# Popular Science Monthly/Volume 18/April 1881/Sketch of Michel Chasles

"IN the death of Michel Chasles," said M. J. Bertrand, in his funeral eulogy of the deceased mathematician, "France has lost one of its glories, and the members of the Academy of Sciences have lost an excellent friend, who, devoted without reserve to the beautiful studies which made his fame, showed an equal and active kindness to all who traveled in different directions along the highways of science." "As far back as the present generation can remember," says Mr. R. Tucker, in "Nature," "Chasles has been a prince of geometers, and it has come upon many of us as a surprise to hear that he was still walking and working in our midst. ... To many," says the same writer, "the man who had surpassed in age Leibnitz by seventeen, Euler by eleven, Lagrange by ten, Laplace and Gauss by nine, and Newton by two years, was a '*venerabile nomen,*' but yet a '*nomen*' only."

M. Chasles was born at Epernon, France, November 15, 1793, and died December 18, 1880. His mathematical tastes were exhibited at a very early age; while a pupil in elementary mathematics in the Imperial Lyceum, he was accustomed to communicate to the students in the rival colleges the problems and exercises of each week, asking them, in return, to furnish him the questions proposed by their masters. He entered the École Polytechnique in 1812, and passed out from it with a diploma in engineering in 1814, after having taken his place in the defense of Paris. He was about to go to Chartres to bid farewell to his mother before proceeding to duty at Metz, when he was waited upon by the father of one of his comrades, who asked him to resign in favor of his son, who had failed to obtain a position, pleading that he had made great sacrifices, which he could not afford to repeat, to prepare the youth for a career suited to his taste. Young Chasles made no reply, but went on to Chartres and told his mother he would stay with her. He returned to the École Polytechnique in 1815, but voluntarily renounced public employment, and went to Chartres to spend ten years working quietly at mathematical occupations. "Always," says M. Bertrand, "passionately fond of geometry, he worked out elaborate problems, discovered elegant theorems every day, invented general and fruitful methods, without attracting the attention of the masters of science, or pretending to do so. . . . Without grieving or complaining 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 École Polytechnique in 1841, and was elected the first occupant of the newly created 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 favorite 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 "Aperçu 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 elaboration of a paper contributed several years before to the Royal Academy of Brussels, and was reprinted in 1875, with a preface, giving a short historical account of the book. It is, says Mr. Tucker, a perfect 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 "Traité de Géométric supérieure," or "Treatise on the Higher Geometry," a work which, of late years scarce and high, has recently appeared in a second edition. This was followed by a sequel, a treatise on conic sections ("Traité des Sections Coniques, faisant suite au Traité de Géométrie superieure," the first volume of which appeared in 1865. The second volume has not been published, but the materials for it have been given from time 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 memoirs 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 that geometry could shed on the most obscure and difficult questions; and M. Bertrand has said of them that they gave demonstrations and results admirable as models of elegance and generality.

M. Chasles gained notoriety a few years ago by his connection with a number of manuscripts and autographs purporting to be by distinguished men of the past, among them Galileo, Pascal, Sir Isaac Newton, and even Julius Caesar and other Roman emperors and the apostles, which he bought of one Irène Lucas and which proved to be nearly all forgeries by that adventurer. Among them were some which claimed for Pascal the merit of Newton's most celebrated discoveries. M. Chasles earnestly defended the authenticity of the documents, of which he was fully and honestly convinced, and was sustained by some eminent members of the Academy, until Lucas was unmistakably shown to have fabricated them. Out of twenty-seven thousand papers which he bought, only about a hundred were genuine.

M. Bertrand, summing up the mathematical work of M. Chasles, says that more than once, without abandoning the geometric method, he "has shown with a rare felicity how all mathematical truths are connected by a close and mysterious bond. We owe to him, in one of the highest and most difficult theories of the integral calculus, elegant theorems admired by analysts; he has added to mechanics a chapter which has become classic on the displacement of solid bodies; he has found in the theory of attraction beautiful and general theorems which have revived the theory of static electricity. . . . All geometricians, without distinction of nationality or school, have bowed before this venerable old man; all have admired his inventive power, his fertility, which age seemed to rejuvenate; his ardor and his zeal continued into his latest days."