Beyond Drawing Basics: Proving Leonardo's Theories on Human Proportions

In our Winter 2009 issue of Drawing, which is currently on newsstands and also available here, we excerpted part of a chapter of Anthony Panzera's forthcoming book on Leonardo da Vinci's notebooks, in which Panzera discusses his research on various aspects of Leonardo's explorations, including Leonardo's examination of human proportions as illustrated in his famous drawing The Vitruvian Man. To help you better understand Panzera's results, we publish this companion piece showing Leonardo's notes on his drawing–his exploration of the proportions of the human body as suggested by Marcus Vetruvius Pollio. Leonardo's text is accompanied by Panzera's modern take on The Vitruvian Man, below, and most notably, by Panzera's "proofs" of Leonardo's assertions, many of which are the root of the drawing basics that are taught today.

Anthony Panzera drawing after The Vitruvian Man drawing by Leondardo Da Vinci

 

Leonardo's Notes

I. Vitruvius, the architect, says in his work on architecture that the measurements of the human body are distributed by Nature as follows: that is, 1. that 4 fingers make one palm, 2. and 4 palms make one foot, 3. 6 palms make one cubit, 4. 4 cubits make a man’s height. 5. And 4 cubits make one pace, 6. and 24 palms make a man; and these measurements are used in his buildings. If you open your legs so much as to decrease your height 1/14 and spread and raise your arms till your middle fingers touch the level of the top of your head you must know that the center of the outspread limbs will be in the navel and the space between the legs will be an equilateral triangle.

II. 7. The length of a man's outspread arms is equal to his height.

III. 8. From the roots of the hair to the bottom of the chin is the tenth of a man's height; 9. from the bottom of the chin to the top of his head is one-eighth of his height; 10. from the top of the breast to the top of his head will be one-sixth of a man. 11. From the top of the breast to the roots of the hair will be the seventh part of a whole man. 12. From the nipples to the top of the head will be the fourth part of a man. 13. The greatest width of the shoulders contains in itself the fourth part of a man. 14. From the elbow to the tip of the hand will be the fifth part of a man; 15. and from the elbow to the angle of the armpit will be the eighth part of a man. 16. The whole hand will be the tenth part of a man; 17. the beginning of the genitals marks the middle of the man. 18. The foot is the seventh part of a man. 19. From the sole of the foot to below the knee will be the fourth part of a man. 20. From below the knee to the beginning of the genitals will be the fourth part of a man. 21. The distance from the bottom of the chin to the nose and from the roots of the hair to the eyebrows is, in each case the same, and like the ear, a third of a face.

 

Author's Notes by Anthony Panzera

Leonardo’s drawing The Vitruvian Man is an icon of such stature that Dr. Martin Kemp referred to it as "probably the most famous drawing in the world.” The drawing was meant to illustrate the essential theories of human proportion as set forth by the 1st-century B.C. Roman architect and engineer Marcus Vitruvius Pollio in his Ten Books On Architecture. The importance of Vitruvius’ history of architecture–the only such history of architecture to have survived ancient times–and its relevant dependence on human proportion was profound. It aided in defining the core of the Italian Renaissance and its emphasis on the classical motif in both architecture and art. Here we will focus only on the theories of proportion proposed by Vitruvius as understood and elaborated on by Leonardo.

Leonardo’s drawing measures about 13½ x 9¾ inches (344 x 245 mm) and is executed in light brown watered ink on a soft, warm, gray paper. It is one of the earliest of his drawings on human proportion and was done during Leonardo’s first Milanese period. His text divides Vitruvius’ information into three paragraphs, and not entirely in the order established by Vitruvius. In the first part Leonardo describes how Nature has determined the measurements of the human body by using smaller parts of the body as modules to define larger parts of the body. He ends the first part of the text by inscribing his famous male figure in a circle using the navel as the center of the compass.

The second paragraph, a single sentence, establishes the height of the figure, from the soles of the feet to the top of the head, as equal to the outstretched arms, and this is defined by the sides of a perfect square.

The third section defines the height of the whole figure using a variety of the parts of the body as modules. In the first paragraph the smaller modules are used incrementally to establish larger modules to eventually arrive at the height of a whole man. In this last paragraph each module is used as a canon to discover the proportional ratio of the part in relation to the height of a whole man.

What follows is an assessment, line by line, of the accuracy of Vitruvius’ theories as interpreted and illustrated by Leonardo using both his drawing and mine. In order to clarify Leonardo’s transcription of Vitruvius we have separated and enumerated each of the theories with bold numbers in the text.

Leonardo begins his interpretation of Vitruvius with, “the measurements of the human body are distributed by Nature as follow:”

1. "4 fingers make one palm." Perfect; a simple measurement with a caliper or compass will confirm this. Just below the figure and the second paragraph (which is only a single sentence) is a horizontal line with markings at both ends. The words diti (fingers) are written directly under four spaces, defined by five small lines, indicating the width of the fingers.  And next to that the word palmi (palms) written directly under five spaces, defined by six small lines, the width of each measures exactly four fingers.

2. "4 palms make one foot." Not quite; the length of the foot in both Leonardo’s drawing and mine is less than three palms.

3. "6 palms make one cubit." Correct. I have found that in verifying Leonardo’s theories one should trust in the ratio of the module to the part being measured. However, in this case, as the cubit is not part of the body, but an ancient form of measurement (18 to 22 inches), we must rely on the accepted measurement of the cubit. So, if the width of a man’s palm is approximately 3.25 inches, then six palms would measure 19 inches, which fits into the width of a cubit. And if we measure this same man of average height at his shoulders we would find that the width of his shoulders, between 18 and 20 inches, would enter into the height of a man four times, proving the theory in numbers 4 and 13.

4. "4 cubits make a man’s height." Usually correct.

5. "And 4 cubits make one pace and 24 palms make one cubit." Variable; One cubit at 18 inches x 4 = 72 inches or 6 feet, but a pace, according to the definition, is smaller at 58 inches–less than 5 feet. The conclusion here is to stick to the anatomical modules to establish a canon, and as for the second part, the measurement is slightly less than 24 palms in a whole man.

6. "If you open your legs so much as to decrease your height by 1/14…the space between the legs will be an equilateral triangle." Variable: In Leonardo’s drawing the decrease–the distance from the feet which rest on the bottom of the equilateral triangle to the feet resting on the bottom of the square–measures slightly more than 1/14, but in my drawing the decrease measures more than 1/17 of the total height of the figure. However, in both drawings the equilateral triangles are perfect. Go figure!

7. In order to bring further clarity to the text, I have rearranged Leonardo’s text by combining a portion of the last sentence in the first paragraph to the single sentence of the second paragraph.

"…and spread and raise your arms till your middle fingers touch the level of the top of your head you must know that the center of the outstretched limbs will be in the navel…” and, “The length of a man’s outspread arms is equal to his height." Perfect. A man standing perfectly erect in a square, stretching his arms upward, will find that his middle fingers touch the top level of the square level with his head, at the exact point where the circle intersects the square. And his navel will be at the compass point of this perfect circle. In addition, we will find that the length of a second set of his horizontally outstretched arms will be equal to his whole height.

Leonardo was the first (after Vitruvius) to comprehend and combine these theories together and the first to combine the circle and the square together in a single drawing, not by trying to square the circle, but by projecting it outside the square. In so doing he surpassed others before him and those who followed.  

Continuing with the third paragraph, Leonardo says:
8. "From the roots of the hair to the bottom of the chin is the tenth of a man’s height." Variable. In this Leonardo quotes Vitruvius’ words verbatim but contradicts it to measure 9 faces in several other examples. But even here in both Leonardo’s and my drawing the full figure measures only slightly larger than 9 faces.

9. "from the bottom of the chin to the top of his head is one-eighth of his height." Correct. This is the standard, acceptable, and reliable measurement, which works perfectly in Leonardo’s and my drawing.

10. "From the top of the breast to the top of his head will be one-sixth of a man." Correct. The measurement must be taken at the pit of the throat formed by the manubrum, the top of the sternum. It is perfect in Leonardo’s drawing and mine.

11. "From the top of the breast to the roots of the hair will be the seventh part of the whole man." Variable, and correct. This forms an unusual module and it measures slightly more in Leonardo’s drawing and slightly less in mine.

12. "…from the nipples to the top of the head will be the fourth part of a man." Correct. Perfect in both Leonardo’s and my drawing.

13. "The greatest width of the shoulders contains in itself the fourth part of a man." Correct. Perfect, in both Leonardo’s and my drawings and proven in several other examples.

14. "From the elbow to the tip of the hand will be the fifth part of a man." Variable. In both Leonardo’s and my drawing it measures no more than one-fourth of a man.

15. "…and from the elbow to the angle of the armpit will be the eighth part of a man." Correct. This should mean that the module is roughly equal to the size of the head; I find it slightly more in both Leonardo’s and my drawing.

16. "The whole hand will be the tenth part of a man." Variable. We already have proven that the hand is equal to the face and is closer to one-ninth of the whole man.

17. "The beginning of the genitals marks the middle of the man." Perfect. This point is the pubis symphasis where the two halves of the pelvis come together in front. This bony landmark is a standard, reliable reference point and is proven several times over in these pages.

18. "The foot is the seventh part of a man." Variable. Here Leonardo parts from Vitruvius, for Vitruvius states unequivocally on several occasions that the foot is one-sixth of the whole height of a man. In both Leonardo’s and my drawing the measurement is closer to seven than to six.

19. "From the sole of the foot to below the knee will be the fourth part of a man." Perfect in both Leonardo’s drawing and mine.

20. "From below the knee to the beginning of the genitals will be the fourth part of a man." If we take 19 and 20 together, they will equal two fourths, and make half a man. See 17 to verify the center of a man.

21. "The distance from the bottom of the chin to the nose and from the roots of the hair to the eyebrows is, in each case the same, and like the ear, a third of the face." Perfect. 

In this third and last paragraph, Leonardo sums up for us all of the major variables of anatomical modules used to measure the whole figure. In some ways it represents the beginning of all his proportional investigations and in others his final conclusions. Whether this is the beginning or the end, in what better place, or finer way, could there be to bring it all together than in his beautiful, iconic, and most famous drawing, The Vitruvian Man?

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Bob Bahr

About Bob Bahr

Hi. I'm the managing editor of American Artist, Watercolor, Drawing, and Workshop magazines. Drawing magazine is primarily my responsibility so I spend a lot of time looking at drawings, talking with draftsmen, and drawing ... but I love to paint, too.

6 thoughts on “Beyond Drawing Basics: Proving Leonardo's Theories on Human Proportions

  1. Marie, I agree.

    It looks like there is a publishing company or two who are talking with Panzera about the book. I hope this comes together quickly so more people can learn from Leonardo’s research and Panzera’s modern interpretation.

  2. It’s remarkable how influential the ideas of the Ancient Greeks have been; and how much Vetruvious, da Vinci, Palladio, etc. did to shape art, architecture, and design by disseminating and interpreting those ideas. It’s great that Mr. Panzera and Drawing magazine are now refreshing our understanding of those core concepts. Thanks, Steve

  3. Thanks for the comments, Marie and Amy.

    There seems to be a couple of publishers asking about Panzera’s book, so hopefully soon more people will get to read about Leonardo’s research and Panzera’s modern interpretation of it.

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