‎Mathématiques‎

‎"KRUSKAL, WILLIAM.‎

‎Helmert's Distribution.‎

‎[No place, no printer], 1946. 8vo. In the original printed wrappers. Offprint from: ""American Mathematical Monthly"", Vol. LIII, No. 8, 1946. A very fine and clean copy. Pp. 435-38.‎

‎Offprint of William Henry Kruskal first published paper. Kruskal, American mathematician and statistician, is famous for having formulated the Kruskal-Wallis one-way analysis of variance (together with W. Allen Wallis), a widely-used nonparametric statistical method.‎

Referenz des Buchhändlers : 48895

‎"HUMBERT, MARIE-GEORGES.‎

‎Sur les courbes algébriques planes rectifiables (+) Sur quelques propriétés des aires sphériques (+) Sur le théorème d'Abel et quelques-unes de ses applications a la geometrie (+) Sur une classe de courbes planes, et sur une surface remarquable du qua...‎

‎Paris, Gauthier-Villars, 1888-1890 4to. Bound with the front wrappers in contemporary half cloth. In ""Journal de Mathématiques pures et appliquées"". With two paper labels to spine and with the author's name to top of each wrapper. A stamp to front free end paper and first wrapper. Otherwise fine.‎

‎First appearance of this collection of important papers which, amongst others, contains the questions to whether the involutes are algebraic.""Besides his two pedagogical works, it was through numerous memoirs (approximately 150, which have been collected) that Humbert held a major place in the mathematical discovery and production of his time. His writings were inspired by his interest in the study of algebraic curves and surfaces and were marked by the lucidity with which he related the problems biography in encountered in this area to questions of analysis and number theory.He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication. He also pointed out the resulting consequence: the existence of a group of transformations of certain surfaces into themselves constitutes an essential difference between the geometry of surfaces and that of curves. But, most important, he completed the work of Hermite by pursuing the applications to number theory throughout his life.""The present volume also contain contribution by Caspary and Hilbert.‎

Referenz des Buchhändlers : 49018

‎"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).‎

Referenz des Buchhändlers : 49049

‎"LIOUVILLE, JOSEPH. - THE EXISTANCE OF TRANSCENDENTAL NUMBERS PROVED.‎

‎Remarques... à des classes très-étendues de quantités dont la valeur n'est ni rationelle ni méme réductible à des irratonnelles algébriques... à un passage du livre des principes ou Newton... (Séance du Lundi 13 mai 1844). (+) Nouvelle démonstratio...‎

‎(Paris, Bachelier), 1844 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 18, No 20 a. 21. Pp. (883-) 898 a. pp. (899-) 960. (Entire issues offered). Liouville's papers: pp. 883-885 a. 910-911.‎

‎First printing of the papers in which Liouville proved the existence of transcendental numbers. ""J. Liouville..... invented a method (1844) for constructing any one of an extensive class of transcendental numbers. His numbers were the first to be proved transcendental" Hermite's proof of the transcendence of e ... followed in 1873" F. Lindemnn's for pi in 1882.""(Bell ""Development of Mathematics"", p. 275).Liouville showed that not only are these numbers irrational, they are always transcendental. Thus he was the first to prove the existence of transcendental numbers and also that there were an infinite number of them. Liouville suggested that e was transcendental, and provided the first example of a provably transcendental number, now known as Liouville’s constant.Parkinson ""Breakthroughs"", 1844 M.‎

Referenz des Buchhändlers : 49077

‎"GUDERMANN, CHRISTOPH.‎

‎Potential oder zyklisch-hyperbolische Funktionen I - II.‎

‎(Berlin, G. Reimer, 1832) 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 8. Band, 1832"", without backstrip. Fine and clean. pp. 64-116"" Pp. 194-212.‎

‎First printing of Gudermann extensive and important papers on hyperbolic functions. During 1830ies Gudermann focused his work on these functions and published extensive on the subject. It was later coined the Gudermannian function.The function was introduced by Johann Heinrich Lambert in the 1760s at the same time as the hyperbolic functions. He called it the ""transcendent angle,"" and it went by various names until 1862 when Cayley suggested it be given its current name as a tribute to Gudermann's work in the 1830ies on the theory of special functions. The present paper together with two later published papers were collected in Theorie der potenzial- oder cyklisch-hyperbolischen functionen (1833), a book which expounded sinh and cosh to a wide audience.The issue also contain a paper by the famous Norwegian mathematician Niels Henrik Abel.""Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written."" (DSB). Gudermann is known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions in 1839, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.‎

Referenz des Buchhändlers : 49082

‎"CHURCH, ALONZO.‎

‎Norwood Russell Hanson. A note on the Gödel theorem (+) David Perlman. A milestone in math - professor's new concept (+) Benson Mates. Stoic Logic.‎

‎[No place], The Journal of Symbolic Logic, 1967. 8vo. In the original printed wrappers. In ""Journal of Symbolic Logic"", Vol. 28, Number 4. December, 1963. Entire issue offered. A very fine and clean copy. Pp. 295 [Entire issue: Pp. 273-346, VI. ].‎

‎First printing of three short reviews by Alonzo Church.‎

Referenz des Buchhändlers : 49084

‎"EULER, LEONHARD.‎

‎Exposition de quelques paradoxes dans le Calcul Intégral. (Explanation of certain paradoxes in integral calculus).‎

‎(Berlin, Haude et Spener, 1758). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome 12 (1756), pp. 300-321 a. 1 folded engraved plate.‎

‎First edition. Euler looks at singular integrals of differential equations (derivation through differentiation"" proof that these integrals are not included in the general solution.) Enestroem: 236. - Also with Euler le Fils: ""Des Cerfs - Volans"", pp. 322-364 a. 1 plate.‎

Referenz des Buchhändlers : 49129

‎"HUSSERL, EDMUND.‎

‎Formale und transzendentale Logik. Versuch einer Kritik der logischen Vernunft. Sonderabdruck aus: ""Jahrbuch für Philosophie und phänomenologische Forschung"", Bd. X. Herausgegeben von E. Husserl, Freiburg I. Br. - [THE FINAL CONCEPTION OF LOGIC]‎

‎Halle, Niemeyer, 1929. 4to. A bit later blue full fabrikoid binding. Gilt lettering to spine. Clean and fresh copy. Old owner's signature to title-page. XI, (1), 298 pp.‎

‎First edition of Husserl's seminal work, which contains his philosophy of logic and mathematics. This important work entitled ""Formal and Transcendental Logic"" with the sub-title ""An Attempted Critique of the Logic Reason"" provides us with Husserl's final conception of logic. Though now famous as the father of phenomenology, Husserl was initially a student of mathematics, and in his two first works ""Über den Begriff der Zahl"" and ""Philosophie der Aritmetik"", his early philosophy is developed on the basis of mathematics with the aim to provide a sound foundation for mathematics by combining it with philosophy and psychology. His main work from 1900-1901, Logische Untersuchungen"", probably one of the two most important and influential philosophical works of the 20th century, Husserl establishes a philosophy that asks the question of the essence of the matter of perception as opposed to the form of perception, as well as the meaning of the difference between formal or pure and material laws, truths and determinations, -all based on his strong interest in the relationship between the formalities of arithmetic and of logic.However, it is in his ""Formal and Transcendental Logic"" that Husserl most thoroughly introduces us to the formal character of logic and formulates his final conception of it. According to Husserl, logic is formal, because it is nothing more than the development of pure reason, and pure reason is a formal concept. As such, logic for Husserl becomes the self-interpretation of pure reason (die Selbstauslegung der reinen Vernunft) which is, again, a formal activity. Husserl also determines that there are two formal ways of conceiving logic, one being a tool for judging sentences true or false, and another, which includes knowledge.And so, this work not only provides us with a genetic-phenomenological investigation of philosophy and of the basis of logic, but it also provides us with an insight into the entire inner systematic structure of late Husserlian thought.‎

Referenz des Buchhändlers : 49150

‎[NOVA ACTA ERUDITORUM]‎

‎Nova Acta Eruditorum MDCCLX [1760].‎

‎Leipzig, Gleditschii & Lanckisii, 1760. 4to. 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. Occassional brownspots throughout, otherwise fine. (4), 622, (28) pp + 2 plates.‎

‎First edition of Acta Eruditorum 1760 containing many reviews by influential contemporary mathematicians, philosophers and historians.‎

Referenz des Buchhändlers : 49307

‎[ACTA ERUDITORUM]‎

‎Indices generales autorum et rerum sexti Actorum Eruditorum.‎

‎Leipzig, Lanckisii, Gleditschii & Blochbergerum, 1745. 4to. 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. Occassional brownspots throughout, otherwise fine.‎

‎First printing of this index volume of Acta Eruditorum 1745.‎

Referenz des Buchhändlers : 49311

‎[ACTA ERUDITORUM]‎

‎Indices generales autorum et rerum sexti Actorum Eruditorum.‎

‎Leipzig, Grossii, Gleditschii & Fritschium, 1714. 4to. 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. Occassional brownspots throughout, otherwise fine.‎

‎First printing of this index volume of Acta Eruditorum 1714.‎

Referenz des Buchhändlers : 49313

‎"DIRICHLET, LEJEUNE (+) DEDEKIND.‎

‎Untersuchungen über ein Problem der Hydrodynamik [Dirichlet] (+) Zusatz zu der vorstehenden Abhandlung [Dedekind].‎

‎Berlin, Georg Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 1861, band 58. Without backstrip. Fine and clean. Pp. 181-228.‎

‎First printing of these two important papers on gravitational interaction from bodies, such pseudo-rigid bodies, thereby ""opened a new direction"", a direction which later inspired Riemann to turn his attention to the problem""Without the gravitational interaction from another body, such pseudo-rigid bodies havereceived attention in many references. The interest was initiated by Newton in Principia, where he showed that a spinning axi-symmetric self-gravitating body of ?uid that is rotating slowly about the symmetry axis will be oblate. Jacobi in 1834 extended the work of Newton, but also work of Maclaurin, to show that a self-gravitating ?uid also can take on ellipsoidal shapes. The solutions of Jacobi, Maclaurin and Newton were, however, still all rigid. In a frame rotating with the body the ?uid is stationary. Dirichlet and Dedekin, [in the present two papers], respectively, opened a new direction when they found a symmetry that applied to Jacobi's solution generated a new solution in which the body isstationary in shape but the ?uid particles follow elliptical paths in planes orthogonal to a principle axis of the ellipsoid. Dirichlet's paper inspired Riemann to turn his attention to the problem. He gave a classi?cation of the solutions of Dirichlet's equations for which the ellipsoidal shape of the body remains constant. At the heart of this classi?cation lies what is now known as Riemann's theorem: the angular velocity and circulation (i) lie in the same principle plane and (ii) if the angular velocity is parallel to a principle axis then the circulation vector must also lie along that same principle axis."" (Kristiansen, The two-body problem of a pseudo-rigid body and a rigid sphere)‎

Referenz des Buchhändlers : 49315

‎"LUSIN, N. [LUZIN].‎

‎Sur le probléme de M. J. Hadamard d'uniformisation des ensembles.‎

‎[Paris, Gauthier-Villars, 1930.] 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 190, No 6, Entire issue offered. No backstrip, stamp to first leaf. Pp. 349-51. [Entire issue: Pp. 337-408].‎

‎First printing of Lusin's important paper on uniformization in set theory. ""The more fundamental uniformization property was introduced in [the present paper]. Lusin established there some difficult uniformization theorems"". (Moschovakis, Descriptive Set Theory)‎

Referenz des Buchhändlers : 49340

‎[ACTA ERUDITORUM]‎

‎Indices generales autorum et rerum Quniti Actorum Eruditorum.‎

‎Leipzig, Grossii, Gleditschii & Martini, 1733. 4to. 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. Occassional brownspots throughout, otherwise fine.‎

‎First printing of this index volume of Acta Eruditorum 1733.‎

Referenz des Buchhändlers : 49344

‎"CAYLEY, A.‎

‎Note sur la transformation de Tschirnhausen (+) Deuxième sur la transformation de Tschirnhausen.‎

‎Berlin, Georg Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 1861, band 58. Without backstrip. Fine and clean. Pp. 259-69.‎

‎First apperance of these two papers in which Cayley obtained the transformed equations for the cubic and quartic equations.‎

Referenz des Buchhändlers : 49346

‎[NOVA ACTA ERUDITORUM].‎

‎Nova Acta Eruditorum. Supplementa. Tomus IV. 1742.‎

‎Leipzig, Grossiim, Gleditschii & Weidemannum, 1742. 4to. 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. Occassional brownspots throughout, otherwise fine. (2), 552, (32) pp.‎

‎First edition containing many reviews by influential contemporary mathematicians, philosophers and historians.‎

Referenz des Buchhändlers : 49349

‎[NOVA ACTA ERUDITORUM].‎

‎Nova Acta Eruditorum MDCCXLI [1741].‎

‎Leipzig, Grossii, Gleditschii & Weidemannum, 1741. 4to. 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. Occassional brownspots throughout, otherwise fine. (6), 720, (42) pp.‎

‎First edition containing many papers and reviews by influential contemporary mathematicians, philosophers and historians.‎

Referenz des Buchhändlers : 49352

‎"CLIFFORD, W.K.‎

‎On Mr. Spottiswoode's Contact Problems.‎

‎(London, Harrison and Sons, 1874). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1874 - Vol. 164 - Part II. Pp. 705-717.‎

‎First printing of one of Clifford's papers in geometry.""William Clifford (1845-1879) was an important mathematician of his day. He is most remembered today for his invention of Clifford algebras, which are fundamental in modern differential geometry and mathematical physics. His ideas on the connection between energy and matter and the curvature of space were important in the eventual formulation of general relativity. Clifford was particularly interested in non-Euclidean geometry. However, in his relatively brief career, he made contributions to diverse fields of mathematics: elliptic functions, Riemann surfaces, biquaternions, motion in Euclidean and non-Euclidean space, spaces of constant curvature, syzygies, and so on.""‎

Referenz des Buchhändlers : 49411

‎"HILBERT, DAVID.‎

‎Hermann Minkowski. - [HILBERT'S OBITUARY OVER MINKOWSKI]‎

‎Leipzig, Teubner, 1910. 8vo. Without wrappers. Extracted from ""Mathematische Annalen. Begründet 1868 durch Alfred Clebsch und Carl Neumann. 68. Band"". Pp. 445-471.‎

‎First edition of Hilbert's obituary over Herbert Minkowski. Minkowski, Hilbert's ""best and truest friend"" (Reid, Hilbert P. 121), died prematurely of a ruptured appendix in 1909. Minkowski and Hilbert, both natives of Königsberg would exercise a reciprocal influence over each other throughout their scientific careers.‎

Referenz des Buchhändlers : 49482

‎"LOBACHEVSKY, N.‎

‎Ob izchezanij trigonometrisheskikh strok. [Russian - i.e. On the Convergence of Trigonometrical Series] [In: ""Uchenye zapiski"" (""Scientific Memoirs"") of Kazan University]. - [THE GENERAL DEFINITION OF A FUNCTION]‎

‎Kazan, 1834. 8vo. Contemporary blank, blue wrappers (original?). A closed tear and a bit of staining to back wrapper and some tears and scratches to spine. Internally very nice and clean. Presumably not an off-print, as there are stitching-holes to the margins, indicating that it has been removed from a volume, although the wrappers could look original, certainly contemporary. With the original title-page for Book 11 of the ""Uchenye zapiski"" + pp. (167)-226.‎

‎Scarce first printing of Lobachavsky's main contribution to his second most important field (after non-Euclidean geometry), namely infinite series, more specifically trigonometric series. This constitutes one of Lobachevsky's earliest papers and the one in which he presents his new results in the theory of trigonometric series. It is here that he gives his definition of a function as a correspondence between two sets of real numbers, the same definition that Dirichlet some three years later discovers independently of Lobachevsky (and is given the general credit for). This important paper was published in the Scientific Memoirs of the Kazan University. ""Some of Lobachevsky's early papers, too, were on such nongeometrical subjects as algebra and the theoretical aspects of infinite series. Thus, in 1834 he published his paper ""Algebra ili ischislenie konechnykh"" (""Algebra, or Calculus of Finites""), of which most had been composed as early as 1825. The first issue of the ""Uchenye zapiski"" (""Scientific Memoirs"") of Kazan University, founded by Lobachevsky, likewise carried his article ""Ob ischezanii trigonometricheskikh strok"" (""On the Convergence of Trigonometrical Series""). The chief thrust of his scientific endeavor was, however, geometrical, and his later work was devoted exclusively to his new non-Euclidean geometry."" (DSB)‎

Referenz des Buchhändlers : 49559

‎"LIPSCHITZ, R.H:2086‎

‎Beiträge zur Theorie der Vertheilung der statischen und der dynamischen Electricität in leitenden Körpern.‎

‎[Berlin, G. Reimer, 1861]. 4to. Without wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 58. Bd. Fine and clean. Pp. 1-53.‎

‎First appearance of Lipschitz's paper on the theory of the distribution of the static and dynamic electricity in conducting bodies.""Lipschitz distinguished himself through the unusual breadth of his research. He carried out many important and fruitful investigations in number theory, in the theory of Bessel functions and of Fourier series, in ordinary and partial differential equations, and in analytical mechanics and potential theory. Of special note are his extensive investigations concerning n-dimensional differential forms and the related questions of the calculus of variations, geometry, and mechanics. This work-in which he drew upon the developments that Riemann had presented in his famous lecture on the basic hypotheses underlying geometry-contributed to the creation of a new branch of mathematics."" (DSB)‎

Referenz des Buchhändlers : 49611

‎"POINCARÉ, H. [DAVID HILBERT].‎

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

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

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

Referenz des Buchhändlers : 49614

‎"POINCARÉ, H.‎

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

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

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

Referenz des Buchhändlers : 49616

‎"HILBERT, DAVID.‎

‎Über ternäre definite Formen.‎

‎Stockholm, Beijer, 1893. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 17, 1883. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 169-197. [Entire volume: (6), 416 pp].‎

‎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....""‎

Referenz des Buchhändlers : 49620

‎"POINCARÉ, H.‎

‎Remarques diverses sur l'équation de Fredholm.‎

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

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

Referenz des Buchhändlers : 49622