De divina proportione

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The first printed illustration of a rhombicuboctahedron, by Leonardo da Vinci, from De divina proportione.
Letter M from De divina proportione
Woodcut from De divina proportione illustrating proportions of the human face.

De Divina Proportione (About the divine proportions) is a book on mathematics written by Luca Pacioli around 1497 in Milan and first printed in 1509. Today only two versions of the original manuscript are believed still to exist. The subject was mathematical and artistic proportions, and the book was illustrated by Leonardo da Vinci.

The Book[edit]

The book consists of three individual manuscripts,[1] which Pacioli worked on between 1496 and 1498.

The first part, Compendio Divina Proportione, studies and describes the Golden ratio from a mathematical point of view and also studies polygons.[1][2] The work also discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì, and Marco Palmezzano.

The second part discusses the ideas of Vitruvius on the application of mathematics in architecture.

The third part, Libellus in tres partiales tractatus divisus, is mainly an Italian translation of Piero della Francesca's Latin writings On [the] Five Regular Solids ("De quinque corporibus regularibus")[1] and mathematical examples.[2]

The book contains illustrations in woodcut after drawings by Leonardo da Vinci.[3] Leonardo drew the illustrations of the regular solids while he lived with and took mathematics lessons from Pacioli. Leonardo's drawings are probably the first illustrations of skeletonic solids which allowed an easy distinction between front and back.


On June 1 1509[3] the first printed edition was released in Venice by Paganinus de Paganinus. The clarity of both the written material and Leonardo's diagrams gave the book a popularity beyond mathematical circles.[4] The book has since then been reprinted several times.

Today two surviving manuscripts exist, one at the Biblioteca Ambrosiana in Milan and the second at the Bibliothèque de Genève in Geneva.

The book was displayed under an exhibition in Milan between October 2005 until October 2006 together with the Codex Atlanticus.[5]

The "M" logo used by the Metropolitan Museum of Art in New York City is adapted from one in De divina proportione.[6]


  1. ^ a b c [1], School of Mathematics and Statistics, University of St Andrews
  2. ^ a b [2], Académie de Poitiers
  3. ^ a b [3], The Metropolitan Museum of Art, New York
  4. ^ [4], University of British Columbia
  5. ^ The Virtual Codex Atlanticus, Leonardo3, retrieved 2014-09-22.
  6. ^ [5], The Met Store (Metropolitan Museum of Art shopping catalog), "Renaissance 'M' Bookmark"

External links[edit]