Étiquette : Vitruvius
By Karel Vereycken, Paris, France.
No visitor of Florence can miss the gilded bronze reliefs decorating the Porta del Paradiso (Gates of Paradise), the main gate of the Baptistery of Florence right in front of the Cathedral of Santa Maria del Fiore surmounted by Filippo Brunelleschi’s splendid cupola.
In this article, Karel Vereycken sheds new light on the contribution of Arab science and Ghiberti’s crucial role in giving birth to the Renaissance.
The Baptistery, erected on what most Florentines thought to be a Roman temple dedicated to the Roman God of Mars, is one of the oldest buildings in the city, constructed between 1059 and 1128 in the Florentine Romanesque style. The Italian poet Dante Alighieri and many other notable Renaissance figures, including members of the Medici family, were baptized in this baptistery.
During the Renaissance, in Florence, corporations and guilds competed for the leading role with artistic creations each one even more prestigious than the other.
While the Arte dei Lana (corporation of wool producers) financed the Works (Opera) of the Duomo and the construction of its cupola, the Arte dei Mercantoni di Calimala (the guild of the merchants dealing in foreign cloth, and exporting cloth), took care of the Baptistery and financed the embellishment of its doors.
The Gates of Paradise
The octagonal building has four entrances (East, West, North and South) of which only three (South, North and East) have sets of artistically important bronze doors with relief sculptures. Three dates are key : 1329, 1401 and 1424.
- In 1329, the Calimala, as recommended by Giotto, ordered Andrea Pisano (1290-1348) to decorate a first set of doors (initialy installed as the East door, i.e. seen when one leaves the Cathedral, but today South). These consist of 28 quatrefoil (clover-shaped) panels, with the 20 top panels depicting scenes from the life of St. John the Baptist (the patron of the edifice). The 8 lower panels depict the eight virtues of hope, faith, charity, humility, fortitude, temperance, justice, and prudence, praised by Plato in his Republic and represented during the XVIth century by the Flemish humanist painter and reader of Petrarch, Peter Brueghel the Elder. Construction took 8 years, from 1330 till 1338.
- In 1401, after having narrowly won the selection contest against Brunelleschi, the 23 year old and inexperienced young goldsmith Lorenzo Ghiberti (1378-1455), is commissioned by the Calima to decorate the doors today in the Northern gate. Ghiberti casted the bronze high reliefs using a method known as « lost-wax casting« , a technique that he had to reinvent entirely since lost since the fall of the Roman Empire. One of the reasons Ghiberti won the contest, was the mere fact that his technique was so advanced that it required 20 % less (7 kg per panel) of metal then that of his competitors, bronze being an onerous material, far more costly than marble. His technique, applied to the entire decoration of the Northern gate, as compated to his competitor, would have saved some estimated 100 kg of bronze. And since in 1401, with the plague regularly hitting Florence, economic conditions were poor, even the wealthy Calima looked at the total costs of the program.
The bronze doors comprise 28 panels, with 20 panels depicting the life of Christ from the New Testament. The 8 lower panels show the four evangelists and the Church Fathers Saint Ambrose, Saint Jerome, Saint Gregory, and Saint Augustine. It took 24 years of construction.
- In 1424, Ghiberti, then at age 46, was given—unusually, with no competition—the task of also creating the East gate. Only in 1452 did Ghiberti, at that time seventy years old, installed the last bronze panels, since construction lasted this time 27 years ! According to Giorgio Vasari (1511-1574), Michelangelo Buonarroti (1475-1564) later judged them « so beautiful they would grace the entrance to Paradise ».
Over two generations, a bevy of well paid assistants and pupils were trained by Ghiberti, including exceptional artists, such as Luca della Robbia, Donatello, Michelozzo, Benozzo Gozzoli, Bernardo Cennini, Paolo Uccello, Andrea del Verrocchio and Ghiberti’s sons, Vittore and Tommaso. And over time, the seventeen-foot-tall, three-ton bronze doors became an icon of Renaissance, one of the most famous works of art in the world.
In 1880, the French sculptor Auguste Rodin was inspired by it for his own Gates of Hell on which he worked for 38 year
Of utmost interest for our discussion here, the dramatic shift of conception and design of the bronze relief sculptures that occurred between the Northern and the Eastern Gates, because it reflects how bot the artist as well as his patrons used the occasion to share to a broad public their newest ideas, inventions and exciting discoveries.
The themes of the northern gate of 1401 were inspired by scenes from the New Testament, excluding de facto the panel made by Ghiberti, « The Sacrifice of Isaac », which had won him the selection competition the same year. To complete the ensemble, it was therefore only logical that the eastern door of 1424 would take up the themes of the Old Testament.
Originally, it was the scholar and former chancellor of Florence Leonardo Bruni (1369-1444) who planned an iconography quite similar to the two previous doors. Hence, after heated discussions, his proposal was rejected for something radically new. Instead of realizing 28 panels, it was decided, for aesthetic reasons, to reduce the number of panels to only 10 much larger square reliefs, between borders containing statuettes in niches and medallions with busts.
Hence, each of the 10 chapters of the Old Testament, so to speak, contains several events, so that the net number of scenes has risen from 20 to 37, and on top, all appear in perspective :
- Adam and Eve,
- Cain and Abel,
- Jacob and Esaü,
- David, and
- Solomon and Sheba.
The general theme is that of salvation based on Latin and Greek patristic tradition. After the first three panels, focusing on the theme of sin, Ghiberti began to highlight more clearly the role of God’s saving and the foreshadowing of Christ’s coming. Later panels are easier to understand. One example is the Isaac panel, where the figures are merged with the surrounding landscape so that the eye is led toward the main scene represented in the top right.
Many of the sources for these scenes were written in ancient Greek, and since knowledge of Greek at that time was not so common, it appears that Ghiberti’s “theological advisor” was Ambrogio Traversari (1386-1439), with whom he had many exchanges. Traversari was a close friend of Nicolas of Cusa (1401-1464), a protector of Piero della Francesca (1412-1492) and a key organizer of the Ecumenical Council of Florence of 1438-1439, which attempted to put an end to the schism separating the Church of the East from that of the West.
The bronze reliefs, known for their vivid illusion of deep space in relief, are one of the revolutionary events that epitomize the Renaissance. In the foreground are figures in high relief, which gradually become less protruding exploiting the full illusionistic potential of the stiacciato technique later brought to its high point by Donatello. Using this form of “inbetweenness”, they integrate in one single image, what appears both as a painting, a low relief as well as a high relief. Or maybe one has to look at it the other way: these are flat images traveling gradually from a surface into the full three dimensions of life, just as Ghiberti, in one of the first self-portraits of art history, reaches his head like out of a bronze medal to look down on the viewers. The artist desired much more than perspective, he wanted breathing space !
This new approach will influence Leonardo Da Vinci (1452-1517). As art historian Daniel Arasse points out :
While many thoughts about perspective existed much earlier, it was in 1435 that the humanist architect Leon Baptista Alberti (1406-1472), in his treaty Della Pictura, outlined a mathematical theory of the representation of three-dimensional harmonious and unified space on a flat surface. Noteworthy, the fact that Alberti’s treaty doesn’t contain or discusses any visual scheme or diagram.
Seven years earlier, the painter Massacchio (1401-1428) had used, at least in part, such a construction in his fresco painting The Trinity. And even before, Brunelleschi had conducted several experiments on this question, most likely based on the ideas presented by another friend of Cusa, the Italian astronomer Paolo dal Pozzo Toscanelli (1397-1482), in the latter’s now lost treaty Della Perspective.
However, Leonardo, who read and studied Ghiberti’s writings on, would use the latter’s arguments to indicate the limits and even demonstrate the dysfunctionality of Alberti’s “perfect” perspective construction especially when one goes beyond a 30 degres angle.
In the Codex Madrid, II, 15 v. da Vinci realizes that « as such, the perspective offered by a rectilinear wall is false unless it is corrected (…) ».
Perspectiva artificialis versus perspectiva naturalis
Alberti’s “perspectiva articifialis” is nothing but an abstraction, necessary and useful to represent a rational organization of space. Without this abstraction, it is fairly impossible to define with mathematical precision the relationships between the appearance of objects and the receding of their various proportions on a flat screen: width, height and depth.
From the moment that a given image on a flat screen was thought about as the intersection of a plane cutting a cone or pyramid, a method emerged for what was mistakenly considered as an “objective” representation of “real” three dimensional space, while it is nothing but an “anamorphosis”, i.e. a tromp-l’oeil or visual illusion.
What has to be underscored, is that this construction does away with the physical reality of human existence since based on the abstraction pretending,
- that man is a single eyed cyclopes;
- that vision emanates from one single point, the apex of the visual pyramid;
- that they eye is immobile;
- that the image is projected on a flat screen rather than on a curved retina.
Slanders and gossip
The crucial role of Ghiberti, an artist which “Ghiberti expert” Richard Krautheimer mistakenly presents as a follower of Alberti’s perspectiva artificialis, has been either ignored or downplayed.
Ghiberti’s unique book, the three volumes of the Commentarii, which also include his autobiography and established him as the first modern historian of the fine arts, are not even translated into English or French and were only published in Italian in 1998.
Today, for his attention to minute detail and figures with wavy and elegant lines, as well as the variety of plants and animals depicted, Ghiberti is generally presented as “Gothic-minded”, and therefore “not really” a Renaissance artist!
Giorgio Vasari, often acting as the paid PR man of the Medici clan, slanders Ghiberti saying he, like lacking any value, wrote « a work in the vernacular in which he treated many different topics but arranged them in such a fashion that little can be gained from reading it. »
Admittedly, tension among humanists, were not uncommon. Self-educated craftsmen, such as Ghiberti and Brunelleschi on the one side, and heirs of wealthy wool merchants, such as Niccoli on the other side, came from entirely different worlds. For example, according to a story told by Guarino Veronese, in 1413, Niccolo greeted Filippo haughtily, « O philosopher without books, » to which Filippo replied with his legendary irony, « O books without philosopher ».
Sure, the Commentarii, are not written according to the rhetorical rules of those days. Written at the end of his life, they even might have been simply dictated by an aging Ghiberti to a poorly trained clerk making dozens of spelling errors.
But they do reveal a highly educated author and a thinker having profound knowledge of many classical Greek and Arab thinkers. Ghiberti was not just some brilliant handcraft artisan but a typical “Renaissance man”. In dialogue with Bruni, Traversari and the “manuscript hunter” Niccolo Niccoli, Ghiberti, who couldn’t read Greek but definitely knew Latin, was clearly familiar with the rediscovery of Greek and Arab science, a task undertaken by Boccaccio’s and Salutati’s “San Spirito Circle” whose guests (including Bruni, Traversari, Cusa, Niccoli, Cosimo di Medici, etc.) later would convene every week at the Santa Maria degli Angeli convent.
First, Ghiberti makes a bold and daring statement, for a Christian man in a Christian world, about how the art of antiquity came to be lost:
Ghiberti understood the importance of multidisciplinarity for artists. According to him, “sculpture and painting are sciences of several disciplines nourished by different teachings”.
The 10 disciplines that he considered important to train artists were grammar, philosophy, history, followed by perspective, geometry, drawing, astronomy, arithmetic, medicine and anatomy.
Now, any serious scholar, having worked through Leonardo’s « Notebooks », who then reads Ghiberti’s I Commentarii, immediately realizes that most of Da Vinci’s writings were basically comments, questions and contributions about things said or issues raised by Ghiberti, especially respecting the nature of light and optics in general. Leonardo’s creative mindset was a direct outgrowth of Ghiberti’s challenging world outlook.
The Composition of the eye
In Commentario 3, 6, which deals with optics, vision and perspective, Ghiberti, opposing those for whom vision can only by explained by a purely mathematical abstraction, writes that “In order that no doubt remains in the things that follow, it is necessary to consider the composition of the eye, because without this one cannot know anything about the way of seeing.” He then says, that those writing about perspective don’t take into account “the eye’s composition”, because too many authors contradict each other.
Ghiberti regrets that despite the fact that many “natural philosophers” such as Thales, Democritus, Anaxagoras, Xenophane and the others determined to take care of human health such as “Hippocrates, Galen and Avicenna” have written about things of nature, so many things remain unclear.
Indeed, he says, “speaking about this matter is obscure and not understood, if one does not have recourse to the laws of nature, because more fully and more copiously they demonstrate this matter.”
Avicenna, Alhazen and Constantine
Therefore, says Ghiberti:
This is quite a statement ! Here we have a, or rather “the”, leading, founding figure or the Italian and European Renaissance and its great contribution of perspective, saying that to get any idea about how vision functions, one has to study three Arab scientists: Ibn Sina, Ibn al Haytham an Qusta ibn Luqa ! Cultural eurocentrism might be one reason why Ghiberti’s writings were kept in the dark.
Ibn al-Haytham (Alhazen) made important contributions to ophthalmology and improved upon earlier conceptions of the processes involved in vision and visual perception in his Treatise on Optics (1021), which is known in Europe as the Opticae Thesaurus. Following his work on the camera oscura (darkroom) he was also the first to imagine that the retina (a curved surface), and not the pupil (a point) could be involved in the process of image formation.
Avicenna, in the Canon of Medicine (ca. 1025), describes sight and uses the word retina (from the Latin word rete meaning network) to designate the organ of vision.
Later, in his Colliget (medical encyclopedia), Averroes (1126-1198) was the first to attribute to the retina the properties of a photoreceptor.
If Avicenna’s writings on anatomy and medical science were translated and circulating in Europe since the XIIIth century, Al Hazen’s treatise on optics, which Ghiberti quotes extensively, had been recently translated in Italian under the title De li Aspecti.
It is now recognized that Andrea del Verrocchio, whose best known pupil was Leonardo da Vinci (1452-1517) was himself one of Ghiberti’s pupils. Unlike Ghiberti, who mastered Latin, neither Verrocchio nor Leonardo mastered a foreign language.
What is known is that while studying Ghiberti’s Commentarii, Leonardo had access in Italian to a series of original quotations from the roman architect Vitruvius and from Arab scientists such as Avicenna, Alhazen, Averroes and those European scientists having studied Arab optics, notably the Oxford Fransciscans Roger Bacon (1214-1294), John Pecham (1230-1292) and the Polish monk working in Padua, Erazmus Ciolek Witelo (1230-1275), known by his Latin name Vitellion.
As stressed by Pr. Dominque Raynaud, Vitellion introduces the principle of binocular vision by geometric considerations.
He gives a figure where we see the two eyes (a, b) receiving the images of points located at equal distance from the hd axis.
He explains that the images received by the eyes are different, since, taken from the same side, the angle grf is larger than the angle gtf. It is thus necessary that these images are joined in only one (Figure). Where does this junction occur? Witelo says: « The two forms, which penetrate in two homologous points of the surface of the two eyes, arrive at the same point of the concavity of the common nerve, and are superimposed in this point
point to become one ».
The fusion of the images is thus a product of the internal nervous activity.
The great astronomer Johannes Kepler (1571-1630) will use Alhazen’s and Witelo’s discoveries to develop his own contribution to optics and perspective. “Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena (1604), “henceforth the representations of objects should be considered as paintings that are actually projected on paper or some other screen.” Kepler was the first to observe that our retina captures an image in an inverted form before our brain turns it right side up.
Out of this, Ghiberti, Uccello and also the Flemish painter Jan Van Eyck, in contact with the Italians, will construct, as an alternative to one cyclopic single eye perspective, revolutionary forms of “binocular” perspective while Leonardo and Louis XIth court painter Jean Fouquet will attempt to develop curvilinear and spherical space representations.
In China, eventually influenced by Arab optical science breakthrough’s, forms of non-linear perspective, that integrate the mobility of the eye, will also make their appearance during the Song Dynasty in China.
Ghiberti will ad another dimension to perspective: light. One major contribution of Alhazen was his affirmation, in his Book of Optics, that opaque objects struck with light become luminous bodies themselves and can radiate secondary light, a theory that Leonardo will exploit in his paintings, including in his portraits.
Already Ghiberti, in the way he treats the subject of Isaac, Jacob and Esau (Figure), gives us an astonishing demonstration of how one can exploit that physical principle theorized by Alhazen. The light reflected by the bronze panel, will strongly differ according to the angle of incidence of the arriving rays of light. Arriving either from the left of from the right side, in both cases, the Ghiberti’s bronze relief has been modeled in such a way that it magnificently strengthens the overall depth effect !
While the experts, especially the neo-Kantians such as Erwin Panofsky or Hans Belting, say that these painters were “primitives” because applying the “wrong” perspective model, they can’t grasp the fact that they were in reality exploring a far “higher domain” than the mere pure mathematical abstraction promoted by the Newton-Galileo cult that became the modern priesthood currently ruling over “science”.
If much more about all of this can and should be said, today, the best way to pay off the European debt to “Arab” scientific contributions, is to reward not just the Arab world but all future generations with a better future by opening them the “Gates of Paradise”.
Watch all of Ghiberti’s works on the WEB GALLERY OF ART
- Arasse, Daniel, Léonard de Vinci, Hazan, 2011;
- Avery, Charles, La Sculpture florentine de la Renaissance, Livre de poche, 1996, Paris.
- Belting, Hans, Florence & Baghdad, Renaissance art and Arab science, Harvard University Press, 2011.
- Borso, Franco et Stefano, Uccello, Hazan, Paris, 2004 ;
- Butterfield, Andrew, Verrocchio, Sculptor and painter of Renaissance Florence, National Gallery, Princeton University Press, 2020 ;
- Butterfield, Andrew, Art and Innovation in Ghiberti’s Gates of Paradise, High Museum of Art, Yale University Press, 2007;
- Kepler, Johannes, Paralipomènes à Vitellion, 1604, Vrin, 1980, Paris;
- Krautheimer, Richard and Trude, Lorenzo Ghiberti, Princeton University Press, New Jersey, 1990.
- Martens, Maximiliaan, La révolution optique de Jan van Eyck, dans Van Eyck, Une révolution optique, Hannibal – MSK Gent, 2020.
- Pope-Hennessy, John, Donatello, Abbeville Press, 1993 ;
- Radke, Gary M., Lorenzo Ghiberti: Master Collaborator
- Rashed, Roshi, Geometric Optics, in History of Arab Sciences, edited by Roshdi Rashed, Vol. 2, Mathematics and physics, Seuil, Paris, 1997.
- Raynaud, Dominique, L’hypothèse d’Oxford, essai sur les origines de la perspective, PUF, 1998, Paris.
- Raynaud, Dominique, Ibn al-Haytham on binocular vision: a precursor of physiological optics, Arabic Sciences and Philosophy, Cambridge University Press (CUP), 2003, 13, pp. 79-99.
- Raynaud, Dominique, Perspective curviligne et vision binoculaire. Sciences et techniques en perspective, Université de Nantes, Equipe de recherche: Sciences, Techniques, et Sociétés, 1998, 2 (1), pp.3-23.;
- Vereycken, Karel, interview with People’s Daily: Leonardo Da Vinci’s « Mona Lisa » resonates with time and space with traditional Chinese painting, 2019.
- Vereycken, Karel, Uccello, Donatello, Verrocchio and the art of military command, 2022.
- Vereycken, Karel, The Invention of Perspective, Fidelio, 1998.
- Vereycken, Karel, Van Eyck, un peintre flamand dans l’optique arabe, 1998.
- Vereycken, Karel, Mutazilism and Arab astronomy, two bright stars in our firmament, 2021.
- Walker, Paul Robert, The Feud That Sparked the Renaissance, How Brunelleschi and Ghiberti changed the World, HarperCollins, 2002.
By Karel Vereycken
Leonardo da Vinci’s « Viruvian Man ». Since we’re commemorating this year (2020) Leonardo Da Vinci, who died 500 years ago, many silly things are presented by fake scholars trying to make a real living.
Since I was introduced into the canon of proportions of the human body during my training as a professional painter and engraver, I want offer you some hints on how to look at what is called Da Vinci’s « Vitruvian man », a drawing currently on exhibit at the Da Vinci show at the Louvre in Paris.
Hence, as Leonardo underlines himself in his notebooks, adopting Cusanus wordings, it is only with the « eyes of the mind » that art becomes visible, because the « eyes of the flesh » are intrensically blind to it.
Canons of proportions
Europe, and Classical Greece, as everybody should know, emerged largely by absorbing several major discoveries accomplished much earlier by other civilizations. Much of it came from Asia, but African and especially Egypt, were key.
The very practice of mummification, a process which takes at least 60 days of work, made Egypt the key area of anatomical research.
As demonstrated by early Egyptian sculpture, the exact size of the entire adult human body is 7,5 times the size of the head. The size of a newborn is only four heads, that of a seven year old, six heads and that of a 17 years old adolescent, 7 heads.
If one subdivides the overall 7.5 proportion, for an adult, from the top of the head till the lowest part of the torso, one measures four heads, one till the nipples, one till the belly button and a fourth one till the lowest part of the pubis. Going up from the sole till the middle of the pelvis, one measures 3.5 heads: 2 heads till the knee and 1.5 till the middle of the pelvis. That brings the total till 7.5 heads for the entire length of the adult human body and it is proportional in the sense that people with smaller heads also have small bodies.
Polikleitos versus Lysippus
In the Vth Century BC, the Greek sculptor Polikleitos’ spear bearer (The “Doryphoros”) of Naples National Archeological Museum applied this most beautiful canon of proportions, known as the “Polikleitos canon”.
During the Renaissance, the nostalgics of the Roman Empire preferred another Greek canon, that of Greek sculptor Lysippus (4th Century BC), formalized by the Roman author, architect and civil engineer, Vitrivius (1st century BC).
Vitruvius only transcribed the prevalent taste of his epoch. Roman sculptors, in order to give an athletic and heroic look to the Emperors which they were portraying, adopting the canon of Lysippus, could reduce the head of their models to only an eight of the total length of the body. The trick was that by reducing the relative size of the head, the body looked more preeminent and powerful, something most emperors, who were often physical failures, appreciated and secured their popularity. Even extreme cases of 12 to 15 heads of body length appeared. In short, Public relations ruled at the detriment of science and truth.
Today’s comic strip drawers chose proportions according to purpose:
–For real life, 7.5 or “normal canon”
–For a movie star, 8 heads, with the “idealistic canon”;
–For a fashion magazine: 8.5 heads;
–For a comic book hero: 9 heads for the “heroic canon”
Text accompanying Leonardo DaVinci’s Vitruvian Man:
Vitruvius, the architect, says in his work on architecture that the measurements of the human body are distributed by Nature as follows that is that 4 fingers make 1 palm, and 4 palms make 1 foot, 6 palms make 1 cubit; 4 cubits make a man’s height. And 4 cubits make one pace and 24 palms make a man; and these measures he 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 centre of the outspread limbs will be in the navel and the space between the legs will be an equilateral triangle.
The length of a man’s outspread arms is equal to his height.
From the roots of the hair to the bottom of the chin is the tenth of a man’s height; from the bottom of the chin to the top of his head is one eighth of his height; from the top of the breast to the top of his head will be one sixth of a man. From the top of the breast to the roots of the hair will be the seventh part of the whole man. From the nipples to the top of the head will be the fourth part of a man. The greatest width of the shoulders contains in itself the fourth part of the man. From the elbow to the tip of the hand will be the fifth part of a man; and from the elbow to the angle of the armpit will be the eighth part of the man. The whole hand will be the tenth part of the man; the beginning of the genitals marks the middle of the man. The foot is the seventh part of the man. From the sole of the foot to below the knee will be the fourth part of the man. From below the knee to the beginning of the genitals will be the fourth part of the man. 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.
Of course, Da Vinci’s exploration of the Vitruvian man doesn’t mean he approves or disapproves the stated fakery in proportions.
Soul or muscle?
It should be known that in Italy, the pure Roman taste has become trendy again following the discovery in 1506 of the statue of the Laocoon on the site of Nero’s villa in Rome. From that moment, artist will feel obliged to increase the volume of the muscular masses in order to appear as working « in Antique style ».
Although Leonardo never openly criticized this trend, it is hard not to think of Michelangelo’s frescoes in the Sistine Chapel, when the artist, seeking to raise the spirit to unequalled philosophical heights, advised painters: « do not give all the muscles of the figures an exaggerated volume » and « if you act differently, it is more a sort of representation of a sack of nuts that you will have achieved than to that of a human figure » (Codex Madrid II, 128r).
No doubt inspired by his friend, the architect Giacomo Andrea, in « The Vitruvian Man », Leonardo is above all interested by other harmonies: if a person extends his arms in a direction parallel to the ground, one obtains the same length as one’s entire height. This equality is inscribed by Leonardo in a square (symbol of the earthly realm). But if one stretches his arms and legs in a star shape, they are inscribed in a circle whose center is the navel. The location of the navel divides the body according to the golden ratio (in this example 5 heads out of a total of 8 heads, 5+3 being part of the Fibonnacci series: 1+2 = 3; 3+2 = 5; 5+3 = 8; 8+5 = 13; 13+8 = 21, etc.).
Leonardo clearly understood what the golden section really means: not a “magical” number in itself, but the reflexion of the dynamic of least action, the very principle uniting man (the square) with the creator and the universe (the circle).
So if you take a look, beware of what you see and especially what you don’t !