On number and vision

Mathematics and Optics

Many sons of Francis recognized the importance of mathematics well before the scientific vision of the world emerged. For Roger Bacon, one of the greatest Franciscan thinkers of the Middle Ages, mathematics opened the doors to understanding the laws of nature and the mutability of phenomena, and constituted the key to building solid scientific knowledge in every field.

Medieval mathematics: between East and West

In medieval universities, the treatise De institutione arithmetica by Severinus Boethius was widely used, here displayed in an incunabulum; but for teaching the basics of calculation, simpler treatises were also used, such as the so-called algorismus, named after the 9th-century Arab mathematician al-Khuwārizmī. The texts contain numerous marginal annotations to facilitate the reader’s orientation, a sign of intense study activity and perhaps a trace of the preparation for exams by anonymous medieval students.

Classical mathematical thought: Euclid

Among the various classics of mathematical thought, Euclid’s Elements stand out, an indispensable reference for the study of the discipline for over two millennia. The work is a precious and systematic reorganization of all the mathematical knowledge accumulated between the 5th and 4th centuries BC, here displayed in an edition published in Venice in 1509 by one of the greatest mathematicians of the Renaissance: the Franciscan Luca Pacioli.

Fra Luca applied the extraordinary practical utility of mathematics learned in the Venetian mercantile environment and, faithful to the Franciscan ideal of total and loving openness to the world, disseminated it in the vernacular to facilitate understanding by students and practitioners.

Optics and perspectiva

In the second part of the section, we also find works on optics or perspectiva, that is, the science of light, studied both from a physical-mathematical and physiological point of view: Roger Bacon, Bartolomeo da Bologna, and John Peckham are just some of the friars who were keenly interested in this discipline, blending theological concepts and scientific theories on light in their treatises.

Noteworthy is a “small” but famous manuscript: the Tractatus de Perspectiva by Peckham, richly accompanied by diagrams and geometric drawings useful for explaining optical phenomena; it is likely a part of the Perspectiva communis, one of the most well-known optics manuals until the 17th century.

The Arab and Latin traditions in the Renaissance

Finally, printed works are displayed that testify to the friars’ interest in the classics of the Arab and Latin traditions. In a volume published in 1572, two works are intentionally united: a treatise on optics, known in Latin as Aspectibus, widely used during the Middle Ages and the Renaissance, by Alhazen, an Arab doctor, philosopher, mathematician, and astronomer; and the Perspectiva by Witelo (Vitellione), a Polish philosopher and scientist who lived in the 13th century, particularly appreciated by scholars well beyond the Middle Ages, counting among its famous readers the “great” Kepler.