LEONARDO DA VINCI 1452-1519

Luca PACIOLI Sansepolcro, 1447–Sansepolcro, 1517 The Construction of an Icosahedron from Twenty Equilateral triangles Pen and brown ink on vellum Completed in 1498 In 1498, in Milan, Leonardo’s close friend and collaborator Luca Pacioli wrote the Divine Proportion, in which he deals with the Euclidean ‘division of a line in mean and extreme ratio’; this principle, known as the ‘golden section’ since the 19th century, consists of dividing a given line into two parts ( a and b ), in such a way that, a being greater than b , a/b = (a + b)/a. This proportion is used to construct the icosahedron and the dodecahedron – two of the regular polyhedrons consi- dered by Plato, in the Timaeus, to be structural compo- nents of the universe University of Geneva Library, Geneva, Manuscript l. e. 210, fol. 33v–34r Luca PACIOLI Sansepolcro, 1447–Sansepolcro, 1517 The Construction of a Dodecahedron from Twelve Regular Pentagons Pen and brown ink on vellum 1498 In 1498, in Milan, Leonardo’s close friend and collaborator Luca Pacioli wrote the Divine Proportion, in which he deals with the Euclidean ‘division of a line in mean and extreme ratio’; this principle, known as the ‘golden section’ since the 19th century, consists of dividing a given line into two parts ( a and b ), in such a way that, a being greater than b , a/b = (a + b)/a. This proportion is used to construct the icosahedron and the dodecahedron – two of the regular polyhedrons considered by Plato, in the Timaeus, to be structural components of the universe University of Geneva Library, Geneva, Manuscript l. e. 210, fol. 37v–38r 118 119