‎Mathématiques‎

‎"PONCELET, J. V. [JEAN-VICTOR].‎

‎Application de la méthode des moyennes à la transformation, au calcul numériques et à la détermination des limites du reste des séries.‎

‎Berlin, G. Reimer, 1835. 4to. In ""Journal für die reine und angewandte Mathematik, 13 Band, 1. Heft, 1835"". In the original printed wrappers, without backstrip. Fine and clean. [Poncelet:] 54 pp. [Entire issue: pp. IV, 54 pp.].‎

‎First printing of this extensive paper by the French mathematician on number theory and infinite series. ""Poncelet's years of study led to his personal belief that geometry could be founded on a series of fundamental principles as general as those on which algebra was based. He carried this belief forward by suggesting that since every straight line and plane extend to a point of infinity, then any new points on a line would be the same for specific parallel lines (or planes). At this time in mathematical history, it was accepted that all infinite elements of space were supposed to lie on the infinite plane of space, known as the projective plane.Early on, Poncelet's colleagues were extremely reluctant to accept his ideas and resulting theories. However, as time went on, several prominent German mathematicians not only accepted them but contributed to the emerging new science. Among those who recognized Poncelet's breakthrough in the field were Karl Georg Christian von Staudt, Felix Klein, Georg Cantor, Richard Dedekind, and Moritz Pasch. They were later joined by Otto Stolz of Austria who made his own contributions to the field.He died on December 22, 1867, in Paris without the recognition he deserved for his brilliant contributions to the world of numbers. His Treatise on the Projective Properties of Figures (1822) is still regarded as the pioneer work in the field."" (Schlager, Science and its Times, P. 261).‎

Référence libraire : 45145

‎"POINCARÉ, H. (+) VITO VOLTERRA.‎

‎L'oeuvre mathématique de Weierstrass (+) Sur les Propriétes du potentiel et sur les Fonctions Abéliennes [Poincaré] (+) Sur la Théorie des Variations des Latitudes [Poincaré].‎

‎Berlin, Stockholm, Paris, Beijer, 1899. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 22, 1899. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 1-18" Pp. 89-178" Pp. 201-358.[Entire volume: (4), 388, 2 pp].‎

‎First printing of these important papers: POINCARÉ: First edition. ""As soon as he came into contact with the work of Riemann and Weierstrass on Abelian Functions and algebraic geometry, Poincaré was very much attracted by those fields. His papers on these subjects occupy in his complete works as much space as those on automorphic functions, their dates ranging from 1881 to 1911. One of his main ideas in these papers is that of ""reduction"" of Abelian functions. Generalizing particular cases studied b Jacobi, Weierstrass, and Picard, Poincaré proved the general ""complete reducibility"" theorem...""(DSB).VOLTERRA: First edition. As the north and south poles, instead of being fixed points on the earth's surface, wander round within a circle of ab. 5o ft. in diameter, the result is a variability of terrestial latitudes generally. Volterra gives an elaborate mathematical analysis of these yearly fluxtuations.‎

Référence libraire : 49640

‎"POINCARÉ, HENRI.‎

‎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).‎

Référence libraire : 45850

‎"POINCARÉ, H. [DAVID HILBERT].‎

‎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.‎

Référence libraire : 49614

‎"POINCARÉ, H.‎

‎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)‎

Référence libraire : 45841

‎"POINCARÉ, H.‎

‎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)‎

Référence libraire : 49622

‎"POINCARÉ, HENRI.‎

‎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).‎

Référence libraire : 39132

‎"POINCARÉ, HENRI.‎

‎Sur une Forme nouvelle des Équations du Probleme des trois Corps. - [THE HAMILTON PRINCIPLE]‎

‎(Berlin, Uppsala & Stockholm, Paris, Almqvist & Wiksell, 1897). 4to. No wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 21, pp. 83-97.‎

‎First edition. In this paper 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.‎

Référence libraire : 39134

‎"POINCARÉ, HENRI.‎

‎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).‎

Référence libraire : 41900

‎"POINCARÉ, H.‎

‎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)‎

Référence libraire : 45787

‎"POINCARÉ, HENRI.‎

‎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.‎

Référence libraire : 45849

‎"POINCARÉ, H.‎

‎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.‎

Référence libraire : 46182

‎"POINCARÉ, HENRI (+) GEORG CANTOR.‎

‎Sur les Fonctions Uniformes qui se reproduisent par des Substitutions Linéaires (+) Ueber ein neues und allgemeines Condensationsprincip der Singularitäten von Functionen.‎

‎Leipzig, B.G. Teubner, 1882. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 37, 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Fine and clean. Pp. 182-228. [Entire volume: IV, 604 pp.].‎

‎First printing of Poincaré's paper on his comprehensive theory of complex-valued functions which remain invariant under the infinite, discontinuous group of linear transformations. In 1881 Poincaré had published a few short papers with some initial work on the topic, and in the 1881, Klein invited Poincaré to write a longer exposition of his results to Mathematische Annalen which became the present paper. This, however, turned out to be an invitation to at mathematical dispute:""Before the article went to press, Klein forewarned Poincaré that he had appended a note to it in which he registered his objections to the terminology employed therein. In particular, Klein disputed Poincaré's decision to name the important class of functions possessing a natural boundary circle after Fuch's, a leading exponent of the Berlin school. The importance he attached to this matter, however, went far beyond the bounds of conventional priority dispute. True, Klein was concerned that his own work received sufficient acclaim, but the overriding issue hinged on whether the mathematical community would regard the burgeoning research in this field as an outgrowth of Weierstrassian analysis or the Riemannian tradition."" Parshall. The Emergence of the American Mathematical Research Community. Pp. 184-5.The issue contains the following important contributions by seminal mathematicians:1. Klein, Felix. Ueber eindeutige Functionen mit linearen Transformationen in sich. Pp. 565-68.2. Picard, Emile. Sur un théorème relatif aux surfaces pour lesquelles les coordnnées d´un point quelconque s´experiment par des fonctions abéliennes de deux paramètres. Pp. 578-87.‎

Référence libraire : 47185

‎"POINCARÉ, H.‎

‎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).‎

Référence libraire : 49616

‎"POINCARÉ, HENRI.‎

‎Theorie des Groupes fuchsiens (+) Mémoire sur les Fonctions fuchsiennes (+) Sur les Fonctions de deux Variables (+) Mémoire sur les groupes kleinéens (+) Sur les groupes des équations linéaires (+) Mémoire sur les fonctions zétafuchsiennes. - [THE DISCOVERY OF AUTOMORPHIC FUNCTIONS]‎

‎Berlin, Stockholm, Paris, F. & G. Beijer, 1882-84. Large4to. As extracted from ""Acta Mathematica"", no backstrip. With title-page and the original wrappers. (except for paper no. 3 and 5 which only has the title page). In ""Acta Mathematica"", volume 1-5. Title pages with library stamp. Internally clean and fine. Vol. I, pp. 1-62" Pp. 193-294 Vol. II, pp. 97-113 Vol. III. pp. 49-92 Vol. IV pp. 201-312" Vol. V pp. 209-278.‎

‎First publication of these groundbreaking papers which together constitute 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. (See Walter, Poincaré, Jules Henri French mathematician and scientist).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...""‎

Référence libraire : 45854

‎"POISSON, (SIMÉON-DENIS). - THE PREAMBLE.‎

‎Théorie mathématique de la Chaleur. (Cet article est le préambule d'un ouvrage actuellement sous presse, et qui paraitra incessamment).‎

‎(Berlin, G. Reimer, 1834). 4to. No wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. XII. Pp. 258-262.‎

‎First apperance of Poisson's preamble to his famous work ""Théorie mathématique de la Chaleur"", published 1835. “Poisson scored a point in this work by demonstrating how the conductibility of heat in the interior of bodies, far from being contained in the notion of flux as Fourier had held, must be derived from an absorption coefficient that restores a neglected functional dimension. It was in this area that … Poisson’s mechanical model for conduction of heat was the most fruitful. That conception enabled Poisson to understand on the molecular scale the complete and correct equation for radiation of heat” (DSB)‎

Référence libraire : 47207

‎"POCHHAMMER, LEO.‎

‎Zur Theorie der Euler'schen Integrale. - [POCHHAMMER CONTOUR]‎

‎Leipzig, B. G. Teubner, 1890. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 35., 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Very fine and clean. Pp. 495-526. [Entire volume: IV, 604 pp.].‎

‎First publication of the paper which named the ""Pochhammer contour"". Pochhammer contour is a contour in the complex plane with two points removed, used for contour integration.Camille Jordan published in 1887 a paper introducing the concept. In 1890 Porchhammer expanded his theories in the present paper.‎

Référence libraire : 47128

‎"POCHHAMMER, LEO.‎

‎Zur Theorie der Euler'schen Integrale. - [POCHHAMMER CONTOUR]‎

‎Leipzig, B. G. Teubner, 1890. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 35., 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Very fine and clean. Pp. 495-526. [Entire volume: IV, 604 pp.].‎

‎"POINCARE, H. (HENRI). - THE DISCOVERY OF AUTOMORPHIC FORMS.‎

‎Sur les fonctions fuchsiennes. (+) Sur les fonctions.... Note. (+) Sur les fonctions.... Note.‎

‎(Paris: Gauthier-Villars), 1882. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences"", Vol 94, No 4 + 15 + 17. Pp. (149-) 184, pp. (997--) 1068 a. pp. (1139-) 1214. (3 entire issues offered). Poincare's papers: pp. 163-168, 1038-1042 a. 1166-67.‎

‎"POINCARÉ, H.‎

‎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.‎

‎"POINCARÉ, H.‎

‎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].‎

‎"POINCARÉ, H.‎

‎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].‎

‎"POINCARÉ, H.‎

‎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.‎

‎"POINCARÉ, H. (+) VITO VOLTERRA.‎

‎L'oeuvre mathématique de Weierstrass (+) Sur les Propriétes du potentiel et sur les Fonctions Abéliennes [Poincaré] (+) Sur la Théorie des Variations des Latitudes [Poincaré].‎

‎Berlin, Stockholm, Paris, Beijer, 1899. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 22, 1899. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 1-18" Pp. 89-178 " Pp. 201-358.[Entire volume: (4), 388, 2 pp].‎

‎"POINCARÉ, HENRI (+) FELIX KLEIN.‎

‎Sur les Fonctions Uniformes qui se reproduisent par des Substitutions Linéaires (+) [Klein's introduction to the present paper].‎

‎Leipzig, B.G. Teubner, 1882. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet 1882 durch Rudolf Friedrich Alfred Clebsch. XIX. [19] Band. 4. Heft."" Entire issue offered. [Poincaré:] Pp. 553-64. [Entire issue: Pp. 435-594].‎