Quadrivium in Varro’s Disciplines

Abstract

This article brings together the evidence concerning the subjects of the quadrivium in Varro’s Disciplines and provides a description of the book’s content, composition, and sources, while at the same time discussing the level of post-school mathematical education in Varro’s time. Polarizing views exist on the matter of post-school mathematical education, with some scholars placing it as early as the beginning of the Hellenistic period, and others linking its emergence to Neoplatonic circles in the fourth century CE. I argue that it is possible to attest to the existence of post-school mathematical education in the first century BCE, even though it was pretty basic in nature and did not go beyond the fundamentals of the subjects of the quadrivium, as the contents of Varro’s book suggest. The first section of the article covers Varro’s unconventional views on the origin of geometry: Varro rejects the Egyptian origin of geometry and traces its invention back to the dawn of human civilization. The second section deals with Varro’s geometrical definitions and their relation to the Euclidean tradition, showing that among his sources, there definitely were some Hellenistic introductions to μαθήματα. The final section focuses on Varro’s conception of optics and canonics; here, his approach to canonics is identified as mostly mathematical with some empirical features.