SKETCH OF MICHEL CHASLES. 841 



plaining of his obscurity, or being discouraged by it, he pursued his 

 studies for the love of them, and found glory without having done 

 anything to secure it except to produce great works." 



M. Chasles was elected a corresponding member of the Academy 

 in 1839, was appointed Professor of Mechanics and Geodesy in the 

 Ecole Polytechnique in 1841, and was elected the first occupant of 

 the newly ci-eated chair of Modern Geometry in 1846. He resigned his 

 position in the cole Polytechnique in 1851, in consequence of the 

 introduction into the school of changes of which he did not approve. 

 He was chosen a foreign member of the Royal Society in 1854, was 

 awarded the Copley medal in 1865, and was elected, in 1867, the first 

 foreign member of the London Mathematical Society. 



M. Chasles's life was one of active, uninterrupted work in his favor- 

 ite field, from the time he left the Lyceum till he was eighty-seven 

 years old a period of sixty-eight years. His contributions of papers 

 to scientific societies and journals are estimated to number nearly two 

 hundred and forty, on subjects which range " over curves and surfaces 

 of the second and any degree, geometry, mechanics (and attractions), 

 history, and astronomy." 



Of his greater works " masterpieces that commanded attention " 

 the earliest was the " Aper5u Historique," or " Historical View of the 

 Origin and Development of Methods in Geometry," which, says M. 

 Bertrand, " under a title that is more than modest, remains the most 

 learned, the most profound, the most original work that the history of 

 science has ever inspired." It was published in 1830, being an elabo- 

 ration of a paper contributed several years before to the Royal Acad- 

 emy of Brussels, and was reprinted in 1875, with a preface, giving a 

 short historical account of the book. It is, says Mr. Tucker, a j^erfect 

 mine of geometrical facts, and is to the present day a high authority 

 on the subject of which it treats. 



The courses of lectures delivered by M. Chasles as Professor of 

 Modern Geometry were embodied in 1852 in the " Ti-aite de Geome- 

 tric superieure," or " Treatise on the Higher Geometry," a work which, 

 of late years scarce and high, has recently appeared in a second edi- 

 tion. This was followed by a sequel, a treatise on conic sections 

 (" Traite des Sections Coniques, faisant suite au Traite de Geometrie 

 supei'ieure," the first volume of which appeared in 1865. The second 

 volume has not been published, but the materials for it have been 

 given from t^me to time in the " Comptes Rendus." 



In 1863 M. Chasles published his " Three Books on the Porisms 

 of Euclid," which was the origin of a short controversy with M. P. 

 Breton. The question of attraction was presented to M. Chasles 

 under several points of view, and gave occasion to a number of me- 

 moirs extending even to the consideration of the general problem of 

 the attraction of a body of any form. Poinsot said of one of these 

 papers that it offered a remarkable example of the elegance and light 



