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The pen and ink drawing by Leonardo da Vinci, depicting a man fitting his body to a circle and a square by
adjusting the position of his arms and legs, is probably the most famous drawing in the world - judging by the fact that I
see it in advertisements and worked into logos for holistic health centers and it is even the wallpaper design for my Windows
main page. However, few people know its name or the secrets that it contains. It is called Vitruvian Man.
Vitruvius was an ancient Roman architect who wrote a series of ten books on architecture - 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,
he states that these 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 the philosophy of Pythagoras seized the imagination of the Renaissance. 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. 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 of correspondences.
The one criticism I have of Tarot decks in general, modern or other, is that at times they lack beauty. Sometimes the creators
make the same mistake as Cesariano and try to make reality fit their ideas instead of discovering them in reality. This is
not to say that there is no underlying wisdom in their assertions, but only that at times their solutions are less than satisfactory.
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. I would like to discuss this further and show how this relates to the Tarot.
Some of you will be asking yourself, why was it so important to the Renaissance artists and philosophers that
a human body could fit into a circle and a square? Some of you probably know the answer, but I will go into it for the benefit
of those who do not.
The ideas that Vitruvius was expressing can be traced back to Pythagoras. Pythagoras lived in a Greek colony
in Southern Italy in the 6th century, BCE, the same time that Buddha lived. Like Buddha, Pythagoras taught his male and female
disciples that life is an endless wheel of reincarnations until we purify ourselves and return to our divine source.
Purification included a vegetarian diet, moral behavior, 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; yet, he is one of a handful of people that were instrumental in creating
Western culture. It is theorized that if he did write anything it would have been poetry and he would have signed it Orpheus.
Orpheus, the mythical, semi-divine musician, was the founder of the first mystery cult, a religion based on
a secret redemptive ritual. This religion is believed to be a major source for the Pythagorean teachings. Many of its followers
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, is born of the incestuous union of Zeus and Persephone.
Zeus' wife, Hera, is jealous and wishes to destroy the child. To accomplish this she has her allies, the Titans, dismember
and devour him. Of course, Zeus is heart broken and in a fit of anger, he burns the Titans to ash with a volley of lightning
bolts. Only Dionysus's heart remained, and from this, Zeus creates 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.
The Orphics, like Pythagoras, saw a connection between music and numerical order. This type of reasoning lead
to sacred geometry. Pythagoras taught that numbers had qualities as well as quantity and that geometric figures were powerful
magical symbols. The circle, being connected to the sky and the cosmos was a symbol of Dionysus, the soul.
The square is the natural way that humans relate to the physical world. This is why there are four directions,
four seasons, and four 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 was a symbol of the Titanic human 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. Many of these
teachings were incorporated into alchemy, and other ancient disciplines. In this way, the teachings - although at times fragmented
- were passed on to the Renaissance. In Venice around the year 1500, Leonardo once again demonstrated geometrically that the
human soul is divine.
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Vitruvius, De Architectura:
THE PLANNING OF TEMPLES
1. The planning of temples depends upon symmetry: and the method of this architects must diligently apprehend.
It arises from proportion (which in Greek is called analogia). Proportion consists in taking a fixed module, in each case,
both for the parts of a building and for the whole, by which the method of symmetry is put to practice. For without symmetry
and proportion no temple can have a regular plan; that is, it must have an exact proportion worked out after the fashion of
the members of a finely-shaped human body.
2. For Nature has so planned the human body that the face from the chin to the top of the forehead and the
roots of the hair is a tenth part; also the palm of the hand from the wrist to the top of the middle finger
is as much; the head from the chin to the crown, an eighth part; from the top of the breast with the bottom
of the neck to the roots of the hair, a sixth part; from the middle of the breast to the crown, a
fourth part; a third part of the height of the face is from the bottom of the chin to the bottom
of the nostrils; the nose from the bottom of the nostrils to the line between the brows, as much; from that line to the roots
of the hair, the forehead is given as the third part. The foot is a sixth of the height
of the body; the cubit a quarter, the breast also a quarter. The other limbs also have their
own proportionate measurements. And by using these, ancient painters and famous sculptors have attained great and unbounded
distinction.
3. In like fashion the members of temples ought to have dimensions of their several parts answering suitably
to the general sum of their whole magnitude. Now the navel is naturally the exact centre of the body. For
if a man lies on his back with hands and feet outspread, and the centre of a circle is placed on his navel,
his figure and toes will be touched by the circumference. Also a square will be found described within the
figure, in the same way as a round figure is produced. For if we measure from the sole of the foot to the top of the head,
and apply the measure to the outstretched hands, the breadth will be found equal to the height, just like sites which are
squared by rule.
4. Therefore if Nature has planned the human body so that the members correspond in their proportions to its
complete configuration, the ancients seem to have had reason in determining that in the execution of their works they should
observe an exact adjustment of the several members to the general pattern of the plan. Therefore, since in all their works
they handed down orders, they did so especially in building temples, the excellences and the faults of which usually endure
for ages.
Book 3, c. I1 |
Leonardo da Vinci, Vitruvian Man, 1513, dim. 25 x 19.2 cm
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The above passage, from Vitruvius' De Architectura, is a source of inspiration for Leonardo's drawing
in his sketchbook, the famous Vitruvian Man. This passage is also providing the Key of the composition of the ancient architecture,
firmly revived in the Renaissance. The emphasize is on rationalisation of geometry, by means of small whole numbers to build
the composition - in this manner Vitruvius delineates the proportion of a male human body that Leonardo so faithfully reproduced.
Rationalisation as the basic rule of composition and the simplicity of an ingenious design (proportioned by means of small
whole numbers) are often ignored.
Both Leonardo and Vitruvius make no mention of the Phallos as the center of the square, but it plays an important
role. The side of the square is 4 cubits or 24 palms as can also be measured on the ruler beneath the square,
and deduced from the Vitruvius' text. The diagonal of such a square comes close to 34 palms (33.94... exactly). If we rotate
the square around Phallos for 45 degrees we get the upper point of the circle, and from this we can calculate the diameter
of the circle as 29 palms (the difference between the square and the circle is 5 palms).
|
cubit |
foot |
palm |
inch |
finger |
| side of square |
4 |
6 |
24 |
72 |
96 |
| diameter of square |
5.66 |
8.48 |
33.94 |
101.8 |
135.8 |
| diameter of circle |
4.833 |
7.25 |
29 |
87 |
116 |
| circumference of square |
16 |
24 |
96 |
288 |
384 |
| circumference of circle |
15.2 |
22.8 |
91.1 |
273.3 |
364.4 |
| area of square |
16 |
36 |
576 |
5184 |
9216 |
| area of circle |
18.35 |
41.28 |
660.52 |
5944.7 |
10568.3 |
Table of comparative measures derived from square and circle
relation between square and circle
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The two squares, the drawn and the projection square, form an octagram Pell's series are the progressions
that approximate the geometry of proportions originating from the octagram The first of Pell's series is:
1 2 5 12 29 70 169 ... Both main numbers 24 (2x12)
and 29 are members of this series. Leonardo used this progression to rationalise irrational geometry of square root of 2 that
rules the geometry of the octagram. As a proof, all other numbers are derived as a combination of the members of the series.
The distance between the two centers, the navel and Phallos, is according to rationalized geometry 2,5 palms, and it seems
that the position of palms touching the square in Thau formation of the figure equals 9,5 palms, again the measure derived
from rational approximation of the geometry of the octagram by means of Pell series. Also the diagonal of the square is calculated
from the series as 2x(5+12) = 34 palms. The composition founded in octagram is one of the most spread cannons of proportions
in ancient and classical architecture clearly presented by enormous opus of research done by Prof. Tine Kurent of Ljubljana
School of Architecture, Slovenia. Almost every important christian church has dome placed on an octagram, and gematric value
of Greek spelling for Jesus, Ihsous = 888 associates the number 8 (octagram) with Jesus Christ.
Most importantly even Vitruvius mentions the value of the octagon, though in a bit obfuscating manner, while
describing the winds:
| 4. Some have held that there are four winds: the Solanus from the equinoctial
east, the Auster from the south, Favonius from the equinoctial west, and Septentrio from the north. But those who have inquired
more diligently lay down that there are eight: especially indeed Andronicus of Cyrrha, who also, for an example,
built at Athens an octagonal marble tower, and, on the several sides of the octagon, had representations
of the winds carved opposite their several currents.
Book I. c. VI: 4 |
Further on he describes that even the town-planning has to be done according to the octagonal scheme of the
winds. It seems that Leonardo incorporated, in multiple layers, the whole cannon suggested by Vitruvius. It is a strange coincidence
that the area of a square with a side of 24 palms is 576 square palms, which is gematric equivalent of Greek word for the
wind meaning also Spirit, Pneuma = 576.
The calculated area of the circle is 660 square palms, and the difference between the circle and the square
is 660-576=84, which is invoking the gematric value of the master himself:
LEONARDO = 12+5+15+14+1+18+4+15 = 84.
The 'fundamental' measure of 24 palms comes directly from Vitruvius' definition of human height being 4 cubits
or 24 palms. Number 4 is of great importance in the composition of the drawing, emphasized with a square. Number 24 is important
because it is 1x2x3x4 = 24, comprising the multiplied members of the Tetraktys. Vitruvius postulates the smallest module the
division of 10 which also resembles the Tetraktys along with the previously mentioned diagonal of the square, 34 palms long:
(1x2x3x4)+(1+2+3+4) = 34 - the Tetraktys numbers multiplied and added up. Half way between 24 and 34 is the diameter of the
circle, 29 palms: (24+34)/2 = 29.
module 8 & 22/7
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The predominating module of the composition of human body is eight and many lines on the drawing coincide
with the lines of the modular plain. The figure in the form of the letter Thau embraces 22 squares of the
composition, whereas on each half remains 21 or 3 x 7 squares. 22 and 7 are connected through
the rational approximation of p = 22/7.
Number 22 also invokes the total number of Hebrew alefbeth, and numbers 3, 7, and 12 (= 22-3-7) are the numbers
of divisions of Hebrew alefbeth into three groups described in Sepher Yetzirah - The Book of Formation, a fundamental kabbalistic
treatise on the nature of letters and words, suspected to originate from 13th century. The 32 Paths of Wisdom described in
Sepher Yetzirah comprise 10 Sephiroth and 22 Letters. 32 Paths are written in the circumference of the modular square 8x4
= 32. The figure is positioned in the shape of T(hau), the 22nd, last letter of alefbeth. The Tetraktys and the kabbalistic
Tree of Life are comparable glyphs, both comprising the ten spheres.
Vitruvius is reporting that the navel is the exact center of the human body. The circle on Leonardo's drawing
has it's center in the navel, but if the figure is 'squared' the center becomes the phallos which is, concerning this drawing
from the compositional point of view, more important, since it is the center of the underlying geometry that outlines the
basic features of the figure.
The most fundamental composition consists of a circle, a square, and a triangle, a sigillum known to magicians
and alchemist, sometimes called the Universal Seal of Light or the Seal of Hermes. The compositional triangle on this drawing
is concealed, even though that it outlines important segments. It is drawn in the circle within the square and it coincides
with the progression of squares as depicted on the illustration.
progression of squares
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The main proportional lines come from the progression of squares, every second square is half the size of
the original, and the measures thus obtained are the same as described by Vitruvius.
Distinguished is also the triangle with the size of a square and apex in the navel.
It seems that the drawing, or better the original design as explained by Vitruvius, contains many layers of
geometry and symbolism that concord in one single image delineating the proportions of the human body. This idea of 'reason'
governing 'form' was the fundamental theme of the Renaissance and is traceable in best architecture and art in general. It
would not be odd if Leonardo had a close contact with scholars that spread the source of the Renaissance thought which didn't
distinguish between art, science, and magick in terms of conflicting or opposing discourses as is the case today.
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