The value of generality in Michel Chasles’s historiography of geometry

Abstract

This article discusses the value of generality in Michel Chasles’s historiography of geometry, articulated in his 1837 book Aperçu historique sur l’origine et le développement des méthodes en géométrie, particulièrement de celles qui se rapportent à la géométrie moderne, suivi d’un mémoire de géométrie sur deux principes généraux de la science: la dualité et l’homographie. In the book, mathematics and history were combined as two kinds of tools useful in achieving a single aim: to show how the recent advances in geometry allowed the strictly geometrical methods in this domain to rival the analytical approach to geometry. Generality, and the related property of simplicity, are Leitmotive in Aperçu historique. This article first examines Chasles’s historical analysis of geometry and his methods related to generality in geometry before considering some aspects of the problem of generality in geometry.