Un cours inédit de Chasles en Sorbonne ‘Considérations sur la théorie des sections coniques’, Discours d'ouverture du cours de géométrie supérieure (1847-1848)

We present an annotated transcription of an unpublished lecture given by the French geometer Michel Chasles (1793-1880), obtained from a manuscript preserved at the archives of the Académie des sciences. This was the opening lecture for the course of higher geometry for the academic year 1847-1848. This year’s teaching dealt with the theory of conic sections. In this lecture, Chasles presents a history of the methods used in the study of conic sections, and justifies his choice in his teaching to go back to the « Method of the Ancients », which he viewed necessary to form a fully general and purely geometrical theory of these curves.