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Concept
Divina proportione
Summary
Divina proportione (15th century Italian for Divine proportion), later also called De divina proportione (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 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, 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.
Some of its content was plagiarised from an earlier book by Piero della Francesca, De quinque corporibus regularibus.
The book consists of three separate manuscripts, which Pacioli worked on between 1496 and 1498. He credits Fibonacci as the main source for the mathematics he presents.
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), giving mystical and religious meanings to this ratio, in seventy-one chapters. Pacioli points out that , 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.
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.
Official source
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