The Geometry of Coincidence: Nicholas of Cusa and the Quadrature of the Circle

This book offers a contribution to our understanding of Nicholas of Cusa’s theory of geometry. It is based not only on his--generally more famous--philosophical texts (e.g., De docta ignorantia, Idiota, etc.), but also, and more significantly, on the strictly speaking mathematical texts drafted between 1445 and 1459, where Cusanus attempts to provide a solution to the vexata quaestio of the squaring of the circle. First critically edited in 2010--and translated into Italian by the author in 2020--Cusanus’ Scripta mathematica are here scrutinized as to their context, genesis, and content, in order to shed light, on the one hand, on the philosophical and theological motives behind Cusanus’ mathematical endeavours; and, on the other hand, on the scope and limits of Cusanus’ geometrical constructive attempts to reach ＂mathematical perfection＂. In addition to providing a scrupulous survey of Cusanus’ sources on mathematics, this book focuses on a little explored aspect in Cusanus’ work, namely his original theory of geometrical space as men’s space, where the activity of mensurare takes place, establishing relations of continuous proportionality to the original unity. In conclusion, the author provides an extensive account on the reception of Cusanus’ mathematical texts, from their early dissemination to the reactions of several thinkers throughout history, ensuring a full and rounded overview of Cusanus’ work in geometry, mathematics, and philosophy.

Federica De Felice is Associate Professor of History of Modern Philosophy, Università G. D’Annunzio Chieti (Italy). Her interests concern mainly early modern philosophy, the philosophy of Spinoza, and the German Enlightenment (especially the relation between mathematics and philosophy). Lately she is interested in the ethical and philosophical implications of Artificial Intelligence.