Ptolemy's method in the Geography as a starting point for his own systematic study of anatomy:
Thus in fifteen entire figures you will have set before you the microcosm on the same plan as, before me, was adapted by Ptolemy in his Cosmography; and so I shall afterwards divide them into limbs as he divided the whole world into provinces; then I will speak of the function of each part in every direction, putting before your eyes a description of the whole form and substance of man, as regards his movements from place to place, by means of his different parts. And thus, if it please our great author, I may demonstrate the nature of men and their customs in the way I describe his figure.
The more closely we examine the system underlying Leonardo's study of the body, the more clearly we recognize its originality. Where earlier authors had relied almost exclusively on verbal descriptions, Leonardo emphasizes the significance of visual descriptions. As Dr. Keele has so acutely noted these are of three basic kinds: a) some are illustrations of previous sources, visualizing theories of Plato, Aristotle and others; b) some involve composite anatomy or 'bodyscapes', i.e. making imaginative compositions or schemata of anatomical parts,; while c) others are based on actual observation. This third kind of drawing will be our chief concern.
In the course of twenty years of study from c.1489 to the end of his life Leonardo dissects at least 19 corpses. More is involved than simply recording the evidence of cadavers. Leonardo recognizes that in the process of dissecting a body, blood and other tissues often get in the way, and prevent one from drawing accurately. As a result he advises that the anatomist should make a model of the organ that he is dissecting and then use this as the basis for his drawing. In other words model making and scientific art go hand in hand: one must reconstruct reality before one can represent it. In the case of a hand or a leg these models are used primarily to reveal structure in terms of relationships between different layers of arteries, muscles, bones etc. These layers vary in number from eight to ten. In other cases these models are intended to reveal both structure and function. For instance, Leonardo makes a glass model of the heart such that the flow of millet seeds in clear water or using water with different coloured dyes so that flow patterns can be traced. Throughout he deals with anatomy and physiology together and does not make a clear distinction between them, as is done in modern medicine.
One of the most striking features of the notebooks is the manner in which Leonardo presents his work. There is effectively no criticism of shortcomings in earlier authors, nor boasting of his own accomplishments. Indeed his style is in the form of a teaching manual with descriptions written as advice: how one must proceed if one wishes to carry out these tasks oneself. These are the not the egocentric scribblings of an isolated, genial misfit. They are attempts to convey to a larger public a new method of presentation. His reliance on diagrams apparently posed serious problems for the printing presses of the day, which would explain Leonardo's plea late in life that financial considerations should not prevent one from publishing the work. According to Vasari, plans for publication continued for decades after his death. However, as far as the anatomical works were concerned, these came to nothing until the early 20th century, and had to wait until Dr. Keele's pioneering work (1979-1981) for a more serious treatment. Hence it is no wonder that various features of Leonardo's method have not received the attention they deserve. Our paper will focus on six of these features: Leonardo's treatment of whole and parts, viewpoints, levels, ages, movements and transformations.
2. Whole and Parts
As noted above, Leonardo's method of showing the body in its entirety and then its parts came from the arrangement of maps in Ptolemy's Geography. Leonardo had a clear plan for demonstrating the body as a whole. There would be sets of drawings. Each set would have three drawings: a frontal view to show height and position; a profile to show the depth of the whole and the parts, and a demonstration of the back parts. An early plan called for four of these sets:
Leonardo revised this and drew up a new plan which would have eight of these sets:
He also outlined a third plan which involved six sets:
On encountering these three different lists, a first impression is that Leonardo kept changing his mind and that he had no coherent plan. Indeed this has been generally assumed. If we look more closely, however, we note that the lists do not contradict each other. Each focusses on different aspects: the first simply on the body and skeleton; the second adds muscles and skin; the third includes other levels. If these be combined an integrated approach of 12 sets emerges:
The above cases all involve different aspects or layers of the body as a whole, corresponding to Ptolemy's views of the earth as a whole. In the passage cited earlier where he makes the connection between Ptolemy's geographical maps and his own anatomical drawings, Leonardo mentions 15 complete drawings of the human figure. The incremental and cumulative dimension of his approach thus emerges. In this case Leonardo begins with a simple instance using 4 drawings. Next he considers 8. Then he considers another configuration of 6. This amounts to 12 in all which he then expands to 15. Since each of these is to be seen from the front, behind and the side, this means that 45 basic drawings are required.
Leonardo is equally interested in various parts of the body. He does a series of drawings of the head, neck and shoulders, arm, hand, leg and foot, in each case drawing these from different points of view and in different layers. It is also a question of showing how these various layers interact. In the case of the head, for instance, he is concerned not just with various views of the skull but also with showing how the optic nerves penetrate the skull on their way to the optic chiasma and the three ventricles. He makes another series of drawings of the eyes in relation to the optical system. These improve over time. His early drawings show no optical chiasma and show the three ventricles as spherical containers following conventional mediaeval drawings. In the period c.1505-1507 he made a wax injection of the ventricles and arrived at a much more accurate representation. He also made accurate drawings of the optic chiasma and made various drawings showing how these parts related to the optical system and the head. The concern is not just to identify different parts of a system, but also to reveal how outer and inner relate.
Leonardo approach is similar with various inner organs: liver, pancreas, kidneys and renal system, sexual organs and particularly the lung and heart. In the case of these last two, he outlines a clear method of exposition, involving first the lung in isolation, then the heart and then the lung and heart together. Each of these is represented from six viewpoints: front, behind, left side, right side, above and below. Elsewhere he expands this into a more systematic approach: lung in isolation; lung and the ramifications of the trachea; heart; heart and ramifications and veins and arteries; veins and arteries of the heart with ramification of the trachea; tessa with heart and lungs joined together.
Each of these is again to be drawn from six points of view: front, behind, left side, right side, above, below. This means that two organs now generate 7 combinations times 6 views, i.e. 42 drawings. In conjunction with this scheme he lists nine other organs: liver, spleen, kidney, womb, testicles, head, bladder, stomach, and intestine. Two of these refer to a specific gender. Even so, including the heart and lung, this still adds up to drawings of ten organs in the case of a man, and an eleventh, namely the womb, in the case of a woman. If all of these were combined in the fashion of the lungs and heart, this would produce 7 combinations, times 6 viewpoints, times 11 organs, i.e. 462 illustrations.
In a perspectival drawing of a regular geometrical object, a combination of two viewpoints is necessary. Usually this involves a ground plan and elevation. In the case of more complex objects, particularly organic ones, more than two viewpoints are required. As we have already noted in the case of his drawings inspired by Ptolemy's geography, Leonardo frequently uses three viewpoints: front, behind and side. In the case of individual parts of the body, such as the hand he typically employs four points of view: front, behind, left side and right side. In the case of inner organs he adds a further two viewpoints, namely, above and below. When dealing with the shoulders he considers no less than eight viewpoints. Accompanying this he sketches a small eight sided star to illustrate this principle of multiple viewpoints adding:
I draw the arm from eight points of view of which three are from the outside, three are from the inside, one is from behind and one is from in front. And I turn it to eight other viewpoints when the two "fociles" of the arm are crossed.
It is precisely this systematic approach which gives his drawings a cinematographic dimension, a sense of an object being carefully considered from different points of view as the eye moves.
4. Levels and Ages
An essential aspect of Leonardo's approach is to show the same object at different levels. In the case of the hand he carefully articulates an approach using eight levels. This he subsequently extends to ten, namely: 1) separate bones from each other, sawn through the centre in order to show which are hollow and which are solid; 2) bones together showing the whole hand; 3) first ligaments of the bones; 4) muscles which bind the wrist and the rest of the hand; 5) tendons which move the first joints of the fingers; 6) tendons which move the second joints of the fingers; 7) tendons which move the third joints of the fingers; 8) nerves which give them a sense of touch; 9) veins and arteries; 10) whole hand complete with skin and measurements. Each of these is again to be seen from four viewpoints: palmar, dorsal, medial and lateral. As a result even a hand requires 40 illustrations in a static position.
Leonardo is also concerned with studying changes that occur with growth. So his method calls for studying a child, a young man and an old man. The drawings of the complete figures would thus increase to 40 and those of the inner organs would potentially expand to 462 drawings times three, i.e. 1386. The human body is no longer something that can be rendered in terms of some random schematic diagrams. It requires an extra ordinary repertoire of bodyscapes.
Although his studies are based on dead cadavers, it is not the static form of the body that interests him. Leonardo wants to understand the principles of motion in the human body. He sees the body as a mechanical device, effectively subject to the laws of mechanics. Indeed his study of the four powers of nature, namely, weight, force, percussion and movement, is intimately connnected with his anatomical studies and he plans to use his book on mechanical principles and the four powers as an introduction to his studies of the human body. Traditional organic metaphors are thus replaced by mechanical metaphors. But much more is involved. Models can now simulate the body, its parts and its functions. The spine can be compared with the mast of a ship; the actions of the shoulders and arms, indeed all the basic human movements, compared with weights and balances. These are evocative images on the one hand. On the other hand they introduce into the study of the human body a new level of objectivity, distance, even coldness. Leonardo can render the nude figure of a woman or a man without a trace of eroticism, even his studies of coitus between a man and a woman become records of a mechanical action. To state this positively, Leonardo's exploration of the human body in terms of mechanical principles leads him to discover a clinical dimension, where objective medical treatment is separated clearly from the subjective world of human feelings, emotions and passions.
In order to understand how the machine of the body works, Leonardo makes physical and mechanical models to simulate its functions. By making model hearts of a man such that they function just as human ones, the way is prepared for the concept of transplants and for the dilemmas of modern medicine where the sick body is seen as a machine which, in extreme cases, needs to be hooked up with other machines such as respirators, in order that the sick machine can continue to function. The discovery of a clinical approach to the body was ironically that which eroded a sense of the body's being something unique requiring treatment by other than purely mechanical ways.
Leonardo's concern with the physical and mechanical principles of the human body leads him to focus on how its various parts move. These concerns lead him to make a catalogue of different kinds of movement:
After a demonstration of all the parts of the limbs of man and other animals you will represent the proper method of action of these limbs, that is, in rising after lying down, in moving, running and jumping in various attitudes, in lifting and carrying heavy weights, in throwing things to a distance and in swimming and in every act you will show which limbs and which muscles are the causes of the said actions and especially in the play of the arms.
Elsewhere we find him making an even more comprehensive list of 18 actions of man :
repose, movement, running, standing, supported, sitting, leaning, kneeling, lying down, suspended. Carrying or being carried, thrusting, pulling, striking being struck, pressing down and lifting up.
In the case of an arm it is not just a question of showing the skin, muscles, arteries and bones. The challenge is to show how the bones move as the arm is twisted, or raised, or as the elbow is bent or stretched. In the case of a hand he lists 10 principal movements:
"that is forwards, backwards, to right and to left, in a circular motion, up or down, to close and to open, and to spread the fingers or to press them together".This applies equally to smaller units. Hence we find him studying how a finger bends at its various junctures, and even making a model to demonstrate how this operates.
His purpose in all this is both scientific and artistic. He wants to represent the human figure in all possible positions and actions. The Codex Huygens and the treatise that has come to us via Thoams Coke confirms that he was also trying to catalogue the geometrical limits of those movements, listing which limbs could be rotated completely and which limbs partially.
In his study of geometry, Leonardo was guided by what was known at the time as the geometrical game (de ludo geometrico), an exploration of the laws governing all transformations of shape. He wanted to apply these same principles to the human body. It is no coincidence therefore that we find him using lunules and other geometrical forms in the context of his drawings of the heart. He is attempting not merely to represent the organ, but to trace how the valves of the heart open and close. Where earlier authors were content with verbal descriptions, Leonardo is concerned with a visual demonstration which can be shown in figures and also reproduced in models. There is an uncanny way in which reproduction in terms of model making and representation go together.
This fascination with movement and change in the human body extends beyond the limits of everyday anatomy and physiology. He is intrigued how the various parts of the body, once isolated, can then potentially be combined in new ways. He recommends this specifically in the creation of convincing, life-like monsters, of which he gives examples in his drawings. His concern here is deeper than simply creating realistic mutants. He sees the artist's role as analogous to God's act of creation. The artist does not merely record nature, he extends nature. In the manner that children now play with meccano and lego sets, Leonardo plays with human form. He studies different kinds of noses, eyes and other facial features, combining them to create ever new faces, showing what happens when a nose is stretched, a chin elongated, doubled or tripled. Some of these studies become a starting point for Dürer's more systematic treatment in the Dresden Sketchbook, which he develops in published form as The Four Books of Human Proportion.
Part of Leonardo's concern is to use external features of physiognomy as expressions of the inner workings of the mind and soul: fear, hope, anger, deceit, indeed the whole range of human emotions. It is no coincidence therefore that his transformations of facial physiognomy are closely related with his masterpiece the Last Supper which, besides being his final attempt to use perspective in the context of man made objects, is also his major study of comparative expressions and emotions. This work prefigures seventeenth century treatises of the passions (e.g. Charles Le Brun), which lead via Lavater to Darwin's famous treatise on the expression of emotions. In this way his study of anatomy is linked with an early form of psychology, using the outer extensions of man's expressions to explore the enormity of an inner world.
Ancient and mediaeval medicine had remained largely a question of touch. One felt whether the body was hot or cold, one used proportions to measure pulse. Some aspects of the process were visual. One examined the person's complexion and the colour of their urine. But for the most part there was no attempt to study the details of what went on inside. If one did one discussed them verbally or decribed them in manuscripts using words. Leonardo's anatomical studies mark a watershed in this respect. They introduce visual diagrams as a standard for communicating knowledge, a conviction that "true knowledge of the shape of any body will be arrived at by seeing it from different aspects." Inherent in this process is a distancing effect: one can see the diagrams without being confronted by the smell, feel and gory sight of the originals. The model making, which is a basic dimension of this approach increases that distancing effect.
Leonardo's approach, with its notions of layers, levels, transparency, cutaways, sections opens up the body in a new way. Surface features and below the surface features are now integrated into the same process of understanding. But at the same time there is a curious way in which the new methods of visualization lead to a process of externalization: everything can be seen, brought out into the open, not just the insides of arms and legs, but also the inner organs and even the inner expressions of the mind and soul. There is a new belief that everything can be brought to the surface. Hence the study of anatomy, art and an early form of psychology emerge together in Leonardo's notebooks.
From the time of Peckham in the latter thirteenth century there had been a conviction that optics, given its links with both mathematics and light offered a key to highest certainty in the physical sciences. The rise of the Franciscan movement, which helped to sponsor the practical application of this philosophy led Giotto and his successors to devote new attention to the surfaces of the visual world. The development pf perspective with Brunelleschi, Alberti and Piero della Francesca provided new tools for this activity. Leonardo took these studies considerably further by recognizing that perspective in its literal sense was not just looking or looking into but looking through. Transparency became more than a simple technique: it became a fundamental dimension of knowledge. Indeed, this approach of rendering visible readily involved an assumption that dissection is all, that anything inside can be brought to the surface and made visible, that everything can be externalized. Herein lies one of the more fascinating and troubling developments of the late fifteenth century, which has brought some of the dilemmas of modern medicine: the notion that knowledge of a patient is only a question of passively recording in terms of images, that inner feelings simply need to be surfaced, outered, externalized, that there is nothing more to knowledge and understanding than this.
Leonardo is aware that more is involved as is clearly shown by his studies of motion in the human body. These implicitly introduce a temporal dimension into his spatial representations: knowledge is no longer in terms of a static object which can be probed for its substance. Knowledge involves seeing that object at a given conjunction of space and time. He would not have spoken of space-time coordinates or spatio-temporal dimensions, but this is the direction in which in his study of the body pointed. Nor would he have spoken of kinematic views or animation, but this is also the direction in which his study of the body pointed: that knowing is a problem of seeing how spatial objects move in time; that it is no longer a question of simply drawing an object or even drawing an object from different viewpoints but one of coordinating these with a time frame. Leonardo would have been delighted with inventions such as the cinema, and computer graphics. Would he also have seen the dangers of studying motion, the dilemmas of becoming so caught up with the changing, the different, the momentary fleeting concatenations of space and time, that all these could become an end in themselves? Probably not. He was so caught up with the challenge of establishing a method, now taken for granted, that all his energies were absorbed. Moreover, his own goal did not stop at dissection. He wanted to understand something deeper, as when he noted:
would that it might please our creator that I were able to reveal the nature of man and his customs even as I describe his figure.
|1.||The standard work on Leonardo's anatomy is the monumental edition of Dr. K.D. Keele with a comentary by Carlo Pedretti, Corpus of the anatomical works in the collection of her Majesty the Queen, New York:Johnson, 1979-1981., 3 vol. See also his fundamental study, Leonardo da Vinci's elements of the science of man, New York: Academic Press, 1983.|
|2.||E.g. Ms A, 55v-56r.|
|3.||E.g. Codex Leicester (Hammer), 21v. Other passages include BM Arundel, 233v, 236v and CA 171r. These and other passages have been colected and translated by J.P. Richter, The literary works of Leonardo da Vinci, London: Phaidon, 1970, (first ed. 1883), vol. 2, pp.158-161 (subterranean watercourses). Further references can be found in the corresponding section of the Commentary by Carlo Pedretti, London: Phaidon, 1977.|
|4.||Martin Kemp, "The crisis of received wisdom in Leonardo's late thought", Leonardo e l'età della ragione, Milan: Scientia, 1982, pp.27-42.|
|5.||E.g W 12592r (K/P 97r); W 19104v (K/P 107r) and W 19015v (K/P 149v).|
|7.||E.g. W19071r (K/P162r) Leonardo even praises drawing over the actual anatomical originals on W 19070v (K/P 113r).|
|8.||Kenneth D. Keele, "Leonardo da Vinci's 'Anatomia naturale'", Yale journal of biology and medicine, New Haven, vol. 52, 1979, 363-409.|
|9.||E.g. W 19008r (K/P 140r) and W 19017r (K/P 151r). For another discussion of these themes see the author's: "Visualization and perspective", Leonardo e l'età della ragione, Milan: Scientia, 1982, pp.185-210.|
|10.||For another discussion see the author's:"Transparency and models: geometry and nature reconciled", Linear perspective and the visual dimensions of science and art, Munich: Deutscher Kunstverlag, 1986, pp.202-239.|
|11.||Cf. Keele, as in 8 above, p.376.|
|12.||E.g. W 19007v (K/P 139v) or Madrid Codex I, 6r. This approach is not limited to his anatomical manuscripts. It is a general characteristic of his method. Sometimes he tells the reader what steps to take, adding, "and thus make your general rule" (e.g. CA 132vb). The question of method is the subject of an as yet unpublished essay by the author: Structure and method in the notebooks of Leonardo da Vinci.|
|13.||W 19007v (K/P 139v):
....and in order that benefit reaches men, I teach the ways to print it methodically and I pray ye, o successors, that avarice not constrain you from printing it.
|14.||Giorgio Vasari, The lives of the painters, sculptors and architects, trans. A. B. Hinds, London: Dent Y1927), 1963, vol. 2, p.157.|
|15.||Keele as in note 1 above. Prior to this there was a partial edition: Quaderni d'anatomia, ed O. C. L. Vangenstein, A Fonahn, H. Hopstock, Christiania: J. Dybwad, 1911-1916. This was followed by (Lord) Kenneth Clark, A catalogue of the drawings of Windsor Castle, New York: The Macmillan Co., 1935, 2nd edition, 1968, which made a fundamental contribution in terms of chronology of the individual drawings, but made little attempt to enter into details of anatomical interpretation.|
|16.||E.g. K/P 58v, 81r,113v,139v,154r.|
|17.||W 19023v (K/P 65v).|
|18.||W 19037r (K/P 81r).|
|19.||W 19061r (K/P 154v).|
|20.||W 19061r (K/P 154r).|
|21.||W 19057r (K/P 43r).|
|22.||W 12626r (K/P 6r).|
|23.||W 12603r (K/P 32r).|
|24.||W 19127r (K/P 104r).|
|25.||W 19052r (K/P 55r). For a discussion of this series of passages see Keele, as in note 1, 1983, pp. 61-68. A full account of Leonardo's work on optics and vision is given in the author's as yet unpublished Leonardo Studies II-III.|
|26.||W 19054v (K/P 53v).|
|29.||E.g W 12619r (K/P 162r). Cf. K/P 53r, 117r, 135v, 145r, 152r, 163r, 196v.|
|30.||W 19054v (K/P 53v).|
|31.||W 19005v (K/P 141v) and W 19008v (K/P 140v).|
|32.||W 19008v (K/P 140v).|
|33.||W 19009v (K/P 143v).|
|34.||W 19061r (K/P 154r). On W 19008v
(K/P 140v) and W 19012v (K/P 142v),
draws a series of six of these layers each of which is carefully numbered.
|35.||W 19061r (K/P 154r):
And thus in the chapter on the hand you will make forty demonstrations; and you should do the same for each limb. And in this way you will present full knowledge. You should then make a discourse on the hands of each animal, in order to show in what way they vary as with the bear.
|36.||W 19009v (K/P 143v).|
|37.||W 19009r (K/P 143r):
Arrange it so that the book On the elements of machines with its practice shall precede the demonstration of the movement and force of man and of other animals and by means of these you will be able to prove all your propositions.
|38.||W 19015v (K/P 149v).|
|39.||E.g. W 19026v (K/P 68v) and W 19061v (K/P 154v).|
|40.||E.g. W 19097v (K/P 35r).|
|41.||W 19010v (K/P 147v).|
|42.||BN 2038 29r, cited in Richter, as in note 3, vol.1 p.264.|
|43.||CA 45v, cited in Richter, as in note 3, vol.1, p. 259.|
|44.||See: Erwin Panofsky, The Codex Huygens and Leonardo da Vinci's art theory. The Pierpoint Morgan library Codex 1139, London: Warburg Institute, 1940, e.g. fol. 21, 22,23, 24,29.|
|45.||Thomas Coke, General instructions for drawing and designing humane figures reduced to geometrical rule from the original drawings of Lionard D'Vinci, London, c.1720. For a reprint and a discussion of this in the context of the Codex Huygens, see Carlo Pedretti, Commentary, as in note 3 , vol. 2. pp.48-75.|
|46.||See, for instance, James Edward McCabe, Leonardo da Vinci's De ludo geometrico, PhD Dissertation, University of California at Los Angeles, 1972|
|47.||E.g. W 19074v (K/P 166v), W 19118v (K/P 116v) and W 19117v, (K/P 115v).|
|48.||E.g. A 109r (BN 2038 29r):
How to make an imaginary animal appear natural.
You know that you cannot make any animal without it having its libs such that each bears some resemblance to that of some one of the animals. If therefore you wish to make one of your imaginary animals appear natural -let us suppose it to be a dragon- take for its head that of a mastiff or setter, for its eyes those of a cat, for its ears those of a porcupine, for its nose that of a greyhound, with the eyebrows of a lion, the temples of an old cock and the neck of a water tortoise.
|49.||E.g. W 12366r and W 12369r.|
|50.||E.g. TPL 68:
The deity which the painter has, causes the mind of the painter to transmute itself into a similitude of the divine mind, such that it can freely summon forth the generation of diverse essences of various animals, plants, fruits, countries, lands, ruins or mountains...
Cf. TPL 133: ...Disegno is not only a science but must be recorded as being a deity which deity
repeats all the evident works made by the most high God.
...Disegno is not only a science but must be recorded as being a deity which deity repeats all the evident works made by the most high God.
But this disegno is of such excellence that not only does it research the works of nature but infinitely more than those which nature makes.
|52.||E.g TPL 288-289.|
|53.||For an early compilation of these faces see the edition by Le comte de Caylus, Receuil de testes de caricature etde charges, Paris: chez Mariette, 1730. For a more recent study see: Sir Ernst Gombrich, "The grotesque heads", The Heritage of Apelles, London: Phaidon, 1976, pp. 57-75.|
|54.||Albrecht Dürer, Skizzenbuch, Dresden, Königliche öffentliche Bibliothek, fol. 94r.|
|55.||Albrecht Dürer, Hierin sind begriffen vier Bücher der menschlicher Proportion, Nürnberg, 1528, fol. Nr-Niiv.|
|56.||E.g. BN 2038, 28v.|
|57.||E.g. W 19070v (K/P 113r).|
|58.||John Pecham and the science of optics, Perspectiva communis, ed. David C. Lindberg, Madison: University of Wisconsin Press, 1970.|
|59.||Albrecht Dürer, Dürers schriftlicher Nachlass, ed. Lange und Fuhse, 1893, p.319, 11: " Item perspectiva ist ein lateinisch Wort, bedeutt ein Durchsehung."|
|60.||Ernst Cassirer, Substance and function, (Chicago: Open Court Publishing Co., 1923), New York: Dover,1953.|
|61.||Cited in: The notebooks of Leonardo da Vinci, ed. Edward MacCurdy, New York: George Braziller, 1955, p. 93. This also contains readily accessible translations of anatomical passages although without the precision of Dr. Keele's standard.|