In the study of the golden section, Luca Pacioli showed an actual ‘cult’ for proportionality, a religious care for this element of the frame of Creation, admirable synthesis of truth and beauty. Leonardo da Vinci proved that the theory of platonic solids could give birth to marvellous artistic productions. Sixty impressive drawings, commissioned by Luca Pacioli himself to the genius from Vinci, close the manuscript kept in the Ambrosian Library.
The golden section, or golden ratio, can be derived with a number of geometric constructions, each of which divides a line at the unique point where the ratio of the whole line (A) to the large segment (B) is the same as the ratio of the large segment (B) to the small segment (C); in other words: A is to B as B is to C.
The plates, in a mixed ink and watercolour technique, visualise the regular platonic solids and their possible variations through a game of perspective and colour. The theoretical part of the treatise needed to be illustrated by examples that only a good artistic hand, well-skilled in perspective, could draw. The meeting between Luca and Leonardo, the mathematician and the artists, was therefore providential.
Ancient mathematicians were fascinated by this interesting ratio, that seemed to contain a spark of divine perfection and harmony, and called this proportion ‘divine’.
Not only do we find the golden section in mathematics and geometry, but obviously also in architecture and engineering, in music, in cartography and grammar, in law and in poetry, in painting and perspective, up to philosophy and cosmology. This very connection between the geometrical-mathematical perfection flowing from the golden section and creation is the legacy Luca Pacioli receives from the traditional philosophical thought, rooted in classical philosophers.
Marco Navoni, The Divine Perfection Code. Milan: Ambrosian Library, p. 1, 2.
Artwork by Leonardo da Vinci, Esaedro tagliato vuoto.