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‎"LEIBNITZ, GOTTFRIED WILHELM., JOHANN BERNOULLI, JACOB BERNOULLI & ISAAC NEWTON - SOLVING THE BRACHISTOCHRONE PROBLEM.‎

‎Communicatio suae pariter, duarumque alienarum ad edendum sibi a Dn. Jo. Bernoulli, deinde a Dn Marchione Hospitalio communicatarum solutionum problematici curvae..descensus a Dn. Jo. Bernpulli....propositi solutione... (Leibniz). + Curvatura Radii in...‎

‎Leipzig, Grosse & Gleditsch, 1697. 4to. No wrappers. In: ""Acta Eruditorum Anno MDCXCVII"", No V, May-issue. Pp. 193-240 (entire issue offered). With titlepage to the volume 1697. Leibniz: pp. 201-205. Johann Bernoulli: pp. 206-211. Jacob Bernoulli: pp. 211-214. Newton: pp. 223-224. As usual, some leaves with browning.‎

‎First appearance of the famous issue of Acta Eruditorum in which the 4 solutions by the 4 most eminent mathematicians at the time, were printed together. There were in all 5 solutions to the posed problem, and Newton's solution was first printed in the Philosophical Transactions (January 1697) and reprinted here. The solution proposed by L'Hopital, not printed here, was not published until 1988.The brachistochrone problem was posed by Johann Bernoulli in Acta Eruditorum in June 1696. He introduced the problem as follows: ""I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise."" Johann Bernoulli and Leibniz deliberately tempted Newton with this problem. It is not surprising, given the dispute over the calculus, that Johann Bernoulli had included these words in his challenge:- ....""there are fewer who are likely to solve our excellent problems, aye, fewer even among the very mathematicians who boast that [they]... have wonderfully extended its bounds by means of the golden theorems which (they thought) were known to no one, but which in fact had long previously been published by others.""According to Newton's biographer Conduitt, he solved the problem in an evening after returning home from the Royal Mint. Newton: ... ""in the midst of the hurry of the great recoinage, did not come home till four (in the afternoon) from the Tower very much tired, but did not sleep till he had solved it, which was by four in the morning.""Newton send his solution to his friend Charles Montague and Montague published anonymously in the Transactions. Newton's solution, presented here in the Acta, is also anonymous. The episode did not please Newton, as he later wrote: ""I do not love to be dunned [pestered] and teased by foreigners about mathematical things ..."" After the competition Johann Bernoulli said "".... my elder brother made up the fourth of these (after Leibniz, himself and Newton), that the three great nations, Germany, England and France, each one of their own to unite with myself in such a beautiful search, all finding the same truth.""Struik (Edt.) ""A Source Book in Mathematics, 1200-1800, pp. 391 ff.‎

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‎"TETENS, JOHANN NICOLAI.‎

‎Formula Polynomiorum. En almindelig Formel for Coefficienterne udi Polynomier.‎

‎(Kiøbenhavn, Johan Rudolph Thiele, 1799). 4to. Without wrappers. In: ""Nye Samling af det Kongelige Danske Videnskabernes Selskabs Skrifter."" Vol. V. Pp. 253-286.‎

‎An importent mathematical memoir by the author of ""Einleitung zur Berechnung der Leibrenten und Anwartschaften"", a landmark work in actuarial science.‎

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‎"EULER, LEONHARD.‎

‎Exposition de quelques paradoxes dans le calcul integral.‎

‎(Berlin, Haude et Spener, 1758). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome XI, 1756 pp. 300-321 and 1 folded engraved plate.‎

‎First appearance of this paper in which Euler examines some peculiar differential equations that can be solved through the rather paradoxical method of integration by differentiation. He presents four such problems, which were found to all be members of the same family of differential equations, thus this presentation will focus on reworking several of these problems to make use of this generalization.Together with a paper by Eulers son (Euler le Fils - Johann Albrecht): Des Cerfs - Volans. Traduit du Latin. Pp. 322-364 and 3 folded engraved plates. - Johann here exposes his electrical theory in relation to kites, and indicates that kites were not only children's toys but had been used by the celebrated Romas in his electrical experiments.Enestroem E236.‎

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‎"LAGRANGE, JOSEPH LOUIS.‎

‎Sur la Force des ressorts pliés. (+) Sur le Probleme de Kepler. (2 Memoirs).‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers, as issued in ""Mémoires des l'Academie Royale des Sciences et Belles-Lettres"", tome XXV, pp. 167-203 a. pp. 204-233 a. 1 folded engraved plate. With titlepage to ""Classe de Mathematique.""‎

‎First appearance of these two importent memoirs, dealing with ""elastic stress"" and the Two-Body problem. In the first paper ""On the Force of bent springs"" Lagrange became the first to investigate mathematically ""elastic stress"" - the physical principles of elasticity - a problem suggested by the design of the spiral spring of a watch.""Although Lagrange's contributions to the strenght of materials are of more theoretical than practical interest, his method of generalized coordinates and generalized forces later found applications in the strenghts of materials and proved a great value in solving problems of practical importence.""(Timoshenko ""History of Strength of Materials""p. 40).The second paper offered deals with the Two-Body problem and here he comes up with the solution later called the lagrangian solution. In 1770 Lagrange read before the Academy his famous paper ""Nouvelle méthode pour résoudre les équations littérales par le moyen des séries."", the discovery of the Lagrange-Series. In the paper offered - read to the Academy on November 1, 1770 - Lagrange applies his Series to ""Kepler's Problem"".Together with 2 other papers, Jean Bernoulli ""Sur les Suites ou Sequences dans la Laotterie de Genes"", pp. 234-253 and D'Alembert ""Extrait d'une Lettre ...à M. de La Grange"", pp. 254-264.‎

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‎"CLIFFORD, W.K. - N-DIMENSIONAL SPACES.‎

‎On the Classification of Loci. Received April 8, - Read May 1878.‎

‎(London, Harrison and Sons, 1880). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1878 - Vol. 169 - Part II. Pp. 663-681.‎

‎First printing of this paper on ""Clifford-Spaces"" is considered a classich in mathematics, - being a general study of curves it is an introduction to the study of n-dimensional space.Clifford, along with Hermann Grassmann, invented what is now termed geometric algebra, a special case being the Clifford algebras named in his honor, which are used in contemporary mathematical physics. He was the first to suggest that gravitation might be a manifestation of an underlying geometrical structure of the universe, and contributed the advancement of non-Euclidean geometry developed by Bernhard Riemann and Nikolai Ivanovich Lobachevsky. In his philosophical writings he coined the expression ""mind-stuff"". Clifford argued that energy and matter are simply different types of curvature of space. These ideas later played a fundamental role in Albert Einstein's general theory of relativity.‎

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‎"CLAIRAUT, (ALEXIS CLAUDE de).‎

‎Indledning til Geometrien. Öfversat ifrån Fransyska Språket.‎

‎Stockholm, Lars Salvius, 1744. Samtidigt hpergamentsbd. (14),190,22 pp. samt 14 kobberstukne plancher. Titelvignetten og andre vignetter og 3 foldeplancher kolorerede. Et par udsnit i titelbladet, hvor gl. ejernavne bortklippet. Uden teksttab. Lidt spredte brunpletter, men ganske velbevaret.‎

‎First Swedish edition of Clairaut's renowned elementary geometry ""Élémens de géométrie"", 1741.Clairaut’s Élémens de géométrie is linked to the more liberal school. He wanted geometry to be rediscovered by beginners and therefore put together, for himself and for them, a very optimistic history of mathematical thought that reflected the concepts of his contemporaries Diderot and Rousseau. (DSB).""I intended to go back to what might have given rise to geometry"" and I attempted to develop its principles by a method natural enough so that one might assume it to be the same as that of geometry’s first inventors, attempting only to avoid any false steps that they might have had to take"" [Élémens de géométrie, preface].‎

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‎BILBERG, JOHAN. (JOHANNES JOHN JOHANN).‎

‎Elementa Geometriae Planae ac Solidae, una cum Sphaericorum doctrina atq praxi Trigonometrica. Ad ductum veterum juxta ac recentium Mathematicorum, in usum juventutis patriae peculiari methodo conscripta, necessariisq" demonstrationibus illustrata. E...‎

‎Stockholm, B.Wankijfwii, Ol...Sumptibus Joh. Siwertz, 1691. Small 8vo. Contemp. full vellum. Minor spots to covers. (8),191,(1) pp., 4 folded engraved plates, textillustrations. A few annotations in old hand. A few brownspots, but well-preserved.‎

‎Second, much expanded, edition of Bilberg's textbook for the Swedish youth, in which he creates his own method of how to learn plane and spherical geometry based both on old mathematicians (Euclid etc.) and also on modern mathematicians. The first edition, published 1687 comprised only 32 pages.Bilberg was professor in mathematics at Uppsala University and later bishop in Strängnäs.Colljin ""1600-Talet"", 79-80.‎

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‎"DIRICHLET, GUSTAV PETER LEJEUNE.‎

‎Solution d'une question relative à la théorie mathematique de la chaleur.‎

‎Berlin, G. Reimer, 1830. 4to. No wrappers. As extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 5. Band"". No backstrip. A fine and clean copy. 287-295 pp. [Entire issue: 287-318 pp].‎

‎First printing of Dirichlet's paper in which he uses his methods to simplify the treatment of a problem by Fourier (theory of Fourier series): the temperature distribution in a thin bar with given temperatures at the endpoints.‎

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‎"JACOBI, C.G.J.‎

‎Über die Vertauschung von Parameter und Argument bei der dritten Gattung der Abelschen und höhern Transcendenten (+) Über einige der Binomialreihe analoge Reihen (+) Über eine neue Methode zur Integration der hyperelliptischen Differentialgleichungen ...‎

‎Berlin, G. Reimer, 1846. 4to. No wrappers. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 32. Band, Drittes Heft"". No backstrip. A fine and clean copy. Pp. 185-196" Pp. 197-204" Pp. 220-226.‎

‎First printing of three paper's by Jacobi on differential mathematics and Abelian functions.""Most of Jacobi's fundamental research articles in the theory of elliptic functions, mathematical analysis, number theory, geometry, and me-chanics were published in Crelle's Journal fue die reine and angewandte Mathematik. With an average of three articles per volume, Jacobi was one of its most active contributors and quickly helped to establish its international famenone of his gifted students could escape his spell: they were drawn into his sphere of thought, worked along the manifold lines he sug-gested, and soon represented a ""school"". C. W. Borchardt, E. Heine, L. O. Hesse, F. J. Richelot, J. Rosenhain, and P. L. von Seidel belonged to this circle"" they contributed much to the dissemination not only of Jacobi’s mathematical creations but also of the new research-oriented attitude in university instruction. The triad of Bessel, Jacobi, and Neumann thus became the nucleus of a revival of mathematics at German universities.."" (DSB)‎

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‎"JACOBI, C.G.J.‎

‎Zur Theorie der ellipschen Functionen (+) Sur l'elimination des noeuds dans le probleme . - [JACOBI ON THE THREE-BODY PROBLEM]‎

‎Berlin, G. Reimer, 1843. 4to. No wrappers. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 26. Band, zwanzigster Heft"". No backstrip. A fine and clean copy. Pp. 93-114"" Pp. 115-131.‎

‎First printing of Jacobi's paper (Sur l'elimination ...) in which ""he showed how to reduce a general three-body problem - that of the motion of two planets about the Sun - to a problem of the motion of two fictive bodies. He subjected the masses, positions and velocities of these fictive bodies to the restrictions that their centre of gravity should be identical to that of the original system, and their accelerations derivable from the force function for that system"" the total force vive was the same, and the conservation of areas still held."" (Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences: v. 2, 1056 p.).‎

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‎"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)‎

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‎"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.‎

‎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.‎

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‎"MAUPERTUIS, (PIERRE LOUIS MOREAU DE). - LOXODROMIC NAVIGATION.‎

‎Traité de la Loxodromie tracee sur la veritable Surface de la Mer.‎

‎(Paris, L'Imprimerie Royale, 1748). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1744."". Pp. 462-774, textillustrations.‎

‎First printing of this importent paper in which Maupertuis proves that the Loxodromic line or Rhumbline is the shortest way between two points on the globe after he had proved, by the measuring results, that the globe is a spheroid. The paper is of great importence in the history of navigation.‎

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‎"FLORIJN, JACOB.‎

‎Verhandeling over het Sommeren en Interpoleren van arithmetische Serien.‎

‎Amsterdam, Hengst en Zoon, 1816. 4to. No wrappers as issued. (4),68 pp. Offprint from ""Koninklijk Nederlandsch Institut van Wetenschappen, Letterkune...""‎

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‎"JOACHIMSTHAL, FERDINAND. - PRESENTATION COPY.‎

‎De Duabus Aequationibus quarti et sexti Gradus quae in Theoria linearum et superficierum Secundi Ordinis occurrunt. Commentatio Algebraica... Universitatum Litterarum Vratislaviensi..‎

‎Berlin, Typis Reimerianis, 1856. 4to.No wrappers as issued. (2),24 pp. Some additions in pencil on the first 3 pages. Inscribed on titlepage ""Viro amicissimo Kummer/ autore"" (Ernst Eduard Kummer, the famous mathematician, was Joachimsthal's teacher).‎

‎First edition of Joachimsthal's second ""Habilitationsschrift"" published the year when he was called to Breslau as professor in mathematics.Today Joachimsthal's name is associated with ""Joachimsthal Surfaces"", which possess a family of plane lines of curvature within the planes of a pencil" the Joachimsthal theorem concerning the intersection of two surfaces in three-dimensional real Euclidean space along a common line of curvature and a theorem on the four normals to an ellipse from a point inside it.‎

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‎"FREDHOLM, IVAR.‎

‎Sur une classe d'equations fonctionnelles. - [ANTICIPATION OF HILBERT SPACES]‎

‎Stockholm, Beijer, 1903. 4to. As extracted from ""Acta Mathematica, 27. Band]. No backstrip. Fine and clean. Pp. 365-390.‎

‎First printing of Fredholm's landmark paper which is considered to be the publication which established operator theory, thereby anticipating Hilbert Spaces. David Hilbert developed the abstraction of Hilbert space in association with research on integral equations prompted by Fredholm's.‎

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‎"HILBERT, DAVID.‎

‎Über ternäre definite Formen.‎

‎Stockholm, Beijer, 1893. 4to. As extracted from ""Acta Mathematica, 17. Band]. No backstrip. Fine and clean. Pp. 169-197.‎

‎First edition. This important paper constitutes Hilbert's own version of part of the solution of his ""Mathematische Probleme"" listed at the International mathematical Congress in Paris 1900 (as problem 17) on the ""Expression of definite forms by squares"". ""....But since as I have shown, not every definite form can be compounded by addition from squares of forms, the question arises - which I have answered affirmatively for ternary forms (the paper offered here)- whether every definite form may be expressed as a quotient of sums of squares of forms....""‎

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‎"VOLTERRA, VITO.‎

‎Sur la stratification d'une masse fluide en équilibre.‎

‎Berlin, Stockholm, Paris, Beijer, 1903. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 27, pp. 105-124.‎

‎First printing of Volterra's paper on the distribution of pressure around spheres in a viscous fluid. ""Volterra’s scientific work covers the period from 1881, when he published his first papers, to 1940 when his last paper was published in the Acta of the Pontifical Academy of Sciences. His most important contributions were in higher analysis, mathematical physics, celestial mechanics, the mathematical theory of elasticity, and mathematical biometrics. His major works in these fields included the foundation of the theory of functionals and the solution of the type of integral equations with variable limits that now bear his name, methods of integrating hyperbolic parctical differential equations, the study of hereditary phenomena, optics of birefringent media, the motion of the earth’s poles and elastic dislocations of multiconnected bodies, and, in his last years, placing the laws of biological fluctuations on mathematical bases and establishing principles of a demographic dynamics that preset analogies to the dynamics of material systems."" (DSB).‎

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‎"BOHR, HARALD.‎

‎Lösung des absoluten Konvergenzproblems einer allgemeinen Klasse Dirichletscher Reihen.‎

‎[Berlin, Stockholm, Paris, Beijer, 1913] 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 36, pp. 197-240.‎

‎First printing.‎

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‎"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)‎

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‎"VOLTERRA, VITO.‎

‎Sur les vibrations lumineuses dans les milieux biréfringents.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.‎

‎First printing of Volterra's paper on the vibrations of light in a birefringence media.‎

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‎"MARKOFF, ANDRÉ.‎

‎Recherches sur un cas remarquable d’epreuves dependantes. [Translated from the Russian: Issledovanie zamechatel’nogo sluchaya zavisimyh ispytanij].‎

‎[Berlin, Stockholm, Paris, Beijer, 1910]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 33, pp. 87-104.‎

‎First translation of Russian mathematician Markoff's important paper. He is best known for his work on theory of stochastic processes. A primary subject of his research later became known as Markov chains.‎

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‎"GYLDÉN, HUGO.‎

‎Nouvelle recherches sur les séries employées dans les théories des planétes.‎

‎Berlin, Stockholm, Paris, Beijer, 1893. 4to. Without wrappers (but with titlepage and table of contents), as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 17 pp. (4), 168.‎

‎First printing of Gyldén's paper on planetary movements. Hugo Gyldén was the most impotant swedish astronomer during the 19th century and he initiated celestial mechanics in Sweden.‎

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‎"PINCHERLE, SALVATORE.‎

‎Sur la géneration de systèmes récurrents au moyen d'une équation linéaire différentielle.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892-93]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 341-363.‎

‎First printing of Italian mathematician Pincherle's paper on linear differential equations.Salvatore Pincherle (1853 -1936) was an Italian mathematician. He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: ""Unione Matematica Italiana""), and was president of the Third International Congress of Mathematicians. The Pincherle derivative is named after him.‎

Référence libraire : 45848

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€107.44 Acheter

‎"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

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‎"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

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€201.45 Acheter

‎"BOREL, EMILE.‎

‎Sur les zéros des fonctions entieres.‎

‎[Berlin, Stockholm, Paris, Beijer, 1897]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 20. Fine and clean. Pp. 357-396.‎

‎First printing.‎

Référence libraire : 45851

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€67.15 Acheter

‎"KOCH, HELGE VON.‎

‎Sur une application des déterminants infinis à la théorie des équations différentielles linéaires (+) Sur les déterminants infinis et les équations différentielles linéaires.‎

‎[Berlin, Stockholm, Paris, Beijer, 1891 - 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 15 and 16. Fine and clean. Pp. 53-63" Pp. 217-295.‎

‎First printing of Koch's two paper which together constitute his doctoral thesis. Von Koch is known principally for his work in the theory of infinitely many linear equations and the study of the matrices derived from such infinite systems. He also did work in differential equations and in the theory of numbers. (DSB).‎

Référence libraire : 45853

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€161.16 Acheter

‎"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

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€2,686.00 Acheter

‎"CANTOR, G.‎

‎Fondements d'une théorie générale des ensembles (+) Sur divers théorémes de la théorie des ensembles de points situs - dans un espace continu a n dimensions. - [SET THEORY]‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1883]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 2. Fine and clean. Pp. 381-414.‎

‎First French translation (and translation in general) of Cantor's fifth, thus most important, paper in his series of papers which founded set theory. (The first mentioned).It contained Cantor's reply to the criticism of the first four papers and showed how the transfinite numbers were a systematic extension of the natural numbers. It begins by defining well-ordered sets. Ordinal numbers are then introduced as the order types of well-ordered sets. Cantor then defines the addition and multiplication of the cardinal and ordinal numbers. In 1885, Cantor extended his theory of order types so that the ordinal numbers simply became a special case of order types. It was later published as a separate monograph.The concept of the existence of an infinity was an important shared concern within the realms of mathematics, philosophy and religion. Preserving the orthodoxy of the relationship between God and mathematics was long a concern of Cantor's. He directly addressed this relationship between these disciplines in the introduction to the present paper, where he stressed the connection between his view of the infinite and the philosophical one. To Cantor, his mathematical views were closely linked to their philosophical and theological implications-he identified the Absolute Infinite with God and he considered his work on transfinite numbers to have been directly communicated to him by God, who had chosen Cantor to reveal them to the world.‎

Référence libraire : 45855

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‎"CANTOR, G.‎

‎Sur une propriété du systéme de tous les nombres algébriques réels. [Translated from the German: Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen]. - [FIRST CONTRIBUTION TO SET THEORY AND THE BIRTH OF THE THEORY OF THE TRANSFINITE]‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1883]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 2. Fine and clean. Pp. 305-328.‎

‎First French [and general] translation of Cantor's famous and exceedingly influential paper which contains the first proof that the set of all real numbers is uncountable"" also contains a proof that the set of algebraic numbers is denumerable. ""This article is Cantor's first published contribution to the theory of sets. The deep and epoch-making result of the paper is not the easy theorem alluded to in the title - the theorem that that the class of real algebraic numbers is countable - but rather the proof, in 2, that the class of real numbers is not countable [...]. And that marks the start of the theory of the transfinite. [Ewald, Pp. 839-40].""The first published writing on set theory [the present paper], contained more than the title indicated, including not only the theorem on algebraic numbers but also the one on real numbers, in Dedekind's simplified version, which differs from the present version in that today we use the ""diagonal process,"" then unknown"" (DSB)‎

Référence libraire : 45857

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€429.76 Acheter

‎"HILBERT, DAVID.‎

‎Ueber die reellen Züge algebraischer Curven.‎

‎Leipzig, B.G. Teubner, 1891. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 38. Band. 1. Heft."".(Entire issue offered). Titlepage to Bd. 38. IV,160 pp. a. 1 folded plate. Hilbert's paper: pp. 115-138.‎

‎First apperance of an importent paper on algebraic geometry.The issue contains also Felix Klein ""Ueber Normierung der linearen Differentialgleichungen zweiter Ordnung"", pp. 144-152.‎

Référence libraire : 45868

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€87.29 Acheter

‎"HILBERT, DAVID. - HABILITATIONS THESIS.‎

‎Ueber einen allgemeinen Gesichtspunkt für invariantentheorietische Untersuchungen im binären Formengebiete.‎

‎Leipzig, B.G. Teubner, 1887. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 28. Band. 3. Heft."". (Entire issue offered). Pp. 309-456. Hilbert's paper: pp. 381-446.‎

‎This is Hilbert's ""Habilitationsschrift"", a fundamental work on algebraic invariants.‎

Référence libraire : 45870

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€161.16 Acheter

‎"ZORAWSKI, KASIMIR.‎

‎Über biegungsinvarianten eine anwendung der Lie'schen gruppentheorie.‎

‎Berlin, Stockholm, Paris, F. & G. Beijer, 1892-93. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16. Including the title page. Fine and clean. (6), 64 Pp.‎

‎First printing of Zorawski's important paper which is one of the very first responses to Sophus Lie's group theory. ""One of the first mathematicians who reacted to Lie's newly introduced concept was Kasimir Zorawaski, a polish scientist who worked in Warsaw. As examples of differential invariants, Zorawski mentioned Gauss curvature, Beltrami operators, and Minding's geodesic curvature. Similar to Lie, he asked for the number of invariants of different orders. From then on, two concepts played a major role within the theory of differential calculus, initiated by Ricci, and the group concept that was introduced by Lie and improved by Zorawski."" (Earman, The Attraction of gravitation: new studies in the history of general relativity, P. 229)‎

Référence libraire : 45900

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€161.16 Acheter

‎"VOLTERRA, VITO.‎

‎Sur les équations intégro-différentielles et leurs applications.‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1912]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 35. Fine and clean. Pp. 295-356.‎

‎First printing.‎

Référence libraire : 45901

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€67.15 Acheter

‎"GYLDÉN, HUGO.‎

‎Untersuchungen über die Convergenz der Reihen, welche zur Darstellung der Coordinaten der Planaten angewendet.‎

‎Berlin, Stockholm, Paris, Beijer, 1887. 4to. With the original wrappers in ""Acta Mathematica, 9:3. Band]. No backstrip. Fine and clean. Pp. 185-294. [Entire issue: Pp. 185-320]‎

‎First printing of Gyldén's paper on planetary coordinates. Hugo Gyldén was the most impotant swedish astronomer during the 19th century and he initiated celestial mechanics in Sweden.‎

Référence libraire : 45903

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€107.44 Acheter

‎"ZELLER, CHR..‎

‎Kalender-Formeln. - [ZELLER'S CONGRUENCE]‎

‎Berlin, Stockholm, Paris, Beijer, 1886. 4to. With the original wrappers in ""Acta Mathematica, 9:2. Band]. No backstrip. Fine and clean. Pp. 131-36. [Entire issue: Pp. 105-184].‎

‎First printing of Zeller's paper important paper in which Zeller's congruence is presented It is an algorithm to calculate the day of the week for any Julian or Gregorian calendar date.‎

Référence libraire : 45904

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€201.45 Acheter

‎"HERMITE, CHARLES.‎

‎Sur quelques consequences arithmetiques des formules de la theorie des fonctions elliptiques.‎

‎Berlin, Stockholm, Paris, Beijer, 1885. 4to. With the original wrappers in ""Acta Mathematica, 5:4. Band]. No backstrip. Fine and clean. Pp. 297-330. [Entire issue: Pp. 297-408, 83-123 + 2 folded plates.].‎

‎First printing of Hermite's paper on the arithmetical consequences of the theory of elliptic functions. Charles Hermite (1822-1901), French mathematician, made significant contributions to pure mathematics, and especially to number theory and algebra. In 1858 he solved the equation of the fifth degree by elliptic functions, and in 1873 he proved that e (the base of natural logarithms) is transcendental. The legacy of his work can be shown in the large number of mathematical terms which bear the adjective 'Hermitian'. The present issue also contain the following paper:Fiedler, W.: Über die Durchdringung gleichseitiger Rotationshyperboloide von parallelen Axen (mit zwei Tafeln).‎

Référence libraire : 45905

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€134.30 Acheter

‎"POINCARÉ, HENRI.‎

‎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...""‎

Référence libraire : 45910

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€604.35 Acheter

‎"LAGRANGE, (LA GRANGE), JOSEPH LOUIS. - LAGRANGE'S CONTINUED FRACTIONS.‎

‎Additions au Mémoire Sur la Résolution des Équations Numériques.‎

‎(Berlin, Haude et Spener, 1770). 4to. Clean and fine without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Tome XXIV, pp. 111-180. With titlepage to ""Classe de Mathematique"".‎

‎First appearance of Lagrange's importent paper in which he developed continous fraction solutions of equations.‎

Référence libraire : 45924

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‎"CAYLEY, (ARTHUR).‎

‎On the Sextactic Points of a Plane Curve. Received November 5, - Read december 22, 1864.‎

‎(London, Taylor and Francis, 1865). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1865 - Vol. 155 - Part II. Pp. 545-578.‎

‎First printing of an importent paper. Cayley was the to determine the sextic curve.‎

Référence libraire : 45984

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€100.72 Acheter

‎"CAYLEY, (ARTHUR).‎

‎On Tschirnhausen's Transformation. Received November 7, - Read December 5, 1861.‎

‎(London, Taylor and Francis, 1862). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1862 - Vol. 152 - Part I. Pp. 561-578.‎

‎First printing.‎

Référence libraire : 45985

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€67.15 Acheter

‎"CANTOR, G.‎

‎Sur les séries trigonométriques (transl. of Über trigonometrische Reihen) (+) Extension d'un théoréme de la théorie des séries trigonométriques.‎

‎Berlin, Stockholm, Paris, Beijer, 1883. 4to. As extracted from ""Acta Mathematica, 2. band."", Clean and fine. Pp. 329-348.‎

‎First transation of Cantor's important papers on trigonometric series.‎

Référence libraire : 46012

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€107.44 Acheter

‎"PONCELET, J. V. [JEAN-VICTOR].‎

‎Sur la valeur approchée linéaire et rationnelle des radicaux de la forme...‎

‎Berlin, G. Reimer, 1835. 4to. In ""Journal für die reine und angewandte Mathematik, 13 Band, 4. Heft, 1835"". Without backstrip. Fine and clean. [Poncelet:] Pp. 277-291. [Entire issue: pp. IV, 54 pp.].‎

‎First printing of Poncelet's paper which introduced the fundamentals of approximation theory.‎

Référence libraire : 46014

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‎"CAYLEY, (ARTHUR)‎

‎A Memoir on the Transformation of Elliptic Functions. Received November 14, 1873, - Read January 8, 1874.‎

‎(London, Taylor and Francis, 1874). 4to. No wrappers as extracted from ""Philosophical Transactions"", Vol. 164. Pp. 397-456.‎

‎First edition. The subject treated here was the substance of his only published book ""Tretise on Elliptic Functions"", published 1876.‎

Référence libraire : 46018

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‎"BERNOULLI, JOANNES.‎

‎Demonstratio Methodi Analyticae, qua usus est pro determinanda aliqua Quadratura exponentiali per seriem.‎

‎Leipzig, Grosse & Gleditsch, 1737. 4to. In: ""Nova Acta Eruditorum Anno MDCCXXXVII"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 82-88. [Entire volume: Pp. (4), 555, (33) + 7 engraved plates.].‎

‎First printing of Bernoulli's paper on the quadratura.The volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Référence libraire : 46046

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‎"COUSIN, P.‎

‎Sur les fonctions triplement périodiques de deux variables.‎

‎Berlin, Stockholm, Paris, Beijer, 1910. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 10. Including the title page. Fine and clean. Pp. 105-232.,‎

‎First printing of Cousin's extensive paper on periodic functions of two variables.‎

Référence libraire : 46047

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‎"POINCARÉ, HENRI.‎

‎Theorie des Groupes fuchsiens. - [THE DISCOVERY OF AUTOMORPHIC FUNCTIONS]‎

‎Berlin, Stockholm, Paris, F. & G. Beijer, 1882. Large4to. As extracted from ""Acta Mathematica"", no backstrip. With title-page and front free end-paper. In ""Acta Mathematica"", volume 1. Title pages with library stamp. A fine and clean copy. Pp. (6), 62.‎

‎First publication of this groundbreaking paper which became Poincaré first paper in his much celebrated and famous six-paper series 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.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 : 46049

Livre Rare Book

Herman H. J. Lynge & Son
Copenhagen Denmark Dinamarca Dinamarca Danemark
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€537.20 Acheter

‎BRIOT, C. & BOUQUET, J.C.‎

‎Lecons de Géométrie analytique. Dix-Huitième Édition. Revueet annotée par M. Appell.‎

‎Paris, Delagrave, (1904). Solid hcloth. Gilt titlelabel on spine. (6),802 pp., textfigs.‎

Référence libraire : 46096

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‎LANCZOS, CORNELIUS.‎

‎Linear Differential Operators.‎

‎London, N.Y. etc., D. van Nostrand Comp., (1961). Orig. full cloth. XVI,564 pp. Free endpapers removed.‎

Référence libraire : 46103

Livre Rare Book

Herman H. J. Lynge & Son
Copenhagen Denmark Dinamarca Dinamarca Danemark
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€40.29 Acheter

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