The Alchemy of Leonardo Da Vinci and The Vitruvian Man

Leonardo da Vinci’s Vitruvian Man is one of the best-known images of Renaissance art, which might be a bit surprising since it appears to be just a pen and ink drawing of a man with his limbs overlapping a circle and a square.

However, this drawing is much more than that; it is Leonardo’s symbolic solution to an ancient mathematical problem that also had relevance in Alchemy, in what is known as “squaring the circle.”

We know how to calculate the area of a circle (the value of π) times the radius squared), and the area of a square (the base times itself). But how to take the area of a circle and create a square with an equal area? This problem cannot be solved mathematically, but philosophically.

Roman architect Marcus Vitruvius found all kinds of mathematical proportions in the human body, which he considered as the measure of all architectural construction, following the ancient saying that man is the measure of all things:

“For without symmetry and proportion no temple can have a regular plan; that is, it must have an exact proportion worked out for it after the fashion of the members of a finely-shaped human body”.

It has been speculated that many of the great temples of antiquity used the golden ratio, something that has been documented by the alchemist René Schwaller de Lubicz in his study of the temple of Luxor (The Temple In Man).

Leonardo studied the writings of Vitruvius, who wrote that a perfect circle can be drawn around the human body if the navel is taken as the center and, the extension of the arms and the height of the body traces a square. Hence, Leonardo devised this drawing and focused on man as the answer to this question.


The Squared Circle: an alchemical symbol (17th century) illustrating the interplay of the four elements of matter symbolising the philosophers’ stone

The philosophers’ stone was the central symbol of the mystical terminology of alchemy, symbolizing perfection at its finest, enlightenment, and heavenly bliss.

Symbolically - in various cultures - the circle represents the spirit and the square represents matter (or the earth, the base in an architectural structure). The one connecting matter and spirit is the human, who has the substance that combines the material and the spiritual: the soul. The soul is also a symbol of the philosopher’s stone, vehicle of divine unity between earth and heaven.

All of this makes Da Vinci’s Vitruvian Man so significant, a true emblem of a way of thinking that combines philosophical, mathematical and alchemical ideas.


I love these kinds of Topics, Thank you @Francisco


Wow this was really neat to read! Thank you for sharing this! The drawing by Da Vinci is so iconic


Yes!! I’ve always been amazed by the golden ratio. It is found in many places in nature, and even outside of earth in galaxies!

I found a graphic that quickly explains what the ratio is and how to get to it:



I had a math instructor who said math is the closest thing to the divine know I know what he meant by that!
Thank you Francisco this is great philosophical idea that helps me put it all in perspective in a mathematical equation too! The square is matter and the circle is spirit and the triangle helps me to understand that the spirit is connected to the soul and the unity to heaven and earth!


Great analysis, Jeannie! I’m glad you found this post interesting.

I understand that alchemy wasn’t really about turning physical lead into gold but instead a philosophical/spiritual enterprise (disguised as a science) in the quest for wisdom and knowledge (when the Church wouldn’t permit it).

So, turning lead to gold = turning ignorance into knowledge.