De divina proportione
Encyclopedia
De Divina Proportione (About the divine proportions) is a famous book on mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
written by Luca Pacioli
Luca Pacioli
Fra Luca Bartolomeo de Pacioli was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and seminal contributor to the field now known as accounting...
around 1497 in Milan
Milan
Milan is the second-largest city in Italy and the capital city of the region of Lombardy and of the province of Milan. The city proper has a population of about 1.3 million, while its urban area, roughly coinciding with its administrative province and the bordering Province of Monza and Brianza ,...
. 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
Leonardo da Vinci
Leonardo di ser Piero da Vinci was an Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer whose genius, perhaps more than that of any other figure, epitomized the Renaissance...
.
The book
The book consists of three individual manuscripts, which Pacioli worked on between 1496 and 1498.The first part, Compendio Divina Proportione, studies and describes the Golden ratio
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...
from a mathematical point of view and also studies polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
s. The work also discusses the use of perspective by painters such as Piero della Francesca
Piero della Francesca
Piero della Francesca was a painter of the Early Renaissance. As testified by Giorgio Vasari in his Lives of the Artists, to contemporaries he was also known as a mathematician and geometer. Nowadays Piero della Francesca is chiefly appreciated for his art. His painting was characterized by its...
, Melozzo da Forlì
Melozzo da Forlì
Melozzo da Forlì was an Italian Renaissance painter and architect. His fresco paintings are notable for the use of foreshortening. He was the most important member of the Forlì painting school.- Biography :...
, and Marco Palmezzano
Marco Palmezzano
Marco Palmezzano was an Italian painter and architect, belonging to the Forlì painting school, who painted in a style recalling earlier Northern Renaissance models, and was mostly active near Forlì.-Biography:...
.
The second part discusses Vitruvius
Vitruvius
Marcus Vitruvius Pollio was a Roman writer, architect and engineer, active in the 1st century BC. He is best known as the author of the multi-volume work De Architectura ....
ideas on the application of mathematics in architecture
Architecture
Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...
.
The third part, Libellus in tres partiales tractatus divisus, is mainly an Italian translation of Piero della Francesca
Piero della Francesca
Piero della Francesca was a painter of the Early Renaissance. As testified by Giorgio Vasari in his Lives of the Artists, to contemporaries he was also known as a mathematician and geometer. Nowadays Piero della Francesca is chiefly appreciated for his art. His painting was characterized by its...
's Latin writings On [the] Five Regular Solids ("De quinque corporibus regularibus") and mathematical examples.
The book contains illustrations in woodcut
Woodcut
Woodcut—occasionally known as xylography—is a relief printing artistic technique in printmaking in which an image is carved into the surface of a block of wood, with the printing parts remaining level with the surface while the non-printing parts are removed, typically with gouges...
after drawings by Leonardo da Vinci
Leonardo da Vinci
Leonardo di ser Piero da Vinci was an Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer whose genius, perhaps more than that of any other figure, epitomized the Renaissance...
. 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.
History
On June 1 1509 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. The book has since then been reprinted several times.Today only two surviving copies of the original print exist, one at the Biblioteca Ambrosiana
Biblioteca Ambrosiana
The Biblioteca Ambrosiana is a historic library in Milan, Italy, also housing the Pinacoteca Ambrosiana, the Ambrosian art gallery. Named after Ambrose, the patron saint of Milan, it was founded by Cardinal Federico Borromeo , whose agents scoured Western Europe and even Greece and Syria for books...
in Milan and the second at the Bibliothèque de Genève
Bibliothèque Publique et Universitaire (Geneva)
The Library of Geneva , known until 2006 under the name Public and University Library , is one of the oldest university libraries of Switzerland...
in Geneva
Geneva
Geneva In the national languages of Switzerland the city is known as Genf , Ginevra and Genevra is the second-most-populous city in Switzerland and is the most populous city of Romandie, the French-speaking part of Switzerland...
.
The book was displayed under an exhibition in Milan between October 2005 until October 2006 together with the Codex Atlanticus
Codex Atlanticus
The Codex Atlanticus is a twelve-volume, bound set of drawings and writings by Leonardo da Vinci, the largest such set; its name indicates its atlas-like breadth. It comprises 1,119 leaves dating from 1478 to 1519, the contents covering a great variety of subjects, from flight to weaponry to...
.
The "M" logo used by the Metropolitan Museum of Art
Metropolitan Museum of Art
The Metropolitan Museum of Art is a renowned art museum in New York City. Its permanent collection contains more than two million works, divided into nineteen curatorial departments. The main building, located on the eastern edge of Central Park along Manhattan's Museum Mile, is one of the...
in New York City is adapted from one in De divina proportione.