Mathematical Culture in Renaissance Paris; University, Print, and the Circle of Lefèvre d'Etaples

Jacques Lefèvre d'Etaples (c.1450-1536) renovated the medieval quadrivium in Renaissance Paris circa 1490-1520. Using Lefèvre and his circle, this dissertation portrays new print and traditional university culture at the origin of mathematics' rise to philosophical and cultural prominence. Joining the histories of the book and mathematical practice, it contributes to the history of manuscript and print, and the history of mathematics in early modern science.

Part one of this dissertation presents Lefèvre's textbooks on arithmetic, music, geometry and astronomy within the first comprehensive effort to reinvent textbooks for university education using the printing press. Lefèvre meant his textbooks to correct the scholastic accretions of traditional university culture ? to simplify student access to the ancient authorities. Lefèvre first circulated them in manuscript among students, who then experimented with them in print. I argue that collective, experimental authorship, visible in paratexts, especially opened these mathematical works to unintended interpretations.

Part two examines Lefèvre's goals for mathematics. He thought mathematics a paradigm for analogies that applied across disciplinary boundaries; reasoning from physical to theological realities permeated his contemplative account of mathematics. From the student notes of his pupil Beatus Rhenanus, I show these ideals in action in Lefèvre's classroom, where mathematics inaugurated the arts cursus (instead of being last, as was traditional). Beatus' notes reveal contemplative concerns, but also a turn to practical, operational mathematics.

Part three argues that Lefèvre's textbooks encouraged unintentional consequences. In particular his appreciation of analogy helped to cross disciplinary boundaries despite his commitment to traditional authorities and disciplines. In music, Lefèvre broke traditional rules of arithmetic to incorporate musical practice. In astronomy, Lefèvre offered Ptolemy's techniques for mapping, effectively transforming medieval astronomy into the early practical genre of cosmography. Thus Lefèvre's analogies and print practices produced a fertile instability, as I show with Lefèvre's student Bovelles, author of the first printed French practical geometry. He encouraged a new public interested in mathematics to uncover the secrets of nature and industry. This dissertation thus addresses the reconfiguration of the disciplines in the scientific revolution, manuscript and print, and new interest among the learned in artisanal crafts.