The pen and ink drawing by Leonardo da Vinci (1452–1519), depicting a man fitting his body into a circle and a square by adjusting the position of his arms and legs, is undoubtedly the most famous drawing in the world. I base this statement on the observation that this drawing is ubiquitous in modern society, from movies and books, to advertisements and logos for holistic enterprises. Few people, however, know its name or the mystical philosophy that it symbolizes. It is called Vitruvian Man.

### Leonardo’s drawing called Vitruvian Man

The title of the drawing refers to Vitruvius, an ancient Roman architect who wrote a series of ten books on architecture, which was one of the few collections of books of its type that survived into the Renaissance. In the third volume, which is on the proportions of temples, Vitruvius states that these sacred buildings should be based on the proportions of man because the human body is the model of perfection. He justifies this by stating that the human body with arms and legs extended fits into the perfect geometric forms, the circle and the square.

This fragment of Pythagorean philosophy added credibility to the Renaissance belief that “man is the measure of all things,” and it seized the imagination of Renaissance artists and philosophers. Many artists tried to illustrate this divine relationship, but with varying success. An illustration of Vitruvian man by Cesariano in his Cosmo Vitruvius of 1521 reeks of failure. Cesariano drew a perfect circle and square tangent to each other at the four points of the square; then he forced a figure of a man into the design so that his hands and feet touch the points. The result was one of the most disproportioned figures of the Renaissance, with arms too long, legs too short, and hands and feet too big. A system of relationships alone did not make beauty happen.

### Cesariano’s version of Vitruvian Man

It took the genius of Leonardo da Vinci to solve the problem. Leonardo started by drawing a perfectly proportioned man and then found the circle and square in the figure. The circle and square are only tangent at one place, the base. The thing that he added was beauty. I keep a copy of his illustration on the wall over my drawing table and refer to it as a guide for my own figures. I believe that beauty in itself is a greater mystical revelation than any system of symbols or correspondences, and I think that Leonardo shared this belief.

I have lived with Leonardo’s Vitruvian Man for many years now and it has taught me many things. It has been like having Leonardo as a teacher. You may be asking yourself, why was it so important to Renaissance artists and philosophers that a human body could fit into a circle and a square? As stated above, the idea that Vitruvius was expressing can be traced back to one of the most influential of the early Greek philosophers, Pythagoras. Pythagoras lived in the Greek colony of Croton, in Southern Italy in the 6thcentury, BCE, the same time that Buddha lived. Like Buddha, Pythagoras taught his male and female disciples that after death we are reborn, we live through many lives, and we are on an endless wheel of reincarnations until we purify ourselves and return to our divine source.

Purification included a vegetarian diet, moral behavior, meditation, and contemplation of the numerical abstractions that underlie reality. Pythagoras was the first person to call himself a philosopher, which means to love *Sophia*(wisdom). We have no writing that can be attributed to Pythagoras. Everything we know about him comes from other authors, particularly the biographies written by Neoplatonic authors in the 3rdand 4thcenturies CE. Yet from what we know, we can credit him as being one of a handful of people that were instrumental in creating Western culture. Because of the similarities between Pythagoras’s philosophy and the Orphic Mysteries, some historians theorize that if he did write anything it would have been poetry and he would have signed it Orpheus.

### Mosaic depicting Orpheus charming animals with his lyre

Orpheus, the mythical, semi-divine musician, was credited as the founder of the first mystery cult, a religion based on a secret redemptive ritual. And as implied above, this religion is believed to be a major source for the Pythagorean teachings. Many followers of Orpheus were poets and musicians who believed that their inspiration came directly from Orpheus; hence, they would sign his name to their work.

In the Orphic creation myth, the beautiful god, Dionysus, was born of the incestuous union of Zeus and his daughter Persephone. Zeus’s wife, Hera, was jealous and wished to destroy the child. To accomplish this she had her allies, the Titans, dismember and devour him. Of course, Zeus was heart-broken and in a fit of anger, he burned the Titans to ash with a volley of lightning bolts. Only Dionysus’s heart remained, and from this, Zeus created a new Dionysus. However, from the ash of the Titans mixed with the devoured Dionysus, the human race was born. Therefore, the human race is part divine and beautiful like Dionysus and part vicious and material like the Titans. The purpose of the Orphic mystery was to redeem the Dionystic soul and make it the dominant influence in the lives of the devotees. This, of course, is similar to most mystical teachings and can be related to Hindu, Buddhist, Gnostic, and Hermetic beliefs.

### Roman Relief depicting Dionysus

The Orphics, like the Pythagoreans, saw a connection between music and numerical order. This type of reasoning led to sacred geometry. Expanding on this logic, Pythagoras taught that geometric figures were powerful magical symbols. The circle, being connected to the sky and the cosmos, with seven spherical planets believed to be circling the earth, was a symbol of the divine Dionystic soul. The square is the natural way that humans relate to the physical world. We have a front and a back, a left and a right. This is why there are four directions, four seasons, and four classical elements. It is why my house has four sides and I am sitting on a four-legged chair while I write this on my square keyboard and read it on my square screen. The square became a symbol of the Titanic physical aspect.

The first step to the liberation of the soul is to recognize that we are made of both aspects. In Pythagorean thinking, if a human can be shown to fit into both symbols this would be a geometric proof of our dual nature. This belief was incorporated into alchemy, and other ancient disciplines where it was called “the squaring of the circle.” In Medieval art the squaring of the circle was symbolized by a hexagon or the octagon, and that is why these shapes were used to depict the Grail and in the construction of baptismal fountains.

In this way, the teaching was passed on to the Renaissance. In Venice around the year 1500, Leonardo, once again making use of the circle and the square, demonstrated geometrically that humans are composed of physical bodies containing a divine soul.

Although this bit of history helps to explain the main theme of Vitruvian Man, we have not yet completed our exploration of its symbols. As we said in the beginning, Leonardo was able to solve this problem by drawing a beautifully proportioned figure and then finding these truths within the figure. To understand this statement fully we have to understand the significance of ratios.

Besides the symbolism of geometric forms, the Pythagoreans believed that whole numbers are symbols equated to specific qualities as well as quantities: one represents unity, two polarity, three the beginning of form, etc. the most powerful way that numbers were seen to impact on reality, however, was as ratios. Ratios are relationships between numbers. For example, the number four has a 1:2 ratio to the number eight, because two fours can fit into eight. Six and nine have a 2:3 ratio. In this example the unit of measurement would be the number three, because two threes can fit into six and three threes into nine. Similarly, nine and twelve have a 3:4 ratio.

The Pythagoreans found that music could also be expressed as ratios, and that these three ratios were essential to its creation. The ratio 1:2 described the whole note, 2:3 the perfect fifth, and 3:4 the perfect forth. It seems that these ratios underlie all musical harmony. Every culture has to find these same notes and create their musical scale around them in order to have music. Beauty has this objective aspect as well as a subjective aspect.

Pythagoras believed that the universe was ordered in this same way. The Pythagoreans believed that the earth was a sphere in the center of the universe and that there were seven planets that circled the earth on a series of ascending crystal spheres, one inside the other, like the layers of an onion. The seven ancient planets are the ones that can be seen with the naked eye: Luna, Mercury, Venus, Sol, Mars, Jupiter, and Saturn. Notice that the moon and the sun were considered planets and the earth was not. Pythagoras called the universe a “cosmos,” which meant that it was a beautiful, musical harmony. He believed that the ratios described by the speed and orbits of the planets could be expressed as musical notes and he used these note to create our Western diatonic music scale with its seven notes. This cosmic music scale has been called “the music of the spheres.”

Classical artists used ratios to develop the perfect figure, and like other Renaissance artists, Leonardo also used ratios. To make use of ratios, Leonardo had to find a way of measuring the figure by making use of relationships within the figure, not by measuring it with an external scale such as inches or any other external system. His unit of choice was the head. Leonardo’s figure has a one 1:8 ratio with its own head. In other words, it is eight heads tall.

You will notice that Vitruvian Man has dividing lines drawn on his body. There is a line at the chin that indicates the limit of the one head unit, a line at the nipples that marks the length of two heads, a line at the groin that marks four heads, a line below the knees that marks six heads, and the base line the marks eight heads. The base line forms the bottom of the square and the top rests on his head. Therefore, the square is eight heads tall as well. Notice that the man’s lower set of extended arms, the ones that are at a right angle to his body, touch the square on both sides. Because the width of a square is equal to its height, the length of the arms has to be eight heads as well. In other words, our extended arms are the same length as our body from head to toe. Try measuring you friends; you will find that this is true with only slight variations.

The vertical lines on the shoulders of Leonardo’s figure measure the two-head width of the torso at the shoulders; the line at the joint of each arm measures an additional one head in each direction; and then we jump another two heads on each side to the fingers and the sides of the square. The dividing line between the hand and the forearm, however, stems from a different unit of measure. This is called the “golden proportion.”

To explain the significance of the golden proportion it will be helpful if we first study the most sacred of the Pythagorean symbols, the Tetractys. The Tetractys is an arrangement of ten dots in a pyramid with one dot at the top and four at the bottom. To the Pythagoreans, it symbolized how the divine unity of the number One, at the top, emanated or gave birth to the physical world, symbolized by the number Four at the bottom. One way of describing this emanation, from the top down, was that the unity of One gave birth to the duality of Two and the dimension length. Two gave birth to a third, which created three points, and with this added dimension the possibility of creating a two-dimensional plan, having height and width. Then with a fourth point, three-dimensional reality could be created, the world of form with length, width, and depth.

### The Pythagorean Tetractys

Now we are ready to discuss proportion. To the Pythagoreans, proportion described a relationship between two ratios. They noticed that there are three different levels of complexity of proportion and they correlated them to the bottom three layers of the Tetractys. At the bottom, the most complex proportion described a relationship of four items: A is to B as C is to D; 1:2 = 4:8. This was called “discontinuous proportion.” For example, a dog (A) is smaller than a man (B) like a horse (C)is smaller than an elephant (D). The next three-dot layer related to “continuous proportion,” which involved three items: A is to B as B is to C; 1:3 = 3:9. For example our dog (A) is related in size to a man (B) as the man (B) is related to the horse (C).

But the most sacred proportion involved two items, thereby drawing us back toward primal unity at the top of the Tetractys. This was called the golden proportion: A is to B as B is to A+B. In Vitruvian Man, the length of his hand (A) relates in size to his forearm (B) in the same way that his forearm (B) relates in size to the length of the entire arm, with forearm and hand combined (A+B). This is the golden proportion, and it can also be found the relationship between the fingers the palm as related to the entire hand and in the divisions of the leg and foot.

Leonardo then related these measurements to other parts of the figure. Notice how he conveniently shows us the man’s left foot in profile. He even places the heel in front of the big toe of the right foot so that we can see the full length. The length of the foot is the same as the length of the forearm, and the length of the hand is the measurement of the face, from the chin to the hairline. The face in turn is divided into thirds, which coincide with the eyebrows and the tip of the nose and is echoed in the length of the ears. However, the most important illustration of the golden portion is the division of the body at the navel. If we divide the figure at the navel into its two unequal parts, we find that the height of the first shorter part, from the top of the head to the navel (A), relates to the longer distance from the navel to the feet (B) in the same way that this length, from the navel to the feet (B), relates to the entire height of the figure (A+B).

If we divide the square in half we will find that the middle falls right at the line drawn through the groin. At the level of sexuality, we are centered in the physical. To find the center of the circle, the spiritual center, we have to move up to the navel, which is the place where we were connected to our mothers at birth, and now we see that it is also the golden division. To Renaissance philosophers, these insights offered further proof that all humans contain a divine spark and that even out physical bodies are based on divine proportions.