Since Burghardt’s “The Civilization of the Renaissance in Italy” (1860), Leonardo da Vinci has been praised by the public as a “uomo universale” during the Renaissance, together with Alberti. For this reason, Leonardo has been mentioned as an artist embodying Western civilization on various subjects not only by art historians but also by researchers in other fields.
Leonardo’s research has been regarded as an extremely difficult field because of the large number of papers and the existence of research books in various languages. The author also thought that Leonardo’s study was fascinating, but before tackling it, it was too difficult for the author to do.
The author, who was fascinated by Leonardo’s paintings and drawings and studied oil painting, read almost all Japanese books about Leonardo during his undergraduate years, and among them, there was Leonardo’s “Vitruvian Man”, which is housed in the Accademia Gallery in Venice. However there was no specific discussion about “circle” and “square” of Leonardo’s “Vitruvian Man”, and there was no translation of Leonardo’s description above and below the figure. At that time, the only thing the author knew about it was that it was based on the description of “De Architectura” written by the ancient Roman architect Vitruvius, and showed the musical harmony proportion of well-proportioned body.
This view has already been prepared in the “norm of body” (κανον) of the ancient Greek sculpture, and the body beauty called “Kalokagatia” (καλοκαγαθια) in ancient Greece is described as being based on the musical harmony proportion of well-proportioned body. This proportion has been associated with the golden ratio, as the navel position of ancient Greek sculptures is commonly referred to the golden ratio of height. However it was widely spread after Zeizing used golden ratio to show the proportions of the body parts of the Greek sculpture in the mid-nineteenth century and it has been thought that there is no material of musical proportionality that conveys the literal description of classical antiquity, other than the description of Vitruvian Man.
What is commonly called musical harmony is the relationship found by the ancient Greek mathematician Pythagoras between the pitch (Sol-fa syllables) and the length of the chord of a monochord or lyre. The so-called Pythagorean scale of Weatern music is a module in which the length of a string is divided into 12 equal parts, and each pitch is the basis of music in which each pitch is determined by the number of modules. Anyone who has learned the guitar or string instrument knows well that the length of a string of 6 units is 12 to 6 with respect to an open string, and the string length is halved, resulting in a pitch one octave higher.
However, the reason why it is difficult to understand this abruptly is that, as with the frets that hold down the strings of a guitar, the intervals gradually decrease from the lower notes to the higher notes. On the other hand, musical harmonic proportion, which captures the length of a string by a simple integer ratio, was shown by Rudolf Wittkower in “Architectural Principals in the age of Humanism” as an architectural theory of the Italian Renaissance beginning with Alberti. It has been regarded as the design principle of ancient Greek temple architecture, which was introduced in Vitruvius’ “De Architectura”.
Leonardo’s theory of proportionality of the human body, which the author considered, used the “Symmetrical Law” in Chapter 3 of “De Architectura” and was derived by solving “circle” and “square” which encircle “Vitruvian Man” and the author found that this human body was drawn by geometric progression of golden ratio.
The author took the first folio of Codex Huygens as the basis for the geometric progression of the golden ratio found in the standard line of proportion of Leonardo’s “Vitruvian Man”. As the result a hypothesis is made that Codex Huygens is a copy of lost “Sforza’s theory of painting”. This is because the author can confirm “mia principi” that Leonard spoke in plural form according to the author’s proposition “Phiogenesis of Double Square”. In this research the author thought the writing “Eye, (visible) ray, distance” at the beginning of the first folio of Codex Huygens dealt with not only the proportion of the human body but also the drawing of perspective shown in the sketch of the background of “Adoration of the Magi”. The difference of Leonardo’s perspective according to the periods would be expressed including “the Last supper” and “Annunciation” in the periods in which this construction system had not been established yet in Chapter 4 and later.
The author’s “Fiogenesis of Double Square” is none other than Leonardo’s principle, which he said in folio 19118r of Codex Windsor, “A person who is not a mathematician should not read my principle”. In the conclusion, after reviewing, it was shown in the final chapter that this was Leonardo’s own interpretation of the ancient Greek “Symmetrician Law” conveyed by Vitruvius’ “De Architectura”.