‎Matemáticas‎

‎"PEANO, GIUSEPPE.‎

‎Operazioni sulle grandezze.‎

‎Torino, Fratelli Bocca, 1922. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. LVII, Disp. 8a e 9a, 1921-1922. Small paper label pasted on to lower left part of front wrapper. A few nicks to front wrapper. A very fine and clean copy. Pp. 310-331. [Entire issue: Pp. 305-347].‎

‎"PEANO, GIUSEPPE.‎

‎Sur une courbe, qui remplit toute une aire plane. - [SPACE-FILLING CURVE - ANTICIPATING THE HILBERT CURVE]‎

‎Leipzig, B. G. Teubner, 1890. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 36., 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Very fine and clean. Pp. 157160. [Entire volume: IV, 602 pp.].‎

‎"PEANO, GUISEPPE.‎

‎Applicazioni geometriche del calcolo infinitesimale. + Calcolo Geometrico secondo l'Ausdehnungslehre di H. Grassmann. Preceduto dalle Operazioni della logica deduttiva. - [THE BEGINNING OF PEANO'S LOGIC AND THE ""GEOMETRICAL CALCULUS""]‎

‎Torino, Bocca, 1887 + 1888. Royal 8vo. Bound uncut w. the original wrappers of both works in one very nice a bit later (ab. 1920) red hcalf w. five raied bands to back. Single gilt lines to raised bands and gilt title on spine. A bit of soiling to wrappers, which have minor lacks to the inner hinges, where they are mounted onto hinge-strips. Front-wrappers w. stamp from ""Fratelli Bocca Editori"". A bit of brownspotting, mainly to first work. A very fine and attractive copy of these two works, very finely bound together. XII, 334, (2) + X, (2), 170, (2) pp.‎

‎"PEARSON, KARL. - ESTABLISHING MODERN MATHEMATICAL STATISTICS AND BIOMETRICS.‎

‎Contributions to the Mathematical Theory of Evolution. (I-) VI. (I. Contributions to...Received October 18, - Read November 18, 1893. - II. Skew Variation in Homogenous Material. Received December 19, 1894 - Read January 24, 1895. - III. Regression, H...‎

‎(London, Harrison and Sons, 1894, 1895, 1897, 1898, 1899 a. 1899. 4to. No wrappers as extracted from ""Philosophical Transactions"", Vol. 185 - Series A, pp. 71-110, textfigs. a. 5 plates. - Vol. 186 - Series A, pp. 343-414 a. 10 plates. - Vol. 187 - Series A, pp. 253-318 - Vol. 191 - Series A, pp. 229-311 - Vol. 192-Series A, pp. 169-244 a. 2 plates. - Vol. 192, Series A, pp. 257-330. All clean and fine.‎

‎"PEARSON, KARL. - INTRODUCING THE ""CHI-SQUARED GOODNESS-OF-FIT TEST""‎

‎On the Criterion that a given System of Deviations from the Probable in the Case of a Correlated System of Variables is such that it can be reasonably supposed to have arisen from Random Sampling.‎

‎London, Taylor and Francis, 1900. Contemp. hcalf, spine gone and covers loose. In: ""The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science"", Vol. 50, Fifth Series. VI,(2),624 pp. a. 5 plates. (Entire volume offered). Pearson's paper: pp. 157-175. A stippled stamp on titlepage. Internally clean and fine.‎

‎"PEIRCE, C(HARLES) S(ANDERS).‎

‎On the Algebra of Logic [In: American Journal of Mathematics. Volume III. Number I.]. - [INTRODUCING MODERN SEMANTICS]‎

‎Cambridge, 1880. 4to, entire issue present (Vol. III, no. 1). With the original printed wrappers. Uncut. Wrappers detached and with tears and loss to extremities. Backtrip gone. Stitching a bit loose. Internally nice and clean. Pp. (15)-57. [Entire issue 96 pp. + 2 plates]‎

‎"PINCHERLE, SALVATORE.‎

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

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

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

Referencia librero : 45848

‎"PINCHERLE, SALVATORE.‎

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

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

‎"PLÜCKER, JULIUS.‎

‎Über ein neues Coordinatensystem. (and the continuation:) Über eine neue Art, in der analytischen Geometrie Puncte und Curven durch Gleichungen darzustellen. (2 Papers). - [FOUNDING ALGEBRAIC GEOMETRY]‎

‎Berlin, G. Reimer, 1830. 4to. Without wrappers as extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von C.L. Crelle"", Bd. 5 u. 6. With titlepage to Bd. 5. Pp. 1-36 and pp. 107-146. One engraved plate.‎

‎First printing of Plückers invention of separate homogenous coordinates. Plücker introduced trilinear coordinates, and he ""starts with a fixed triangle and takes the coordinates of any point P to be the signed perpendicular distances from P to the sides of the triangle" each distance can be multiplied by the same arbitrary constant...by using homogenous coordinates and Euler's theorem on homogenous functions.....Plücker was able to give elegant algebraic representations of geometric ideas...and his efforts to treat duality algebraically led him to a beautiful idea, line coordinates....With this notion of line coordinates Plücker was able to give an algebraic formulation and proof of the principle of duality. (Morris Kline).‎

Referencia librero : 40444

‎"PLÜCKER, JULIUS.‎

‎Über ein neues Coordinatensystem. (and the continuation:) Über eine neue Art, in der analytischen Geometrie Puncte und Curven durch Gleichungen darzustellen. (2 Papers). - [FOUNDING ALGEBRAIC GEOMETRY]‎

‎Berlin, G. Reimer, 1830. 4to. Without wrappers as extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von C.L. Crelle"", Bd. 5 u. 6. With titlepage to Bd. 5. Pp. 1-36 and pp. 107-146. One engraved plate.‎

‎"PLÜCKER, JULIUS. - ""THE PLÜCKER EQUATIONS""‎

‎Solution d'une question fondamentale concernant la théorie générale des courbes.‎

‎(Berlin, G. Reimer, 1834) 4to. No wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd.12. - Plücker's paper pp. 105-108.‎

‎"PLÜCKER,JULIUS. - RECONSTRUCTION OF ANALYTICAL GEOMETRY.‎

‎On a New Geometry of Space. Received December 22, 1864, - Read February 2, 1865.‎

‎(London, Taylor & Francis, 1865) Large 4to. Without wrappers. Extracted from ""Philosophical Transactions of the Royal Society of London."", Vol. 155 - Part II. Pp. 725-791. Fine and clean.‎

‎"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.‎

Referencia librero : 42609

‎"POINCARÉ, HENRI.‎

‎La Méthode de Neumann et le Probleme de Dirichlet.‎

‎(Berlin, Uppsala & Stockholm, Paris, 1895). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler"", Bd. 20, pp. 59-142.‎

‎First edition. In this paper Poincaré succeeded in converting differential equations into integral equations. ""It became a major technique for solving initial-and boundary-value problems of ordinary and partial differential equations and was the strongest impetus for the study of integral equations."" (Morris Kline).‎

Referencia librero : 39131

‎"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...""‎

Referencia librero : 45910

‎"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.‎

Referencia librero : 49614

‎"POINCARÉ, H.‎

‎Remarques diverses sur l'équation de Fredholm.‎

‎[Berlin, Stockholm, Paris, Beijer, 1910] 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 33, pp. 57-86.‎

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

Referencia librero : 45841

‎"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)‎

Referencia librero : 49622

‎"POINCARÉ, HENRI.‎

‎Sur les Intégrales irrégulieres des Equations linéaires. - [THE FORMAL THEORY OF ASYMPTOTIC SERIES]‎

‎(Berlin, Uppsala & Stockholm, Paris, 1886). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 8, pp. 295-344.‎

‎First edition. ""The full recognition of the nature of those divergent series that are useful in the representation and calculation of functions and a formal definition of those series wer achieved by Poincaré and Stieltjes independently in 1886. Poincaré called these series asymptotic while Stieltjes continued to use the term semiconvergent. Poincaré took up the subject in order to further the solution of linear differential equations. Impressed by the usefulness of divergent series in astronomy, he sought to determine which were useful and why. he succededed in islolating and formulating the essential property...Poincaré applied his theory of asymptotic series to diffrential equations, and theree are many such uses in his treatise on celestical mechanics, 'Les Methodes nouvelles de la mechanique céleste"". (Morris Kline).‎

Referencia librero : 39132

‎"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.‎

Referencia librero : 39134

‎"POINCARÉ, HENRI.‎

‎Sur les Groupes des Equations linèaires.‎

‎(Stockholm, F.& G. Beier), 1885. 4to. Orig. printed wrappers (to Acta Mathematica 4:3). Extracted from ""Acta Mathematica"", Vol. 4. Pp. 201-312. Clean and fine.‎

‎First appearance of a major paper on differential equations of the first order""...the whole theory of automorphic functions was from the start guided by the idea of integrating linear differential equations with algebraic coefficients. Poincaré simultaneously investigated the local problem of linear differential equation in the neighborhood of an ""irregular"" singular point, showing for the first time how asymptotic developments could be obtained for the integrals. A little later (1884, the paper offered) he took up the question, also started by I.L. Fuchs, of the determination of all differential equations of the first order (in the complex domain) algebraic in y and y' and having fixed singular points"" his rechearches was to be extended by Picard for equations of the second order, and to lead to the spectacular results of Painlevé and his school at the beginning of the tweentieth century.""(DSB).‎

Referencia librero : 41900

‎"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)‎

Referencia librero : 45787

‎"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.‎

Referencia librero : 45849

‎"POINCARÉ, H.‎

‎Sur les rapports de l'analyse pure et de la physique mathématique.‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1897]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 21. No backstrip. Fine and clean. Pp. 331-341.‎

‎First printing of Poincaré's principal address at the first International Congress of Mathematicians held in Zürich in 1897.‎

Referencia librero : 46182

‎"POINCARÉ, HENRI (+) GEORG CANTOR.‎

‎Sur les Fonctions Uniformes qui se reproduisent par des Substitutions Linéaires (+) Ueber ein neues und allgemeines Condensationsprincip der Singularitäten von Functionen.‎

‎Leipzig, B.G. Teubner, 1882. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 37, 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Fine and clean. Pp. 182-228. [Entire volume: IV, 604 pp.].‎

‎First printing of Poincaré's paper on his comprehensive theory of complex-valued functions which remain invariant under the infinite, discontinuous group of linear transformations. In 1881 Poincaré had published a few short papers with some initial work on the topic, and in the 1881, Klein invited Poincaré to write a longer exposition of his results to Mathematische Annalen which became the present paper. This, however, turned out to be an invitation to at mathematical dispute:""Before the article went to press, Klein forewarned Poincaré that he had appended a note to it in which he registered his objections to the terminology employed therein. In particular, Klein disputed Poincaré's decision to name the important class of functions possessing a natural boundary circle after Fuch's, a leading exponent of the Berlin school. The importance he attached to this matter, however, went far beyond the bounds of conventional priority dispute. True, Klein was concerned that his own work received sufficient acclaim, but the overriding issue hinged on whether the mathematical community would regard the burgeoning research in this field as an outgrowth of Weierstrassian analysis or the Riemannian tradition."" Parshall. The Emergence of the American Mathematical Research Community. Pp. 184-5.The issue contains the following important contributions by seminal mathematicians:1. Klein, Felix. Ueber eindeutige Functionen mit linearen Transformationen in sich. Pp. 565-68.2. Picard, Emile. Sur un théorème relatif aux surfaces pour lesquelles les coordnnées d´un point quelconque s´experiment par des fonctions abéliennes de deux paramètres. Pp. 578-87.‎

Referencia librero : 47185