‎Mathématiques‎

‎WOLFF, CHRISTIAN.‎

‎Elementa Matheseos Universae. Editio Nova priori multo auctior et correctior.Tomus I-II (von 5).(I. Qui Commentationem de Method Mathematica, Arithmeticam, Geometriam, Trigonometriam Planam, et Analysin tam Finitorum, quam Infinitorum, comlectitur. - ...‎

‎Halæ Magdeburgicæ, 1730-33. 4to. 2 contemp. full calf. Wear to the gilt lettering on spines. Spine ends worn. Part of leather at upper compartment on vol. one, gone. Some wear to spines. Engraved portrait of Wolff. First titlepage in red/black. (22),678(8),506 pp. and 61 (31 + 30) folded engraved plates.‎

书商的参考编号 : 45332

‎"CLAIRAUT, (ALEXIS CLAUDE de).‎

‎Indledning til Geometrien. Öfversat ifrån Fransyska Språket.‎

‎Stockholm, Lars Salvius, 1744. Samtidigt hldrbd. Øverste rygfelt med bortslid af noget af skindet. Uden forreste friblad. (14),190,22 pp. samt 14 kobberstukne plancher.‎

‎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].‎

书商的参考编号 : 45459

‎"RAILLIER DES OURMES. - THE MATHEMATICS OF THE MAGIC CUBE.‎

‎Mëmoire sur les Quarrés Magiques.‎

‎(Paris, L'Imprimerie Royale, 1763). 4to. No wrappers.Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome IV. Pp. 196-246 a. many textfigs. A very faint dampstain to outer margin.‎

书商的参考编号 : 45504

‎"BOSSUT, (CHARLES)‎

‎Usages de la Differentiation des Parametres, pour la Solution de plusieurs Problèmes de laa méthode inverse des Tangentes.‎

‎(Paris, Imprimerie Royale, 1755). 4to. Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome II. Pp. 435-451 a. 1 folded engraved plate.‎

‎First printing of Busset's first mathematical paper.""Bossut was one of a very few whom d’Alembert took as students, and as such he was admitted as a correspondant to the Académie des Sciences on 12 May 1753" subsequently, he rose to géométre, mécanicien, and mathématicien. In 1761, 1762, and 1765 he won or shared prizes given by the Academy for memoirs on mechanics applied to the operation of ships and on the resistance of the ether in planetary motions. He won additional prizes for his mechanics memoirs from the academies of Lyons and Toulouse, and was elected to the scientific academies of Bologna, Turin, and St. Petersburg. In 1775 he participated with d’Alembert and Condorcet in a well known series of experiments on fluid resistance. Never more than a minor mathematician or physicist, Bossut is nevertheless one of the important figures in the history of physics and engineering education. (DSB).‎

书商的参考编号 : 45595

‎"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.‎

书商的参考编号 : 45644

‎"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.‎

书商的参考编号 : 45702

‎"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.‎

书商的参考编号 : 45712

‎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.‎

书商的参考编号 : 45770

‎"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)‎

书商的参考编号 : 45783

‎"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)‎

书商的参考编号 : 45787

‎"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.‎

书商的参考编号 : 45802

‎"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.‎

书商的参考编号 : 45811

‎"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....""‎

书商的参考编号 : 45838

‎"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.‎

书商的参考编号 : 45840

‎"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.‎

书商的参考编号 : 45842

‎"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.‎

书商的参考编号 : 45845

‎"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.‎

书商的参考编号 : 45849

‎"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.‎

书商的参考编号 : 45851

‎"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...""‎

书商的参考编号 : 45854

‎"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)‎

书商的参考编号 : 45857

‎"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.‎

书商的参考编号 : 45870

‎"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.‎

书商的参考编号 : 45901

‎"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.‎

书商的参考编号 : 45904

‎"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...""‎

书商的参考编号 : 45910

‎"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.‎

书商的参考编号 : 45984