Geometrical letter 'S'. 16th-century diagram of a geometrical calligraphic letter 'S', from 'On the Divine Proportion' (1509) by Italian mathematician Luca Pacioli (c.1447-1517). This book was about mathematical proportions such as the 'golden ratio' referred to in the title. The book popularised geometry. It included artworks and diagrams by Leonardo da Vinci, though these artworks of letters of the alphabet were drawn by Pacioli using a ruler and compass to construct letters using squares and circles. These precisely constructed drawings, using Platonic architectural principles, were intended to be used as templates for calligraphy.