This essay explores the research practice of French geometer Michel Chasles, from his 1837 Aperçu historique up to the preparation of his courses on ‘higher geometry’ between 1846 and 1852. It argues that this scientific pursuit was jointly carried out on a historiographical and a mathematical terrain. Epistemic techniques such as the archival search for and comparison of manuscripts, the deconstructive historiography of past geometrical methods, and the epistemologically motivated periodization of the history of mathematics are shown to have played (...) a crucial role in the shaping of Chasles's own theories. In particular, we present Chasles's approach to the ‘material history’ of algebraic symbolism and argue that it motivated and informed his subsequent invention of a novel notational technology for the writing of geometrical proofs and propositions. In return, this technology allowed Chasles to carry out a programme for the modernization of geometry in keeping with epistemic requirements he had also delineated via a form of historical writing. (shrink)

French mathematician Michel Chasles, a staunch defender of pure geometrical methods, is now mostly remembered as the author of the Aperçu historique. In this book, he retraced the history of geometry in order to expound epistemological theses on what constitutes a virtuous practice of geometry. Amongst these stands out the assertion that the values of generality and simplicity in mathematics are intimately connected. In this paper, we flesh out this claim by analysing Chasles’s geometrical solutions to the century-old problem of (...) the attraction of the ellipsoids. We show how these solutions echo Chasles’s evaluation of the relative strengths of geometrical and analytical methods, and how they embody a set of normative rules for the geometer’s practice whose observance Chasles deemed necessary and sufficient for the development of general methods and theories. (shrink)