Daniel L. Newsome

This dissertation is a study of the relationships between the quadrivial disciplines of Boethius: arithmetic, music, geometry, and astronomy. These disciplines are specifically arranged from the most basic abstract notion of arithmetical numbers, to the proportions of harmonics to the physics of motion and the cycles of astronomy and astrology. The quadrivium represents a Platonic worldview of number as cosmic order, but these four fields in premodern times do not correspond to the same four disciplines today. What happened? This dissertation tracks the four topics of the quadrivium and the relationships between them, focusing on case studies of quadrivial masters from the Late Middle Ages and Renaissance.