## Thèses présentées a la Faculté des sciences de Paris pour obtenir le grade de docteur des sciences mathématiques. 1re These. Sur les propriétés des fonctions définies par les équations aux différences partielles. 2e These. Propositions données par la Faculté. Soutenues le 1er aout 1879, devant la commission d'examen.

Paris: Gauthier-Villars, 1879.

A fine copy, with the original printed wrappers, of Poincaré's thesis for his doctorate in science from the University of Paris. “Poincaré's doctoral thesis [was] on differential equations (not on methods of solution, but on existence theorems), which led to one of his most celebrated contributions to mathematics-the properties of automorphic functions” (Boyer & Merzbach, History of Mathematics, p. 675). “The theory of differential equations and its applications to dynamics was clearly at the center of Poincaré’s mathematical thought; from his first (1878) to his last (1912) paper, he attacked the theory from all possible angles and very seldom let a year pass without publishing a paper on the subject” (DSB XI: 56).

“Poincaré's thesis, which was examined by Bouquet, Bonnet and Darboux, concerned the study of integrals of first-order partial differential equations in the neighbourhood of a singular point. It was his second paper of the theory of differential equations and, as Hadamard remarked, it contained a strong pointer towards his future success with the topic and its applications to celestial mechanics: ‘Even Poincaré 's thesis contained a remarkable result which was destined later to provide him with a powerful tool in his researches in celestial mechanics.’

“Looked at in the context of the theory of differential equations already in existence at the time, Poincaré's thesis was the natural convergence of two streams of thought. On the one hand, Cauchy, and later Kovalevskaya, had applied Cauchy’s method of majorants to obtain results about the solutions of partial differential equations in the neighbourhood of an ordinary point, while on the other, Briot and Bouquet. and later Fuchs, using similar methods, had studied the solutions of ordinary differential equations in the neighbourhood of a singular point. Poincare followed both Cauchy, by considering the solutions of partial differential equations, and Briot and Bouquet, by considering these solutions in the neighbourhood of a singular point” (June Barrow-Green, Poincaré and the three-body problem, Vol. 2, p. 44).

“The development of mathematics in the nineteenth century began under the shadow of a giant, Carl Friedrich Gauss; it ended with the domination by a genius of similar magnitude, Henri Poincaré. Both were universal mathematicians in the supreme sense, and both made important contributions to astronomy and mathematical physics... Poincaré remains the most important figure in the theory of differential equations and the mathematician who after Newton did the most remarkable work in celestial mechanics” (DSB XI: 52).

Large 4to (262 x 210 mm), pp [iv] 93 [3], bound in a fine recent half cloth binding over marbled boards, gilt morocco title label to spine, original brown printed wrappers with bound (small hole to the front wrapper, paper flaw?), a fine copy copy.

Item #2928

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Price:
$1,500.00
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