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De divina proportione

De divina proportione
Title page of De divina proportione
Title page of 1509 edition
Author Luca Pacioli
Illustrator Leonardo da Vinci
Country Republic of Venice
Language Italian
Subject Geometry, Architecture
Publisher Paganini (Venice)
Publication date
1509

De divina proportione (On the Divine Proportion) 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 (the title refers to the golden ratio) and their applications to geometry, visual art through perspective, and 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.

The book consists of three separate manuscripts, which Pacioli worked on between 1496 and 1498.

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. 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.

The second part, Trattato dell'architettura (Treatise on Architecture), discusses the ideas of Vitruvius (from his De architectura) on the application of mathematics to architecture in twenty chapters. The text compares the proportions of the human body to those of artificial structures, with examples from classical Greco-Roman architecture.


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