‎Mathématiques‎

‎"JACOBI, C. G. J.‎

‎Observatio arithmetica de numero classium divisorum quadraticorum formae yy + Azz, designante A numerum primum formae 4n+3.‎

‎[Berlin, G. Reimer, 1832]. 4to. Without wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 1832, Pp. 189-192.‎

‎First appearance of Jacobi's very first paper on class number formula. The search for a class number formula probably began with Gauss, but the first formula in print was proposed by Jacobi (1832). He conjectured it on the evidence of some results of Cauchy in the theory of circle division, and his own brilliant extrapolation (or einduction"" as they called it then) from numerical results. Jacobi's formula was correct, but by no means proved by him. In a memorial speech for Jacobi, Dirichlet later said ""I believe it should be mentioned, regarding the previously unknown origin of this result, that Jacobi's communication is a noteworthyexample of shrewd induction, even though it is not possible to base a rigorous proof on circle division" it appears necessary to use essentially different principles, involving integral calculus and the theory of series, which were only later introduced into the subject. (Dirichlet, 1852).‎

書籍販売業者の参照番号 : 49762

‎"JACOBI, C. G. J.‎

‎Ueber die integration der partiellen differentialgleichungen erster ordnung.‎

‎Berlin, G. Reimer, 1832. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 1832, band 8"". Without backstrip. Fine and clean. Pp. 317-329 [Entire extract: Pp. 307-346 ].‎

‎First appearance of Jacobi's paper on the integration of partial differential equations of first order.""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 fame. Yet his tireless occupation with research did not impair his teaching. On the contrary- never satisfied to lecture along trodden paths, Jacobi presented the substance of his own investigations to his students. He would lecture up to eight or ten hours a week on his favorite subject, the theory of elliptic functions, thus demanding the utmost from his listeners. He also inaugurated what was then a complete novelty in mathematics-research seminars-assembling the more advanced students and attracting his nearest colleagues."" (DSB).‎

書籍販売業者の参照番号 : 49049

‎"JACOBI, C. G. J.‎

‎Ueber eine besondere Gattung algebraischer Functionen, die aus der Entwicklung der Function (1 - 2xz + z2)1/2 entstehen. - [RODRIGUES'S FORMULA]‎

‎Berlin, G. Reimer, 1827. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 2. Band, 1827""., without backstrip. Fine and clean. [Gudermann:] Pp. 223-226. [Entire volue: Pp. 198-292 + two folded plates].‎

‎First printing of Jacobi's accouncement of the Rodrigues's formula (formerly called the Ivory-Jacobi formula). Rodrigues's formula is a formula for Legendre polynomials independently introduced by Olinde Rodrigues in 1816 and Sir James Ivory in 1824 and Carl Gustav Jacobi in 1827 [The present]. The name ""Rodrigues formula"" was introduced by Heine in 1878, after Hermite pointed out in 1865 that Rodrigues was the first to discover it, and is also used for generalizations to other orthogonal polynomials.‎

書籍販売業者の参照番号 : 47282

‎"JACOBI, C. G. J.‎

‎Untersuchungen über die Differentialgleichung der hypergeometrischen Reihe. - [JACOBI POLYNOMIALS]‎

‎Berlin, Georg Reimer, 1859. 4to. No wrappers. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 56, 1859. Entire volume offered. Fine and clean. 149-65 pp. [Entire volume: IV, 375, (1) pp.].‎

‎First printing of Jacobi's paper (published posthumously) in which Jacobi polynomials was first introduced. Jacobi polynomials (occasionally called hypergeometric polynomials) are a class of classical orthogonal polynomials. The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials.‎

書籍販売業者の参照番号 : 49768

‎"JACOBI, C. G. J.‎

‎Über die Abbildung eines ungleichaxigen Ellipsoids auf einer Ebene, bei welcher die kleinsten Theile ähnlich bleiben.‎

‎Berlin, G. Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 59. Band, 1861"". Without backstrip. Fine and clean. [Jacobi:] Pp. 74-88.‎

‎First printing.‎

書籍販売業者の参照番号 : 48051

‎"JACOBI, C. G. J.‎

‎Über die Pfaffsche Methode, eine gewöhnliche lineare Differentialgleichung zwischen 2n Variabein durch ein System von n Gleichungen zu integriren.‎

‎Berlin, G. Reimer, 1832. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 1832, band 8"". Without backstrip. Fine and clean. Pp. 347-57 [Entire extract: Pp. 347-384 ].‎

‎First appearance of Jacobi's paper on the Pfaffian method. ""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 fame. Yet his tireless occupation with research did not impair his teaching. On the contrary- never satisfied to lecture along trodden paths, Jacobi presented the substance of his own investigations to his students. He would lecture up to eight or ten hours a week on his favorite subject, the theory of elliptic functions, thus demanding the utmost from his listeners. He also inaugurated what was then a complete novelty in mathematics-research seminars-assembling the more advanced students and attracting his nearest colleagues."" (DSB).‎

書籍販売業者の参照番号 : 49048

‎"JACOBI, C.G.J.‎

‎De functionibus ellipticis commentatio.‎

‎(Berlin, G. Reimer, 1829). 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 4. Jacobi's paper: pp. 371-390.‎

‎First printing of a key memoir in the establishment of ""Elliptic Functions"". The acknowledged founders of the theory of ""Elliptic Functions"" are Abel and Jacobi. Both had arrived at the key idea of working with inverse functions of the elliptic integrals, an idea Abel had since 1823. Jacoby next gave proof of the results he had published in 1827 ( a paper published in ""Astronomische Nachrichten"" in several articles in Crelle's Journal for the years 1828-30, -the offered paper is one of these.""The most celebrated results of his research were those in elliptic functions, published in 1829, which brought him the praise of Legendre.""(Boyer). The offred paper was incorporated in Jcobi's main work ""Fundamenta nova theoriae functionum ellipticarum"", published 1829.‎

書籍販売業者の参照番号 : 41615

‎"JACOBI, C.G.J.‎

‎De functionibus ellipticis commentatio. - [ELLIPTIC FUNCTIONS]‎

‎(Berlin, G. Reimer, 1829). 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 4. Band"". No backstrip. A fine and clean copy. [Jacobi:] pp. 371-390. [Entire issue: Pp. 311-422 + 1 folded plate].‎

‎First printing of a key memoir in the establishment of ""Elliptic Functions"". The acknowledged founders of the theory of ""Elliptic Functions"" are Abel and Jacobi. Both had arrived at the key idea of working with inverse functions of the elliptic integrals, an idea Abel had since 1823. Jacoby next gave proof of the results he had published in 1827 ( a paper published in ""Astronomische Nachrichten"" in several articles in Crelle's Journal for the years 1828-30, -the offered paper is one of these.""The most celebrated results of his research were those in elliptic functions, published in 1829, which brought him the praise of Legendre.""(Boyer). The offred paper was incorporated in Jcobi's main work ""Fundamenta nova theoriae functionum ellipticarum"", published 1829. Selvom‎

書籍販売業者の参照番号 : 45095

‎"JACOBI, C.G.J.‎

‎De motu puncti singularis. - [SOLUTION TO THE INVERSE-SQUARE PROBLEM]‎

‎Berlin, G. Reimer, 1842. 4to. No wrappers. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 24. Band, erstes Heft"". No backstrip. A fine and clean copy. Pp. 5-27. [Entire issue: (6), 99 pp.].‎

‎First printing of this important memoire by Jacobi in which Jacobi presented his solution to the inverse-square problem. ""In a memoir written in Latin, Jacobi published in 1842 a simple, concise, and elegant solution of the inverse-square problem. This note argues that Jacobi's solution has not attracted the attention that it deserves and that it should prove valuable to teachers and students in introductory mechanics courses. A translation of the excerpt in which Jacobi describes his solution is given, and the method is then recast in the now more familiar language of vectors."" (Gauthier)‎

書籍販売業者の参照番号 : 47254

‎"JACOBI, C.G.J.‎

‎De resolutione aequationum per series infinitas.‎

‎(Berlin, G. Reimer, 1830). 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 6. Band"". No backstrip. A fine and clean copy. [Jacobi:] pp. 257-286. [Entire issue: Pp. 215-310 + 1 folded plate.].‎

‎First printing of Jacobi's paper on infinit series. ""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 fame."" (DSB)‎

書籍販売業者の参照番号 : 45096

‎"JACOBI, C.G.J.‎

‎Uber die Differentialgleichung, welcher die Reihen 1 ± 2q etc. Geniige leisten (+) Über die particuläre Lösung der partiellen Diffenrentialgleichung ... (+)‎

‎Berlin, G. Reimer, 1848. 4to. In the original wrappers, no backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 36. Band, Zweites [2] Heft"". Entire issue offered. A fine and clean copy. Pp. 97-113. [Entire volume: 97-184, (4) pp. + 1 plate].‎

‎First printing of these two papers influential papers by Jacobi published in the epoch-making year 1848.""In the revolutionary year of 1848 Jacobi became involved in a political discussion in the Constitutional Club. During an impromptu speech he made some imprudent remarks which brought him under fire from monarchists and republicans alike. Hardly two years before, in the dedication of volume I of his Opuscula mathematica to Friedrich Wilhelm IV, he had expressed his royalist attitude"" now he had become an object of suspicion to the government. A petition of Jacobi’s to become officially associated with the University of Berlin, and thus to obtain a secure status, was denied by the ministry of education. Moreover, in June 1849 the bonus on his salary was retracted. Jacobi, who had lost his inherited fortune in a bankruptcy years before, had to give up his Berlin home. He moved into an inn and his wife and children took up residence in the small town of Gotha, where life was considerably less expensive."" (DSB).‎

書籍販売業者の参照番号 : 46354

‎"JACOBI, C.G.J.‎

‎Ueber die Entwicklung des Ausdrucks.‎

‎Berlin, G. Reimer, 1843. 4to. In the original wrappers, no backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 26. Band, Ersters [1] Heft"". Entire issue offered. A fine and clean copy. Pp. 81-87. [Entire volume: 92, (4) pp.].‎

‎First printing.‎

書籍販売業者の参照番号 : 46283

‎"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.).‎

書籍販売業者の参照番号 : 45784

‎"JACOBI, C.G.J.‎

‎Über die unmittelbare verification einer Fundamentalformel der Theorie der elliptischen Functionen (+) Über die partielle Differentialgleichung, welcher die Zähler und Nenner der elliptischen Functionen.‎

‎Berlin, G. Reimer, 1848. 4to. In the original wrappers, no backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 36. Band, Erstes [1] Heft"". Entire issue offered. A fine and clean copy. Pp. 75-89. [Entire volume: IV, (2), 96, (2) pp.].‎

‎First printing of these two papers influential papers by Jacobi published in the epoch-making year 1848.""In the revolutionary year of 1848 Jacobi became involved in a political discussion in the Constitutional Club. During an impromptu speech he made some imprudent remarks which brought him under fire from monarchists and republicans alike. Hardly two years before, in the dedication of volume I of his Opuscula mathematica to Friedrich Wilhelm IV, he had expressed his royalist attitude"" now he had become an object of suspicion to the government. A petition of Jacobi’s to become officially associated with the University of Berlin, and thus to obtain a secure status, was denied by the ministry of education. Moreover, in June 1849 the bonus on his salary was retracted. Jacobi, who had lost his inherited fortune in a bankruptcy years before, had to give up his Berlin home. He moved into an inn and his wife and children took up residence in the small town of Gotha, where life was considerably less expensive."" (DSB).‎

書籍販売業者の参照番号 : 46355

‎"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)‎

書籍販売業者の参照番号 : 45783

‎"JACOBI, C.G.J. - ABELIAN TRANSCENDENTAL FUNCTIONS.‎

‎Considerationes generales de transcendentibus Abelianis. - [ABELIAN TRANSCENDENTAL FUNCTIONS]‎

‎Berlin, G. Reimer, 1832. 4to. Without wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 9. Bd., Heft 4, pp. 313-403. Jacobi's paper pp. 394-403. With titlepage to vol. 9.‎

‎First printing of this important paper, bringing the problem with the Abelian integral to a solution. ""The further step was made by Jacobi in the short but very importent memoir ""Considerationes generales..."" (the paper offered): viz. he here shows for the hyper-elliptical integrals of any class (but the conclusion may be stated generally) that the direct functions to which Abel's theorem has reference are not functions of a single variable, such as the elliptic sn, cn, or dn, but functions of ""p"" variables...(Arthur Cayley in his ""Presidential Address to the British Association 1883).""Carl Jacobi in reviewing Adrien Legendre's third supplement to his ""Traite des fonctions elliptiques et des integrales Euleurienne"", suggests renaming Legendre's ""hyperelliptical transcendental functions"" as ""Abelian transcendental functions"" after Niels Henrik Abel. acobi, whiose work on hyperelliptic integrals helps lead to the extensive nineteenth-century development of the theory of abelian functions of n variables, suggests, in partial analogy to doubly periodic functions, that hyperelliptic integrals can be inverted to hyperelliptic functions through a generalization of elliptic theta functions."" (Parkinson in ""Breakthroughs (1832"").‎

書籍販売業者の参照番号 : 41658

‎"JACOBI, C.G.J. - KINETICS OF THE TOP.‎

‎Sur la rotation d'un corps.‎

‎(Berlin, Georg Reimer, 1850). 4to. Later marbled wrappers. In ""Journal für die reine und angewandte Mathematik, 39. Band, 24 Heft. Jacobi's paper takes up the whole issue . pp. 293-350.‎

‎"JACOBI, C.G.J. - PAVING THE WAY FOR DOUBLE PERIODIC FUNCTIONS.‎

‎De functionibus duarum variabilium quadrupliciter periodicis, quibus theoria transcendentium Abelianarum innititur.‎

‎(Berlin, G. Reimer, 1835) 4to. No wrappers as extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 13. Jacobi's paper: pp. 55-78.‎

‎"JACOBI, CARL G.J.‎

‎Collection of 4 Memoirs: 1. De formatione et proprietatibus Determinantium. 2. De determinantibus functionalibus. 3. De functionibus alternantibus earumque divisione per productum e differentiis elementorum conflatum. - 4. Zum combinatorischen Analysis. - [INTRODUCING ""DETERMINANTS"" AND ""JACOBIANS""]‎

‎Berlin, G. Reimer, 1841. 4to. Without wrappers as Heft 4 in ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 22, heft 4. Titlepage to Heft 4. and pp. 285-380 +(2) pp. and 1 engraved plate. Jacobis papers: 1. pp. 285-318, 2. pp. 319,359, 3. pp. 360-371 and 4. pp. 372-374.‎

‎"JESSEN, BØRGEN.‎

‎Bidrag til Integralteorien for Funktioner af uendelig mange Variable.‎

‎København, Gads Forlag, 1930. 4to. In the original printed wrappers. With author's presentation inscription to front wrapper: ""Hr Docent Dr Phil A. F. Andersen / fra deres hengivne / Børge Jessen"". Light sunning to extremities, otherwise fine and clean. 66 pp.‎

‎"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).‎

‎"JORDAN, CAMILLE.‎

‎Commentaire sur Galois.‎

‎Leipzig, B.G. Teubner, 1869. 8vo. Bound in later half cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 1., 1869. Entire volume offered. Library stamp to front free end-paper and title-page. Internally a few light brown spots.. Pp. 141-160. [Entire volume: Pp. IV-636.]‎

‎"KARHUNEN, KARI.‎

‎Über die Struktur stationärer zufälliger Funktionen.‎

‎Stockholm, Almqvist & Wiksells Boktryckeri AB, 1949. 8vo. In the original printed wrappers. Offprint from: ""Arkiv för matemativ, Utgivet av Kungl. Svenska Vetenskapsakademien"", Band 1, Nr 13. Previous owner's name to top of front wrapper. Pp. 141-160.‎

‎"KEES, F. K. [FRIEDRICH KÖES].‎

‎Ratio Complanandi Superficies Curvas Corporum quorumlibet Geometricorum.‎

‎Leipzig, Grosse & Gleditsch, 1729. 4to. In: ""Actorum Eruditorum Supplementa Tomus IX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two 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. 45-50. [Entire volume: (2), 509, (24), + two engraved plates.].‎

‎"KEILL, IOANNES [JOHN KEILL] (+) CHRISTIANUS WOLFFIUS [CHRISTIAN WOLFF].‎

‎Epistola ad Clarissimum Virum Christianum Wolfium in Academia Regio Fridericiana Mathematum Professorem [Keill] (+) Responsio ad epistolam viri clarissimi Johannis Keill (+) Monitum circa experimentum de circulatione aeris per poros ligni [Wolf].‎

‎Leipzig, Grosse & Gleditsch, 1710. 4to. In: ""Acta Eruditorum Anno MDCCX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps 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. 11-15" Pp. 78-80 Pp. 80-1. [Entire volume: Pp. (4), 535, (37) + seven engraved plates.].‎