page_title: Divina proportione
section_title: Compendio divina proportione
hierarchical_section_title: Divina proportione / Contents of the book / Compendio divina proportione
caption_attribution_description: English: Illustration of a human head with its proportions indicated by an equilateral triangle and grid lines. From Luca Pacioli's De Divina Proportione, 1509, page 70
context_page_description: Divina proportione, later also called De divina proportione is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, composed around 1498 in Milan and first printed in 1509. Its subject was mathematical proportions and their applications to geometry, to visual art through perspective, and to architecture. The clarity of the written material and Leonardo's excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images.
context_section_description: The first part, Compendio divina proportione (Compendium on the Divine Proportion), studies the golden ratio from a mathematical perspective (following the relevant work of Euclid) and explores its applications to various arts, in seventy-one chapters. Pacioli points out that golden rectangles can be inscribed by an icosahedron, and in the fifth chapter, gives five reasons why the golden ratio should be referred to as the "Divine Proportion":
  Its value represents divine simplicity.
  Its definition invokes three lengths, symbolizing the Holy Trinity.
  Its irrationality represents God's incomprehensibility.
  Its self-similarity recalls God's omnipresence and invariability.
  Its relation to the dodecahedron, which represents the quintessence
  It also contains a discourse on the regular and semiregular polyhedra, as well as a discussion of the use of geometric perspective by painters such as Piero della Francesca, Melozzo da Forlì and Marco Palmezzano.
caption: Woodcut illustrating proportions of the human face
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