HOW A BOOK PUBLISHED IN 1509 INSPIRED THE WAY WE APPLY TODAY GEOMETRY TO ARCHITECTURE, VISUAL ARTS AND DESIGN: “DE DIVINA PROPORTIONE”

“De divina proportione” was a book based on mathematics content written by Luca Pacioli and entirely illustrated by Leonardo da Vinci. The book was started its development by 1498 in the Italian city of Milan and was published in 1509.

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Cover of the book by Luca Pacioli – History of Science Collections, University of Oklahoma Libraries; copyright the Board of Regents of the University of Oklahoma, Attribution, https://commons.wikimedia.org/w/index.php?curid=38183799 

The main purpose of the book is to put in evidence how the mathematical proportions, in other cases referred as the “golden ratio” can be applied through geometry to visual arts and architecture using “perspective” principles.

The way the book was compiled and Da Vinci´s illustrations component to the content, represented a huge breakthrough, even outside the mathematics community until today for artists, architects, graphic and industrial designers and so on.

The book consists of three specific sections:

1. Compendio Divina Proportione

Based on the analysis on how the “golden ratio”  from a mathematical perspective could be leveraged exploring their practical implementation to art development.  It also contains an analysis on “polyhedra” and the use of geometric perspective by painters.

2. Trattato dell’architettura

Comprehend the works of famous and acclaimed roman architect and engineer Vitruvius on the application of mathematics. This section compares the proportions of the human body to artificial structures, with examples from Greco-Roman architectures.

3. Libellus in tres partiales divisus

The third part, which is subdivided in 3 sections is an Italian translation of Piero della Francesca´s writings on the five regular solids with mathematical examples.

Illustrations

Ilustration of the “rhombicuboctahedron” by Leonardo da Vinci, the first illustration published in the book.  

The first printed illustration of a “rhombicuboctahedron”, by Leonardo da Vinci.

After these three parts are appended two sections of illustrations, the first showing twenty-three capital letters drawn with a ruler and compass by Pacioli and the second with some sixty illustrations in woodcut after drawings by Leonardo da Vinci.

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.

800px-Divina_proportione

 

Woodcut illustrating proportions of the human face. 

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Author: Jesus Padilla

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