Divina proportione: Opera a tutti glingegni perspicaci e curiosi necessaria que ciascun studioso… (On the Divine Proportion)

The textbook On the Divine Proportion is a scholarly treatise on architecture, which has not lost its significance over the centuries. The work was composed by the Italian mathematics professor Luca Pacioli and printed in the workshop of the famous Paganino de Paganini. Together, they published a series of important algebraic and geometric formulas for practical use in the 15th century. On the Divine Proportion was the high point of their scientific work. For the modern reader, this work represents a historical source of information of immeasurable worth.

Geometry for the Duke

On the Divine Proportion was composed ca. 1498 in Milan, at the court of Duke Ludovico Sforza. It was he who commissioned the splendidly designed work. The writing contains numerous high-quality, printed graphics. The illustrations serve as visual support for the mathematic text. This very same text is ennobled through the application of various fonts, finally designed initials, and luminous colors. The last page of the masterpiece is particularly impressive, showing an illustration with the title Arbor proportio et porportionalitas. The elaborately designed, realistic, and three-dimensional-seeming image before a dotted background is one of the most beautiful miniatures to come out of medieval Italian illumination.

The Principle of Beauty

The architectural treatise consists of three parts. In the first, mathematical terms are explained and with the help of these terms, providing access to perspective, architecture, and the science of cosmography. With the help of the Euclid’s theorem, information is given about the correct understanding of proportions. The second part deals with solid chemical materials and their influence on the divine proportion. In the third part, architecture according to the divine proportion is finally addressed. Collectively, this principle is described in the following way: “architecture (like any other form of art) must reflect the mathematical structure of the universe. The mathematical proportion, the universal principle, and the beauty of the object should be a reference point for every art form”. This principle is found on page 25 of the informative masterpiece.