Federica De Felice

A full review is provided in this chapter of the mathematical texts Cusanus writes between 1445 and 1459 on the vexata quaestio of the squaring of the circle and of the straightening of the curve: De geometricis transmutationibus, De arithmeticis complementis, De circuli quadratura, Quadratura circuli, De mathematicis complementis, Declaratio rectilineationis curvae, De una recti curvique mensura, Dialogus de circuli quadratura, De caesarea circuli quadratura, De mathematica perfectione, Aurea propositio in mathematicis.Detailed information on their context, genesis, and content is provided for each text.

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.

The theory of infinite modes is not only one of the most controversial points in the philosophy of Spinoza, but also a kind of crossroads concept on whose clarification or interpretation the definition of his philosophy’s overall meaning depends. This article aims to examine Spinoza’s theory of infinite modes, mediate and immediate, in relation to other elements of Spinoza’s theory. Through an analysis of Spinoza’s writings, it proposes an inner reconstruction of the theory in order to ensure the consistency of the difficulties pointed out by several critics and to provide a solution. Spinoza’s identification of immediate infinite in motion, rest, and infinite intellect involves the questions of “what” they really are and what their role is within his system. About mediate infinite modes, Spinoza talks very little and only in terms of facies totius universi. This “silence” is closely linked to the “false” problem of the deduction/mediation of the finite from the infinite, a problem for which Spinoza himself was partly responsible by his statements on motion and the need to analyze the topic in more depth.