THE news of the death of Michel Chasles, perhaps the oldest and best-known mathematician in Europe, will be everywhere learned with deep regret. For the fifty-five years over which his writings extend he has devoted himself with persistent industry to the history of geometry and to the perfection of those geometrical methods with which his name will be always associated. The “Apergu historique sur l'Origine et le Développement des Méthodes en Géométrie,” which in fact forms an elaborate history of the subject from the time of Thales and Pythagoras to the beginning of the present century, is the best known of his works; it was first published in 1837, and a second edition appeared only a few years ago. His restoration of the Porisms of Euclid was published in 1860. The last great work of Chasles related to the investigation of the number of conies satisfying any five conditions: the special method which he invented for these researches, termed by him geometrical substitution, involved the consideration of the characteristics of systems of conies, i.e. of the numbers of conies satisfying four common conditions and (1) passing through an assumed point; (2) touching an assumed line.