Divina Proportione

Divina Proportione is based from the original studies from Luca Pacioli. Luca Pacioli was born in 1446 or 1447 in Sansepolcro (Tuscany) where he received an abbaco education. 

Luca Pacioli was born in 1446 or 1447 in Sansepolcro (Tuscany) where he received an abbaco education. [This was education in the vernacular (i.e. the local tongue) rather than Latin and focused on the knowledge required of merchants.] He moved to Venice around 1464 where he continued his own education while working as a tutor to the three sons of a merchant. It was during this period that he

wrote his first book -- a treatise on arithmetic for the three boys he was tutoring. Between 1472 and 1475, he became a Franciscan friar. In 1475, he started teaching in Perugia and wrote a comprehensive abbaco textbook in the vernacular for his students during 1477 and 1478. It is thought that he then started teaching university mathematics (rather than abbaco) and he did so in a number of Italian universities, including Perugia, holding the first chair in mathematics in two of them. He also continued to work as a private abbaco tutor of mathematics and was, in fact, instructed to stop teaching at this level in Sansepolcro in 1491. In 1494, his first book to be printed, Summa de arithmetica, geometria, proportioni et proportionalita, was published in Venice. In 1497, he accepted an invitation from Lodovico Sforza ("Il Moro") to work in Milan. There he met, collaborated with, lived with, and taught mathematics to Leonardo da Vinci. In 1499, Pacioli and Leonardo were forced to flee Milan when Louis XII of France seized the city and drove their patron out. Their paths appear to have finally separated around 1506. Pacioli died aged 70 in 1517, most likely in Sansepolcro where it is thought he had spent much of his final years.

De divina proportione (written in Milan in 1496–98, published in Venice in 1509). Two versions of the original manuscript are extant, one in the Biblioteca Ambrosiana in Milan, the other in the Bibliothèque Publique et Universitaire in Geneva. The subject was mathematical and artistic proportion, especially the mathematics of the golden ratio and its application in architecture. Leonardo da Vinci drew the illustrations of the regular solids in De divina proportione while he lived with and took mathematics lessons from Pacioli. Leonardo's drawings are probably the first illustrations of skeletonic solids, an easy distinction between front and back. The work also discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì, and Marco Palmezzano. As a side note, the "M" logo used by the Metropolitan Museum of Art in New York City is taken from De divina proportione. “ The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilateral square. ” —De divina proportione