CHASLES, shal, StICIIEL (1793-1880). A French mathematician. He was born at Eper non, entered the Eeole Polytechnique, of Paris, in 1812, took part in the defense of Paris in 1814, and reentered the school in the following year. At graduation he secured the much coveted pro motion to a commission in the engineer corps, but resigned it, with rare generosity, to allow one of his fellow classmates to take the place, retiring to Chartres for the purpose of studying geometry. For a quarter of a century Chasles devoted the leisure which his wealth afforded to a profound study of this science. After a perusal of the works of Lagrange or Laplace, he read Apollonius and Archimedes, and sought to clarify the obscure passages of Pappus. Charles's classi cal work. .Ipereu historique sur l'origine et le de •eloppement des methodes en geometric (1837, 2d ed., 1875), while modest in title, is powerful in exposition. clear in style, and rich in ingenious comparisons. In 1841 he was made professor of geodesy and mechanics at the Ecole Polytech nique, and in 1846 professor of geometry at the Sorbonne, which chair he occupied for twenty one years. The appendix to the Apercu histo ripe contains the general theory of homography and reciprocity. Synthetic or projective geom etry was elaborated by him, as was also the 'method of characteristics•' the basis of enumer ative geometry afterwards extended by Schubert to a-dimensional space. Chasles contributed also some valuable propositions to integral calculus; his discussions of the displacement of solid bodies and of static electricity have become classics in the field of science, and his solution (1845) by projective geometry of the difficult problem of the attraction of an ellipsoid on an external point is noteworthy. The words of an illustrious
Englishman, "M. Chasles is the emperor of geom etry," rightly suggest his title to fame.
It is not an uninteresting fact that Chasles was duped by the notorious forger Vrain Lucas. In Ps67 Chasles announced that he was in pos session of 27,000 letters and documents, of great value: among them were papers believed to have been written by Dante. Tetrarch. Rabelais. Julius Caesar. and Shakespeare. as well as some by Pas cal. which were intended to prove that Pascal had anticipated some of the greatest discoveries of Newton. Scarcely one hundred of them prov ing genuine, Chasles suffered not only the em barrassment of being deceived. hut also the loss of his expenditure of 200,000 francs.
Among the chief works of Chasles are, besides the .tpereu historique mentioned above, the fol lowing: Trait(' de ge'ometrie superieure (1852; 2d ed. ISSO) ; Trait(' des sections eoniques ( 1868 76) ; Rapport sur Ics progris de la geometric (1871) ; and Trois urns de porismes d'Euelide ( 1S63 . carious memoirs on perspective and projective fignres, duality, tortuous curves, and the principle of correspondence were pub lished in the ./ou•na/ de l'Ecolc Polyteehnique (1840-65).