For more than five centuries, Leonardo da Vinci’s Vitruvian Man has fascinated art
historians, scientists, and philosophers. This emblematic drawing of the Renaissance
represents a human body simultaneously inscribed within a circle and a square,
reconciling two geometric figures that appear incompatible while respecting human
anatomy. But what method did Leonardo da Vinci employ to achieve such a synthesis?
A recent study, published in the British academic journal Arts and Sciences, ISTE Open
Science, provides a new and well documented answer. This research is conducted by
Jean-Charles Pomerol, emeritus professor of mathematics at Sorbonne University, and
Nathalie Popis, who specializes in the study of Leonardo da Vinci’s work. It is based on a
combined analysis of the proportions visible in the drawing, Leonardo’s manuscripts,
and mathematical systems inherited from Antiquity.
The authors show that Leonardo did not merely illustrate Vitruvius’s text. He developed a
genuine construction method based on a coherent proportional grid. This approach was
first grounded in a clearly identifiable duodecimal system, already present in his
preparatory studies of human proportions. In these drawings, Leonardo divided the body
and the face using simple fractions, such as one half, one third, one quarter, or one sixth,
revealing a rigorous organization of anatomical ratios. However, in order to extend this
logic to the entire body and to account precisely for its smallest parts, such as the hands
or extremities, he expanded this framework to a subdivision of one hundred and twenty
units. This number, chosen for its very high divisibility, makes it possible to express a wide
range of proportions as whole numbers and offers a flexibility of construction that the
decimal system does not allow.
Leonardo thus organized the human body according to simple ratios, doubled, tripled, or
multiplied by six. This organization ensured a rigorous coherence between the vertical
and horizontal dimensions of the body while remaining faithful to anatomical
observation. Each measurement referred to another through constant ratios and formed
a unified proportional structure.
Thus, in the drawing, the length of the hand is equal to that of the face and to the distance
between the navel and the pubis. The length of the foot is equal to that of the forearm and
to the distance between the navel and the chest. These correspondences repeat at
different scales throughout the body, as they appear in the graphic construction. They
reveal an internal structure based on harmony and self-similarity, in which each part
becomes a rational multiple or submultiple of the whole.
The number one hundred and twenty also possesses a symbolic dimension inherited
from Antiquity. As the product of the first five integers, it was associated in the
Pythagorean tradition with the idea of order and harmony in the world. It is also part of the
legacy of Mesopotamian measurement systems based on sixty, which still structure
today the division of time and the circle.
This unified logic of proportion echoes a central idea of ancient Greek philosophy. The
harmony of living beings is based on the existence of a common measure linking all their
parts. Leonardo developed this intuition in other fields of research, notably in his
botanical studies, where he observed that the sum of the thicknesses of a tree’s
branches is equal to that of its trunk.
The study also highlights a precise geometric construction based on alignments, right
angles, and points of convergence. Unlike Vitruvius, who placed the center of the body at
the level of the navel, Leonardo positioned it at the level of the pubis. This shift modified
the geometry of the triangle formed by the legs and introduced the notion of movement
and balance in the human body.
This research thus shows that the Vitruvian Man is not a simple symbolic illustration. It is
a rigorous construction based on mathematical, anatomical, and philosophical
principles. It renews our understanding of Leonardo da Vinci’s scientific thinking and
sheds new light on the deep links between art and science during the Renaissance.
Link of the scientific publication:
https://www.openscience.fr/IMG/pdf/iste_artsci26v10n1_1_en.pdf
