Geometry and the Gods: Theurgy in Proclus’s Commentary on the First Book of Euclid’s Elements

Abstract

Proclus’s Commentary on the first book of Euclid’s Elements contains one of the most important discussions of the nature of mathematical objects, and preserves a wealth of historical information about mathematics from antiquity. However, large sections of the text have been neglected by scholars since the text’s first publication in the sixteenth century. Proclus expounds at length on correspondences between mathematical objects and the gods. At times he uses the language of “theurgy,” the ritual practices that later Neoplatonists insisted were necessary for the human soul to ascend to the intelligibles. The contention of this article is that the Commentary, taken as a whole, concerns the practice of “inner theurgy,” mental rituals used by advanced students to raise the soul beyond its assigned bounds. This practice can be traced back to Plotinus and the very beginnings of Neoplatonism; however, the particular methods presented by Proclus are his own development. This interpretation of the Commentary is supported by Proclus’s Commentary on the Parmenides and his Platonic Theology. Parts of the Commentary that have been studied carefully by modern scholars, especially the theory of the mathematical phantasia or imagination, will be shown to be crucial elements in Proclus’s theory and practice of inner theurgy.