CHASLES, shal, Michel, French engineer: b. near Chartres, 15 Nov. 1793; d. Paris, 18 Dec. 1880. He entered the Ecole Polytechnique in 1812, and on leaving was classed among the engineers; but with rare generosity he re nounced his place as an officer in order to assure a career to one of his unsuccessful com rades. In December 1829 he addressed to the Brussels Academy a memoir on two general principles of geometry, duality and homography. The introduction to this memoir expanded into the well-known historique sur l'origine et le developpement des mithodes en geome trie,' the first edition of which was published in 1837. In 1841 he was appointed to the chair of machines and geodesy at the Ecole Poly technique, and in 1846 to that of higher geome try, which had just been instituted at the Sor bonne. Some of his published works are 'Treatise on Higher Geometry' (1852) ; 'The Three Books of Euclid's Porisms Re-established for the First Time> (1860) ; 'Treatise on Conic Section' (1865); 'Reports on the Progress of Geometry' (1870). These, his principal works,
are geometrical and historical. His contribu tions to the 'Comptes Rendus' of the Academy of Sciences and to other scientific publications are extremely numerous, and though in the main geometrical, are not exclusively so. In particular he treated in several memoirs the question of attraction, and gave the first syn thetic demonstration of a celebrated theorem of Maclaurin on the attraction of ellipsoids. Two of his memoirs on the properties of cones of the second degree, and on the spherical conics, were translated into English, and published, with additions, by Charles Graves in 1841. He contributed much to projective geometry (see GEOMETRY, PROJECTIVE) and to the "method of 'characteristics) (q.v.). During his long life he was the recipient of many scientific distinc tions, and he will always be cited as one of the great geometers of the present century.