The principle of the golden ratio and the Vitruvian man: Leonardo's brilliant collaboration with the mathematician Luca Pacioli

De Divina Proportione

De Divina Proportione

De Divina Proportione

  1. Leonardo da Vinci (1452–1519) and the mathematician Luca Pacioli (ca. 1447–1517) collaborated on this masterpiece

  2. Three 1509 printed works deal with the mathematical relationship known as the golden ratio

  3. This principle is applied in various ways illustrated by Leonardo's 60 woodcuts, e.g. the *Vitruvian Man*

La Divina Proporción

De Divina Proportione

Skeletal Polyhedron

This polyhedron is virtually perfect and may even originate from the hand of Leonardo da Vinci, a friend and collaborator of Luca Pacioli, the work’s author. In fact, the two Renaissance geniuses lived together in Milan for a time until 1499, when they were forced to flee due to the invasion of King Louis XII of France. Their work from the 1480’s endured after they parted ways in 1506 and became a standard mathematical text as well as one of the most important treatises of the Renaissance.

De Divina Proportione

Alternative Titles:
  • La Divina Proporción
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
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  1. Short Description
  2. Codicology

Short Description

With their treatise on the golden ratio and its application to various arts, the mathematician Luca Pacioli and the painter Leonardo da Vinci managed to create a work, which was the most-widely disseminated mathematical work for several centuries. Thanks to its clearly understandable texts and gorgeous and interesting illustrations, it has lost none of its impact outside of mathematical circles. The text consisting of three separate manuscripts originated ca. 1488 in Milan and was published on the 1st of July, 1509 in Venice. Particularly worthy of note are da Vinci’s illustrations, which follow the text and are probably the first depictions of skeletons to make possible the distinction of the front side from the back.

De Divina Proportione

For more than one hundred years, the De Divina Proportione was the most widely circulated mathematical work, which also had a great impact outside of mathematical circles. Ca. 1488, Leonardo da Vinci (1452–1519) induced his friend, the mathematician and Franciscan monk Luca Pacioli (1445–1517), to create a treatise on the golden ratio. In doing so, a work consisting of three separate manuscripts illustrated by the first truly instructive spatial representations of polyhedrons.

The Union of Mathematics and Art

The three-part text originated between 1496 and 1498 and concerns the mathematical proportions and their applications to geometry and art through perspective and architecture. The first manuscript is focused on the study of the golden ratio from a mathematical perspective and devoted itself to the application thereof in various arts. It is followed by treatises concerning the use of perspective in the works of painters such as Piero della Francesca (ca. 1420–1492), Melozza da Forli (1438–1494), and Marco Palmezzano (1456–1539). The 20 chapters of the second part discuss the ideas of Vitruvius (1st c. B.C.E.) concerning the application of mathematics to architecture, while the third manuscript is predominantly an Italian translation of Piero della Francesca’s Latin texts concerning the five Platonic solids.

Astounding Geometric Illustrations

Two excerpts with interesting illustrations follow the text portion. The first part consists of 23 large initials with a ruler and compass by Pacioli himself. Having said this, the 60 woodcuts of drawings by Leonardo da Vinci are even more significant. They are probably the first depictions of skeletons to make the distinction between the front and back sides possible. Additionally, one finds the famous Vitruvian Man in da Vinci’s work, which discovers a correlation to the human aspiration according to the knowledge of god.

Codicology

Alternative Titles
La Divina Proporción
La Divina Proporción

De Divina Proportione

Presentation Miniature

Dressed in the simple brown robes of a Franciscan friar, the author of this important mathematical treatise, Luca Pacioli, is depicted here presenting the work to the man who patronized his labor, Ludovico Sforza. One of the greatest art patrons of Renaissance Italy, Ludovico’s coat of arms as Duke of Milan are presented at the bottom of the page.

The attention to detail is incredible for an image this size, especially with regard to the gestures and postures of the figures and their garments’ fall of folds. Presented within an elegant golden frame as though it were a small panel painting, this miniature is only a centerpiece of a perfectly composed page, including a brilliant crimson field of golden text at the top of the page.

1 available facsimile edition(s) of „De Divina Proportione“

La Divina Proporción
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
De Divina Proportione – Ms. 170 sup. – Biblioteca Ambrosiana (Milan, Italy)
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La Divina Proporción

1 volume: Exact reproduction of the original document (extent, color and size)
Publisher
Ediciones Grial – Valencia, 2007
More Information
Reproduction of the entire original document as detailed as possible (scope, format, colors). The binding may not correspond to the original or current document binding.
Price Category: €€ (1,000€ - 3,000€)
Edition available
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