‎Leçons sur les hypothèses cosmogoniques professées à la Sorbonne. Rédigées par Henri Vergne.‎

‎ P., Librairie scientifique A. Hermann et fils, 1911 ; in-8 broché. XXV- 294 pp.-43 fig. Exemplaire complet du papillon derrata, bon état.‎

‎EDITION ORIGINALE ‎

‎Théorie analytique de la propagation de la chaleur. Leçons professées pendant le premier semestre 1893-1894. Rédigées par MM. Rouyer et Baire.‎

‎ P., Georges Carré, 1895 ; in-8 broché. 316 pp. Dos renforcé de papier blanc, couverture fragilisée avec des manques et déchirures.‎

‎PREMIERE EDITION ; étiquette « Paris, Gauthier-Villars, imprimeur libraire » collée sur ladresse de léditeur Carré (voir photo). ‎

‎Théorie des tourbillons - Leçons professées pendant le deuxième semestre 1891-1892 ‎

‎Sceaux, Editions Jacques Gabay, 1990, in-8 br. (16 x 24), 211 p., réimpression de l'édition de 1893, leçons rédigées par M. Lamotte, très bon état. ‎

4 Images

‎"On a tenté aussi de trouver, dans l'existence de pareils mouvements tourbillonnaires, l'explication mécanique de l'univers. Au lieu de se représenter l'espace occupé par des atomes que séparent des distances immenses vis - à-vis de leurs propres dimensions, sir William Thomson admet que la matière est continue, mais que certaines portions sont animées de mouvements tour billonnaires, qui, d'après le théorème de Helmholtz, doivent conserver leur individualité". Voir le sommaire sur photos jointes. ‎

‎Théorie des tourbillons. Leçons professées pendant le deuxième semestre 1891-92. Rédigées par M. Lamotte, licencié ès-sciences.‎

‎ P., Georges Carré, 1893 ; fort in-8 broché. 2 ff.-211 pp.- 1p. (erratum). Dos renforcé de papier blanc, couverture fragilisée avec des manques et déchirures.‎

‎EDITION ORIGINALE ‎

‎CALCUL DES PROBABILITES, LECONS PROFESSEES PENDANT LE 2e SEMESTRE 1893-1894‎

‎Georges Carré, Paris. 1896. In-8. Relié demi-cuir. Etat d'usage, Couv. convenable, Dos très frotté, Intérieur acceptable. 274 pages. Auteur, titre, fleurons et filets dorés sur le dos. Etiquette de code sur le dos. Tampons de bibliothèque en page de titre.. . . . Classification Dewey : 510-Mathématiques‎

‎'Cours de la Faculté des Sciences de Paris', par l'Association amicale des élèves et anciens élèves de la Faculté. Rédigé par A. Quiquet, ancien élève de l'ENS. Classification Dewey : 510-Mathématiques‎

‎La valeur de la science. Les sciences mathématiques ; les sciences physiques ; la valeur objective de la science.‎

‎Paris, E. Flammarion 1935. Bel exemplaire broché, couverture ornée d'éd., in-8, 278 pages.‎

‎Remarques diverses sur l'équation de Fredholm.‎

‎[Berlin, Stockholm, Paris, Beijer, 1910] 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 33, pp. 57-86.‎

‎First printing of Poincaé's work on Fredholm's equation.""... heuristic variational arguments convinced Poincaré that there should be a sequence of ""eigenvalues"" and corresponding ""eigenfunctions"" for this problem, but for the same reasons lit was not able to prove their existence. A few years later, Fredholm's theory of integral equations enabled him to solve all these problems"" it is likely that Poincareé's papers had a decisive influence on the development of Fredholm's method, in particular the idea of introducing a variable complex parameter in the integral equation. It should also be mentioned that Fredholm's determinants were directly inspired by the theory of ""infinite determinants"" of H. von Koch, which itself was a development of much earlier results of Poincaré in connection with the solution of linear differential equations."" (DSB)‎

‎Remarques diverses sur l'équation de Fredholm.‎

‎Berlin, Uppsala & Stockholm, Paris, Almqvist & Wiksell, 1909. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 33, 1909. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 195-200.[Entire volume: (6), 392, 12 pp].‎

‎First printing of Poincaé's work on Fredholm's equation.""... heuristic variational arguments convinced Poincaré that there should be a sequence of ""eigenvalues"" and corresponding ""eigenfunctions"" for this problem, but for the same reasons lit was not able to prove their existence. A few years later, Fredholm's theory of integral equations enabled him to solve all these problems"" it is likely that Poincareé's papers had a decisive influence on the development of Fredholm's method, in particular the idea of introducing a variable complex parameter in the integral equation. It should also be mentioned that Fredholm's determinants were directly inspired by the theory of ""infinite determinants"" of H. von Koch, which itself was a development of much earlier results of Poincaré in connection with the solution of linear differential equations."" (DSB)‎

‎Remarques sur les intégrales irrégulières deséquations linéaires.‎

‎Berlin, G. Reimer, 1887. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 10, 1887. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 310-12. [Entire volume: (4), 397 pp].‎

‎First printing of Poincaré's reply to Thomé's critique of an earlier paper by Poincaré. In his reply Poincaré ""seems to have created a theory of asymptotic expansions where previously there had only been ad hoc techniques, and to have opened the door for the return into rigorous mathematics of divergent series."" (Bottazzini, Hidden Harmony).‎

‎Sur la méthode horistique de Gyldén. - [POINCARÉ ON GYLDÉN'S HORISTIC METHODS]‎

‎Berlin, G. Reimer, 1905, 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 29, 1905. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 235-72. [Entire volume: (4), 433 pp].‎

‎First printing of Poincaré's final and most extensive paper on Gyldén's horistic methods.‎

‎Sur les rapports de l'analyse pure et de la physique mathématique.‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1897]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 21. No backstrip. Fine and clean. Pp. 331-341.‎

‎First printing of Poincaré's principal address at the first International Congress of Mathematicians held in Zürich in 1897. ‎

‎Sur L'Uniformisation des Fonctions Analytiques. - [THE UNIFORMIZATION THEOREM]‎

‎Berlin, Stockholm, Paris, Almqvist & Wiksell, 1908. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 31, 1908. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 1-64. [Entire volume: (8), 408, (2), 12 pp].‎

‎First appearance of Poincaré's important paper in which he presented the first solution to the problem of the uniformization of curves - now know as The Uniformization Theorem. Clebsch and Riemann tried to solve the problem of the uniformization for curves. ""In 1882 Klein gave a general uniformization theorem, but the proof was not complete. In 1883 Poincaré announced his general uniformization theorem but he too had no complete proof. Both Klein and Poincaré continued to work hard to prove this theorem but no decisive result was obtained for twent-five years. In 1907 Poincare (in the offered paper) and Paul Koebe independently gave a proof of this uniformization theorem...With the theorem on uniformization now rigorously established an improved treatment of algebraic functions and their integrals has become possible."" (Morris Kline).‎

‎Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation. - [POINCARÉ'S PEAR-SHAPE]‎

‎(Stockholm, Beijer), 1885. 4to. As extracted from ""Acta Mathematica, 21. Band]. No backstrip. Fine and clean. Pp. 259-380.‎

‎First printing of Poincaré's famous paper in which he proved that a rotating fluid such as a star changed its shape from a sphere to an ellipsoid to a pear-shape before breaking into two unequal portions. ""This work, which contained the discovery of new, pear-shaped figures of equilibrium, aroused considerable attention because of its important implications for cosmogony in relation to the evolution of binary stars and other celestial bodies."" (The Princeton Companion to Mathematics, P. 786)Another famous paper of Poincaré in celestial mechanics is the one he wrote in 1885 on the shape of a rotating fluid mass submitted only to the forces of gravitation. Maclaurin had found as possible shapes some ellipsoids of revolution to which Jacobi had added other types of ellipsoids with unequal axes, and P. G. Tait and W. Thomson some annular shapes. By a penetrating analysis of the problem, Poincaré showed that still other ""pyriform"" shapes existed. One of the features of his interesting argument is that, apparently for the first time, he was confronted with the problem of minimizing a quadratic form in ""infinitely"" many variables."" (DSB)‎

‎Sur une Forme nouvelle des Équations du Probleme des trois Corps (+) Sur les rapports de l'analyse pure et de la physique mathématique.‎

‎Berlin, Uppsala & Stockholm, Paris, Almqvist & Wiksell, 1897. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 21, 1897. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 83-97"" Pp. 331-341.[Entire volume: (6), 376 pp + 4 plates].‎

‎First printing of this paper in which Poincaré arrives at a new theorem about canonical transformation, and in his later ""Methodes Nouvelles"", he proved this theorem using a variiational principle of mechanics, known today as the Hamilton principle.Also included is the first printing of Poincaré's principal address at the first International Congress of Mathematicians held in Zürich in 1897. ‎

‎Sur un theoreme de M. Fuchs.‎

‎Stockholm, Beijer, 1885. 4to. As extracted from ""Acta Mathematica, 21. Band]. No backstrip. Fine and clean. Pp. 83-97.‎

‎First printing of Poincaré's paper in which he developed the idea published by Fuchs in 1884. Fuchs established that the equation with fixed branch points can be made into a Riccati equation if its genus - the genus of the corresponding Riemann surface - with respect to u and du/dz is zero and can be integrated using elliptic functions if the genus is 1. ‎

‎Rapport sur le Prix Bolyai. - [POINCARÉ APPRAISAL OF HILBERT]‎

‎Berlin, G. Reimer, 1912. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 35, 1912. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 1-28. [Entire volume: (4), 398, (1), 27, 19 pp].‎

‎First appearance of Poincaré's report on 1910 Bolyai Prize which was awarded to David Hilbert in recognition of his work in fields of invariant theory, transcendent number (e constant after Lindemann), arithmetic, the (Hilbert-)Waring theorem, geometry, integral equations and the Dirichlet’s principle.In 1910, Hilbert became only the second winner of the Bolyai Prize of the Hungarian Academy of Sciences. It was the recognition of the fact that Hilbert was one of the leading mathematicians of his time. The first winner of the prize in 1905 was Henri Poincare, the most prolific mathematician of the 19th century.Poincaré about the works and achievements of David Hilbert in fields of invariant theory, transcendent number (e constant after Lindemann), arithmetic, the (Hilbert-)Waring theorem, geometry, integral equations and the Dirichlet’s principle.‎

‎La Méthode de Neumann et le Probleme de Dirichlet.‎

‎(Berlin, Uppsala & Stockholm, Paris, 1895). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler"", Bd. 20, pp. 59-142.‎

‎First edition. In this paper Poincaré succeeded in converting differential equations into integral equations. ""It became a major technique for solving initial-and boundary-value problems of ordinary and partial differential equations and was the strongest impetus for the study of integral equations."" (Morris Kline).‎

‎La méthode de Neumann et le problème de Dirichlet.‎

‎[Berlin, Stockholm, Paris, Beijer, 1897]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 20, pp. 59-142.‎

‎First printing of Poincaré's paper in which he succeeded in converting differential equations into integral equations. ""It became a major technique for solving initial-and boundary-value problems of ordinary and partial differential equations and was the strongest impetus for the study of integral equations."" (Morris Kline).‎

‎Mémoire sur les Fonctions fuchsiennes.‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1882]. Large4to. As extracted from ""Acta Mathematica"", In ""Acta Mathematica"", volume 1. Clean and fine. Pp. 193-294.‎

‎First printing of Poincaré's famous paper which conjectured the uniformization theorem for (the Riemann surfaces of) algebraic curves. It also constitute the second paper in Poincaré's exceedingly important series of six paper's which together represent the discovery of Automorphic Functions. ""Before he was thirty years of age, Poincaré became world famous with his epoch-making discovery of the ""automorphic functions"" of one complex variable (or, as he called them, the ""fuchsian"" and ""kleinean"" functions)."" (DSB).These manuscripts, written between 28 June and 20 December 1880, show in detail how Poincaré exploited a series of insights to arrive at his first major contribution to mathematics: the discovery of the automorphic functions. In particular, the manuscripts corroborate Poincaré's introspective account of this discovery (1908), in which the real key to his discovery is given to be the recognition that the transformations he had used to define Fuchsian functions are identical with those of non-Euclidean geometry.The idea was to come in an indirect way from the work of his doctoral thesis on differential equations. His results applied only to restricted classes of functions and Poincaré wanted to generalize these results but, as a route towards this, he looked for a class functions where solutions did not exist. This led him to functions he named Fuchsian functions after Lazarus Fuchs but were later named automorphic functions. First editions and first publications of these epochmaking papers representing the discovery of ""automorphic functions"", or as Poincaré himself called them, the ""Fuchsian"" and ""Kleinian"" functions.""By 1884 Poincaré published five major papers on automorphic functions in the first five volumes of the new Acta Mathematica. When the first of these was published in the first volume of the new Acta Mathematica, Kronecker warned the editor, Mittag-Leffler, that this immature and obscure article would kill the journal. Guided by the theory of elliptic functions, Poincarë invented a new class of automorphic functions. This class was obtained by considering the inverse function of the ratio of two linear independent solutions of an equation. Thus this entire class of linear diffrential equations is solved by the use of these new transcendental functions of Poincaré."" (Morris Kline).Poincaré explains how he discovered the Automorphic Functions: ""For fifteen days I strove to prove that there could not be any functions like those I have since called Fuchsian functions, I was then very ignorant" every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds I felt them collide until pairs interlocked, so to speak, making a stable combination. By the next morning I had established the existence of a Class of Fuchsian functions, those which come from hypergeometric series" i had only to write out the results, which took but a few hours...the transformations that I had used to define the Fuchsian functions were identical with those of Non-Euclidean geometry...""‎

‎Oeuvres d'Henri Poincaré - Tome 2. Fonctions fuchsiennes‎

‎Jacques Gabay , Les Grands Classiques Gauthier-Villars Malicorne sur Sarthe, 72, Pays de la Loire, France 1995 Book condition, Etat : Bon broché, sous couverture imprimée éditeur blanche fort et grand In-8 1 vol. - 703 pages‎

‎ réimpression de l'édition Gauthier-Villars de 1916 Contents, Chapitres : Préface de Gaston Darboux, Eloge historique d'Henri Poincaré par Gaston Darboux, LXXI (71 pages), Texte, 632 pages couverture à peine jaunie, avec d'infimes traces de pliures sur les plats, sinon bon état, intérieur frais‎

‎Sur la méthode horistique de Gyldén.‎

‎(Berlin, Uppsala & Stockholm, Paris, 1905. 4to. Bound in contemporary half cloth. In ""Acta Mathematica Hrsg. von G. Mittag-Leffler."", Bd. 29. Entires issue offered. Fine and clean. Pp. 235-272. [Entire volume: (4), 433 pp.].‎

‎Second of this paper in which Poincaré comments on the Swedish astronomer work.The offered issue contain many other papers by contemporary mathematicians. ‎

‎Sur la Polarisation par Diffraction. (Premier-Secon partie). 2 vols. - [THE POINCARÉ SPHERE]‎

‎(Berlin, Uppsala & Stockholm, Paris, 1892 a. 1897. 4to. Without wrappers as extracted from ""Acta Mathematica Hrsg. von G. Mittag-Leffler."", Bd. 16 and 20, pp. 297-339 and pp. 313-355.‎

‎First edition of these importent papers on the polarization of light. The geometrical representation of different states of polarization by points on a sphere are due to Poincare. The method shown to visualize the different states of polarization is given in these two papers and the method is called Poincare's Sphere.‎

‎Sur la Polarisation par Diffraction. (Premier-Second partie). 2 vols. - [THE POINCARÉ SPHERE]‎

‎(Berlin, Uppsala & Stockholm, Paris, 1892 a. 1897. 4to. Without wrappers as extracted from ""Acta Mathematica Hrsg. von G. Mittag-Leffler."", Bd. 16 and 20. Fine and clean. Pp. 297-339 (+) pp. 313-355.‎

‎First edition of these important papers on the polarization of light. The geometrical representation of different states of polarization by points on a sphere is due to Poincare. The method shown to visualize the different states of polarization is given in these two papers and the method is called Poincare's Sphere.‎

‎Sur les Groupes des Equations linèaires.‎

‎(Stockholm, F.& G. Beier), 1885. 4to. Orig. printed wrappers (to Acta Mathematica 4:3). Extracted from ""Acta Mathematica"", Vol. 4. Pp. 201-312. Clean and fine.‎

‎First appearance of a major paper on differential equations of the first order""...the whole theory of automorphic functions was from the start guided by the idea of integrating linear differential equations with algebraic coefficients. Poincaré simultaneously investigated the local problem of linear differential equation in the neighborhood of an ""irregular"" singular point, showing for the first time how asymptotic developments could be obtained for the integrals. A little later (1884, the paper offered) he took up the question, also started by I.L. Fuchs, of the determination of all differential equations of the first order (in the complex domain) algebraic in y and y' and having fixed singular points"" his rechearches was to be extended by Picard for equations of the second order, and to lead to the spectacular results of Painlevé and his school at the beginning of the tweentieth century.""(DSB).‎

‎Sur les Intégrales irrégulieres des Equations linéaires. - [THE FORMAL THEORY OF ASYMPTOTIC SERIES]‎

‎(Berlin, Uppsala & Stockholm, Paris, 1886). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 8, pp. 295-344.‎

‎First edition. ""The full recognition of the nature of those divergent series that are useful in the representation and calculation of functions and a formal definition of those series wer achieved by Poincaré and Stieltjes independently in 1886. Poincaré called these series asymptotic while Stieltjes continued to use the term semiconvergent. Poincaré took up the subject in order to further the solution of linear differential equations. Impressed by the usefulness of divergent series in astronomy, he sought to determine which were useful and why. he succededed in islolating and formulating the essential property...Poincaré applied his theory of asymptotic series to diffrential equations, and theree are many such uses in his treatise on celestical mechanics, 'Les Methodes nouvelles de la mechanique céleste"". (Morris Kline).‎