‎Mathematics‎

‎"POINCARÉ, HENRI.‎

‎Sur les Propriétes du potentiel et sur les Fonctions Abéliennes.‎

‎(Berlin, Uppsala & Stockholm, Paris, Almqvist & Wiksell, 1898). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 22, pp. 89-178.‎

‎First edition. ""As soon as he came into contact with the work of Riemann and Weierstrass on Abelian Functions and algebraic geometry, Poincaré was very much attracted by those fields. His papers on these subjects occupy in his complete works as much space as those on automorphic functions, their dates ranging from 1881 to 1911. One of his main ideas in these papers is that of ""reduction"" of Abelian functions. Generalizing particular cases studied b Jacobi, Weierstrass, and Picard, Poincaré proved the general ""complete reducibility"" theorem...""(DSB).‎

Bookseller reference : 39135

‎"POINCARÉ, HENRI.‎

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

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

‎First edition. In this paper Poincaré arrives at a new theorem about canonical transformation, and in his later ""Methodes Nouvelles"", he proved this theorem using a variiational principle of mechanics, known today as the Hamilton principle.‎

Bookseller reference : 39134

‎"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...""‎

Bookseller reference : 45854

‎"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...""‎

Bookseller reference : 46049

‎"POINCARÉ, HENRI. - A FAMOUS PAPER ON CELESTIAL MECHANICS.‎

‎Sur L'Équilibre d'une Masse fluide animée d'un Mouvement de Rotation.‎

‎(Stockholm, F.& G. Beier), 1885. 4to. No wrappers as extracted from ""Acta Mathematica"", Vol. 7. Pp. 259-288. Clean and fine.‎

‎"POISSON, (SIMÉON-DENIS). - COINING THE PHRASE ""LAW OF LARGE NUMBERS""‎

‎Recherches sur la probabilité des jugements, principalement en matière criminelle. (+) Note sur la loi des grands nombres. (+) Note sur le calcul des probabilités. (+) Formules relatives aux probabilités qui dépendent de très grands nombres. (3 papers).‎

‎(Paris, Bachelier), 1835-36. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 1, Séance du Lundi 14 Décembre 1835 and tome 2, Séance Lundi 11 Avril 1836 + Séance Lundi 27 Juin 1836 + Séance du Lundi 18 Avril 1836. + Pp. (467-) 498, (355-) 386, (387-) 402 a. pp. (601-) 630. (4 entire issues offered. Poisson's papers: pp. 473-495 (1835), pp. 377-380, pp. 395-400 and pp. 603-13. (1836). Clean and fine.‎

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

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

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

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

Bookseller reference : 47207

‎"POISSON, SIMEON PIERRE.‎

‎Recherches sur le Mouvement des Projectiles dans L'Air, et ayant égard a leur Figure et leur Rotation, et a L'Influence du Mouvement diurne de la Terre.‎

‎Paris, Bachelier, 1839. 4to. Contemporary hcalf, gilt spine with gilt lettering. A paperlabel pasted on spine. Stamps on titlepage. VIII,226,(1) pp. Broadmargined on good paper. Light scattered brownspots.‎

‎First edition. Poisson made importent contribution to many categories in mathematics and mathematical physics, ""Poisson'sTheorem"", the mathematical treatment of attractive forces etc.. ""The Recherches sur le Mouvement...projectiles (the item offered) is the first workto deal with the subject by taking into account the rotation of the earth and the complementary acceleration resulting from the motion of the system of reference. A decade after its publication it inspired Focault's famous experiment demonstrating the earth's rotation""(Pierre Costabel in DSB). - In this researchhe extended Lapalce's analysis to allow also for the rotation of the projectile in motion, and it helped Léon Foucault to conceive of his pendulum to demonstrate the rotation of the earth. - The work is a collection of memoirs. ""Ce recherches se composent de plusieurs Mémoires lus par l'Auteur à l'Academie des Sciences et insérés dans les XXVIe et XXVIIe cahiers du Journal de l'Ecole Polytechnique."" (From verso of halftitle) - Bibliotheca Mechanica p. 261.‎

Bookseller reference : 39951

‎"PONCELET, J. V. [JEAN-VICTOR].‎

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

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

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

Bookseller reference : 45145

‎"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.‎

Bookseller reference : 46014

‎"POST, EMIL LEON.‎

‎Finite Combinatory Processes-Formulation 1. [In: The Journal of Symbolic Logic, Vol. 1, Number 3, Sept. 1936]. - [A SIMULTANEOUS VERSION OF THE ""TURING MACHINE""]‎

‎[No place], 1936. 8vo. Extract, unbound, unstapled. Pp. 103-105.‎

‎The uncommon first printing of Post's seminal paper, in which he, simultaneously with but independently of Turing, describes a logic automaton, which very much resembles the Turing machine. The Universal Turing Machine, which is presented for the first time in Turing's seminal paper in the Proceedings of the London Mathematical Society for 1936 (same year as the present paper), is considered one of the most important innovations in the theory of computation and constitutes the most famous theoretical paper in the history of computing. ""Post [in the present paper] suggests a computation scheme by which a ""worker"" can solve all problems in symbolic logic by performing only machinelike ""primitive acts"". Remarkably, the instructions given to the ""worker"" in Post's paper and to a Universal Turing Machine were identical."" (A Computer Perspective, p. 125). ""The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, indepently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper [the paper offered]. Post's paper was intended to fill a conceptual gap in Alonzo Churchs' paper on ""An unsolvable problem of elementary number theory"" (Americ. Journ. of Math. 58, 1936). Church's paper had answered in the negative Hilbert's question as to whether a definite method existed for proving the truth or falsity of any mathematical statement (the Entscheidungsproblem), but failed to provide the assertion that any such definite method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be written in the form of instructions to a mindless worker operating on an infinite line of ""boxes"" (equivalent to Turing's machine's ""tape""). The worker would be capable only of reading the instructions and performing the following tasks... This range of tasks corresponds exactly to those performed by a Turing machine, and Church, who edited the ""Journal of Symbolic Logic"", felt it necessary to insert an editorial note referring to Turing's ""shortly forthcoming"" paper on computable numbers, and ascertaining that ""the present article... although bearing a later date, was written entirely independently of Turing's"" (p. 103)."" (Origins of Cyberspace, pp. 111-12).Hook & Norman, Origins of Cyberspace, 2002: 355.Charles & Ray Eames, A Computer Perspective, 1973: 125.‎

Bookseller reference : 42609

‎"QUINE, W.V. - GILBERT RYLE edt.‎

‎On Frege's Way Out. (In: Mind. A Quarterly Review of Psychology and Philosophy. Vol. LXIV. No. 254. April, 1955).‎

‎Edinburgh & N.Y., Thomas Nelson & Sons, 1955. 8vo. Orig. printed grey wrappers w. small nicks to extremities. Internally mint. Advertisement-leaves laid in loose at front. Pp. 145 - 159 (the rest of the volume: pp. 160 - 288, [4 pp. -advertisements] ).‎

‎"QUINE, WILLARD ORMAN VAN.‎

‎A System of Logistic. - [MAGNIFICENT PRESENTATION-COPY]‎

‎Cambridge, Massachusetts, Harvard University Press, 1934. Original full red cloth with gilt line-borders to boards, original dust-jacket, somewhat worn, with a red label over the price and chips and nicks to extremities. Minor loss to corners of dust-jacket, and a large loss of upper part of spine of dust-jacket (ca. 6 x 2 cm), thus lacking the title to spine of dust-jacket, and leaving the cloth of the same part of the spine sunned and the gilding of the title on spine almost faded off. Some soiling to dust-jacket. Internally nice and clean. X, (2), 204 pp.‎

‎"RABIN, M. O.‎

‎Decidability of Second-Order Theories and Automata on Infinite Trees. - [THE INFINITE TREE AUTOMATON]‎

‎Providence, Rhode Island, The American Mathematical Society, 1969. Royal8vo. In the original blue printed wrappers. In ""Transactions of the American Mathematical Society"", Volume 141, July, 1969. Entire issue offered. Spine faded and a few bumps to extremities, otherwise fine and clean. Pp. 1-35. [Entire volume: (4), 527 pp.].‎

‎"RADO, TIBOR.‎

‎On Non-Computable Functions (Contained in The Bell System Technical Journal, volume 41, number 3, pp.877-884). - [THE BUSY BEAVER GAME]‎

‎N.Y., 1962. Entire issue in wrappers.‎

‎"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.‎

‎"REDERN, LE COMTE (SIGISMUND EHRENREICH). - NEWTONIAN OPTICS.‎

‎Considérations sur L'Influence que L'illustre Newton attribue a la diverse Réfrangibilité de la Lumiere sur les Lunettes à Réfraction.‎

‎(Berlin, Haude et Spener, 1767). 4to. No wrappers, as issued in ""Memoires de l'Academie des Sciences et Belles-Lettres"". Tome XVI, pp. 1-44 and 2 folded engraved plates.‎

‎"REICHENBACH, HANS.‎

‎Philosophie der Raum-Zeit-Lehre.‎

‎Berlin, Walter de Gruyter, 1928. 8vo. In the original full blue cloth with gilt lettering to spine and front board. Spine a bit faded. Light wear to spine ends and wear along edges. Stamps to foot of title-page. VI, 380, (2) pp.‎

‎First edition of the ""first comprehensive and systematic representation of geometry in physics."" ""This work was an important landmark in the development of the empiricist conception of geometry"". (Carnap, Introduction to the present work in the first English translation).‎

Bookseller reference : 49741

‎"REICHENBACH, HANS.‎

‎Philosophie der Raum-Zeit-Lehre.‎

‎Berlin, Walter de Gruyter, 1928. 8vo. In the original full blue cloth with gilt lettering to spine and front board. Spine a bit faded. Light wear to spine ends and wear along edges. Stamps to foot of title-page. VI, 380, (2) pp.‎

‎"RICCATO, JACOBO. (JACOPO FRANCESCO RICCATI) - DANIELIS BERNOULLI (DANIEL BERNOULLI).‎

‎[Riccati:] Animadversiones in aequationes differentiales secundi gradus. + [Bernouilli:] Notata in praecedens schediasma III. Co. Jacobi Riccati. (In: Actorum Eruditorum, Supplementa. Tomus VIII, 66-75 pp.). - [THE RICCATI-EQUATION]‎

‎Leipzig, Gross & Fritsch, 1724. 4to. Entire volume present. Nice contemporary full vellum. Small yellow paper label pasted to top of spine and library-label to inside of front board. Two smaller library stamps to title-page. Internally some browning and brownspotting, due to the paper quality. Overall a nice and tight copy. [Riccati-paper:] pp. 66-73. [Bernouilli-paper:] pp. 73-75. [Entire volume: (2), 532, (34) pp.].‎

‎"RICE, S. O.‎

‎Mathematical Analysis of Random Noise. - [THE RICE DISTRIBUTION]‎

‎New York, American Telephone and Telegraph Company, 1945. 8vo. Original full green cloth. Volume XXIV, 1945 of ""The Bell System Technical Journal"". Library stamp to free front end-paper and title-page. Minor bumping to extremities. A nice and clean copy. [Mentioned article:] Pp: 46-156. [Entire issue: V, (3), 467].‎

‎"RICHELOT, A.‎

‎De resolutione algebraica aequationis x257 = 1, sive de divisione circuli per bisectionem anguli septies repetitam in partes 257 inter se aequales commentatio coronat. - [CONSTRUCTION OF A 257-GON]‎

‎Berlin, Georg Reimer, 1832. 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 9, 1832, Fine and clean. 26 pp.‎

‎"RICHELOT, F.‎

‎De integralibus Abelianis primi ordinis commentatio prima.‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1834]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 12. No backstrip. Fine and clean. Pp. 181-233.‎

‎"RICHELOT, F.‎

‎De integralibus quibusdam definitis, quorum summa ad quadraturam divisionemque circuli revocatur.‎

‎Berlin, G. Reimer, 1840. 4to. In ""Journal für die reine und angewandte Mathematik, 21. band, 4. heft."". Entire issue offered in the original printed wrappers, without backstrip. Fine and clean. Pp. 293-327 [Entire volume: Pp. 293-380, (2) + 1 folded plate.].‎

‎"RICHELOT, F. J.‎

‎Eine neue Lösung des Problems der Rotation eines festen Körpers um einen Punct.‎

‎Berlin, G. Reimer, 1852. 4to. In the original printed wrappers, without backstrip. In ""Journal für die reine und angewandte Mathematik, 44 Band, 1. Heft, 1852"". Fine and clean. Pp. " Pp. 60-65. [Entire volume: IV, 92 + 1 plates.].‎