The Ancients and the Moderns: Chasles on Euclid's lost Porisms and the pursuit of geometry.

Of Euclid's lost manuscripts, few have elicited as much scholarly attention as the Porisms, of which a couple of brief summaries by late-Antiquity commentators are extant. Despite the lack of textual sources, attempts at restoring the content of this absent volume became numerous in early-modern Europe, following the diffusion of ancient mathematical manuscripts preserved in the Arabic world. Later, one similar attempt was that of French geometer Michel Chasles (1793-1880). This paper investigates the historiographical tenets and practices involved in Chasles' restoration of the porisms, as well as the philosophical and mathematical claims tentatively buttressed therewith. Echoes of the Quarrel of the Ancients and the Moderns, and of a long-standing debate on the authority and usefulness of the past, are shown to have decisively shaped Chasles' enterprise-and, with it, his integration of mathematical and historical research.