‎Mathématiques‎

‎"PEARSON, KARL AND ALICE LEE. - COINING THE CONCEPTS 'MULTIPLE CORRELATION"" AND 'PARTIAL CORRELATION'.‎

‎On the Distribution of Frequency (Varation and Correlation) of the Barometric Heigh at Divers Stations. Received June 15, - Read June 17, 1897.‎

‎(London, Harrison and Sons, 1897). 4to. No wrappers as extracted from ""Philosophical Transactions"" Year 1897, Volume 190 - Series A. - Pp. 423-469 and 9 plates. 1 textillustr.‎

‎First appearance of the statistical paper in which the authors introduced the conceptS of 'Multiple Correlation' and 'Partial Correlation'. ""Pearson did not pursue the theory of multiple and partial correlation beyond the point to which he had carried it in his basic memoir on correlation (1896). The general theory of multiple and partial correlation and regression was developed by his mathematical assistant, G. Udny Yule, in two papers published in 1897. Yule was the first to give mathematical expressions for what are now called partial correlation coefficients, whcih he termed ""net correlation coefficients."" What Pearson had called coefficients of double regression, Yule renamed net regressions"" they are now called partial regression coefficients. The expressions ""multiple correlation"" and ""partial correlation"" stem from the paper written Alice Lee and read to the Royal Society in 1897.""(DSB).‎

书商的参考编号 : 44863

‎"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.‎

‎First appearance of the founding papers of modern mathematical statistics, out of which grew Pearson's creation of Biometrics.""Founder of biometrics, Karl Pearson was one of the principal architects of the modern mathematical statistics. He was a polymath whose interests ranges from astronomy, mechanics, meteorology and physics, to biological sciences in particular, including...eugenics, evolotionary biology,heredity......Largly owing to his interests in evolutionary biology, Person created, almost single-handedly, the modern theory of statistics in his Biometric School at University College London.... In his creation of biometrics, out of which the discipline of mathematical statistics had develoiped by the end of the nineteenth century, Person introduced a new vernacular for statistics (including such termss as the standard deviation, mode, homoscedasticity, heteroscedasticity, kurtosis and the producct-moment correlation coefficient."" (Heyde in Statisticians of the Centuries).In the first paper offered here Person introduced the method of moments as a mean curve fitting assymetrical distributions (""point-binominals"") and he applies the theory to crabs and prawns. This is a general method for determining the values of the parameters of a frequency distribution.In the second paper offered here, Pearson develpoed the general formula to use for subsets of six types of frequency curves, now known as ""Pearson Type Curves"".In his seminal paper ""Regressin, Heredity and Panmixia"", the third papers offered here, Pearson introduced matrix algebra into statistical theory and also introducing 'eta' as a measure for curvilinear relationship, the standard error of an estimate, multiple regression and multiple and partial correlation, and devises the coefficient of variation as a measure of the ratio of a standard deviation to the corresponding mean expressed as a percentage.In the fourth paper he deals with the theory of probable erros and of correlations of errors...In the fifth paper he deals with the theory as involving multiple correlations...stature in biology is shown to be best reconstructed from measurements of long bones.The last paper offered deals with a variety of biological correlations, inheritance of characters etc. etc.G.M. Morant: A Bibliography ofthe Statistical and other writings of Karl Pearson Nos 2, 4, 6, 16, 17 and 20. - Eiasenhart in DSB, pp. 449-453.‎

书商的参考编号 : 42461

‎"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).‎

‎A Quincuncial Projection of the Sphere + On the Ghosts in Rutherfurd's Diffraction-Spectra. [In: American Journal of Mathematics. Volume II. Number 4.]. - [THE PEIRCE QUINCUNCIAL PROJECTION + ""GHOSTS""]‎

‎Baltimore, John Murphy & Co., 1879. 4to, entire issue present (Vol. II, no. 4). With the original printed wrappers. Uncut. Wrappers loose and with tears and loss to extremities. Backtrip gone. Stitching a bit loose. Internally nice and clean. First paper: A Quincuncial Projection of the Sphere pp. (394)-396 + 1 folded table. Second paper: On the Ghosts in Rutherfurd's Diffraction-Spectra pp. (330)-347. [Entire issue: pp. (293)-404 + IV, (2) pp]‎

‎"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]‎

‎"PERRON, OSKAR.‎

‎Zur Theorie der Matrices. - [Perron-Frobenius theorem]‎

‎Leipzig, B. G. Teubner, 1907. 8vo. Bound in contemporary half calf with gilt lettering to spine. In ""Mathematische Annalen"", 64. Band, 1907. Hinges and extremities with wear. Bookplates to pasted down front free end-paper. Internally fine and clean. Pp. 248-263. [Entire volume: IV, 576 pp].‎

‎"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.‎

‎"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.‎

书商的参考编号 : 45848

‎"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.‎

‎Über ein neues Princip der Geometrie und den Gebrauch allgemeiner Symbole und unbestimmter Ciëfficienten‎

‎(Berlin, G. Reimer, 1830). 4to. No wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 5. - Plücker's paper pp. 268-286.‎

‎"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.‎

‎"POCHHAMMER, L.‎

‎Ueber hypergrometrische Functionen n-ter Ordnung. - [GENERALIZED HYPERGEOMETRIC FUNCTIONS]‎

‎Berlin, G. Reimer, 1870. 4to. As extracted without backstrip with the original front wrapper from ""Journal für die reine und angewandte Mathematik"". 71. band, 4. heft, 1870. Occasional brown spots, otherwise fine and clean. Pp. 316-52. [Entire volume: Pp.305-84].‎

‎First printing of Pochhammer's seminal publication in which Generalized Hypergeometric Functions (or Pochhammer Symbols) was introduced for the first time. Pochhammer symbols are now generally used for expressing hypergeometric functions in a compact notation.‎

书商的参考编号 : 47280

‎"POCHHAMMER, LEO.‎

‎Zur Theorie der Euler'schen Integrale. - [POCHHAMMER CONTOUR]‎

‎Leipzig, B. G. Teubner, 1890. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 35., 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. 495-526. [Entire volume: IV, 604 pp.].‎

‎First publication of the paper which named the ""Pochhammer contour"". Pochhammer contour is a contour in the complex plane with two points removed, used for contour integration.Camille Jordan published in 1887 a paper introducing the concept. In 1890 Porchhammer expanded his theories in the present paper.‎

书商的参考编号 : 47128

‎"POINCARE, H. (HENRI). - THE DISCOVERY OF AUTOMORPHIC FORMS.‎

‎Sur les fonctions fuchsiennes. (+) Sur les fonctions.... Note. (+) Sur les fonctions.... Note.‎

‎(Paris: Gauthier-Villars), 1882. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences"", Vol 94, No 4 + 15 + 17. Pp. (149-) 184, pp. (997--) 1068 a. pp. (1139-) 1214. (3 entire issues offered). Poincare's papers: pp. 163-168, 1038-1042 a. 1166-67.‎

‎"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.‎

‎"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)‎

书商的参考编号 : 49622

‎"POINCARÉ, H.‎

‎Remarques sur les intégrales irrégulières deséquations linéaires.‎

‎Berlin, G. Reimer, 1887. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 10, 1887. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 310-12. [Entire volume: (4), 397 pp].‎

‎First printing of Poincaré's reply to Thomé's critique of an earlier paper by Poincaré. In his reply Poincaré ""seems to have created a theory of asymptotic expansions where previously there had only been ad hoc techniques, and to have opened the door for the return into rigorous mathematics of divergent series."" (Bottazzini, Hidden Harmony).‎

书商的参考编号 : 49613

‎"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).‎

书商的参考编号 : 49616

‎"POINCARÉ, H.‎

‎Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation. - [POINCARÉ'S PEAR-SHAPE]‎

‎(Stockholm, Beijer), 1885. 4to. As extracted from ""Acta Mathematica, 21. Band]. No backstrip. Fine and clean. Pp. 259-380.‎

‎First printing of Poincaré's famous paper in which he proved that a rotating fluid such as a star changed its shape from a sphere to an ellipsoid to a pear-shape before breaking into two unequal portions. ""This work, which contained the discovery of new, pear-shaped figures of equilibrium, aroused considerable attention because of its important implications for cosmogony in relation to the evolution of binary stars and other celestial bodies."" (The Princeton Companion to Mathematics, P. 786)Another famous paper of Poincaré in celestial mechanics is the one he wrote in 1885 on the shape of a rotating fluid mass submitted only to the forces of gravitation. Maclaurin had found as possible shapes some ellipsoids of revolution to which Jacobi had added other types of ellipsoids with unequal axes, and P. G. Tait and W. Thomson some annular shapes. By a penetrating analysis of the problem, Poincaré showed that still other ""pyriform"" shapes existed. One of the features of his interesting argument is that, apparently for the first time, he was confronted with the problem of minimizing a quadratic form in ""infinitely"" many variables."" (DSB)‎

书商的参考编号 : 45787

‎"POINCARÉ, H.‎

‎Sur la méthode horistique de Gyldén. - [POINCARÉ ON GYLDÉN'S HORISTIC METHODS]‎

‎Berlin, G. Reimer, 1905, 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 29, 1905. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 235-72. [Entire volume: (4), 433 pp].‎

‎First printing of Poincaré's final and most extensive paper on Gyldén's horistic methods.‎

书商的参考编号 : 49615

‎"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.‎

书商的参考编号 : 46182

‎"POINCARÉ, H.‎

‎Sur un theoreme de M. Fuchs.‎

‎Stockholm, Beijer, 1885. 4to. As extracted from ""Acta Mathematica, 21. Band]. No backstrip. Fine and clean. Pp. 83-97.‎

‎First printing of Poincaré's paper in which he developed the idea published by Fuchs in 1884. Fuchs established that the equation with fixed branch points can be made into a Riccati equation if its genus - the genus of the corresponding Riemann surface - with respect to u and du/dz is zero and can be integrated using elliptic functions if the genus is 1.‎

书商的参考编号 : 45788

‎"POINCARÉ, H.‎

‎Sur une Forme nouvelle des Équations du Probleme des trois Corps (+) Sur les rapports de l'analyse pure et de la physique mathématique.‎

‎Berlin, Uppsala & Stockholm, Paris, Almqvist & Wiksell, 1897. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 21, 1897. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 83-97"" Pp. 331-341.[Entire volume: (6), 376 pp + 4 plates].‎

‎First printing of this paper in which 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.Also included is the first printing of Poincaré's principal address at the first International Congress of Mathematicians held in Zürich in 1897.‎

书商的参考编号 : 49621

‎"POINCARÉ, H. (+) VITO VOLTERRA.‎

‎L'oeuvre mathématique de Weierstrass (+) Sur les Propriétes du potentiel et sur les Fonctions Abéliennes [Poincaré] (+) Sur la Théorie des Variations des Latitudes [Poincaré].‎

‎Berlin, Stockholm, Paris, Beijer, 1899. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 22, 1899. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 1-18" Pp. 89-178" Pp. 201-358.[Entire volume: (4), 388, 2 pp].‎

‎First printing of these important papers: POINCARÉ: 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).VOLTERRA: First edition. As the north and south poles, instead of being fixed points on the earth's surface, wander round within a circle of ab. 5o ft. in diameter, the result is a variability of terrestial latitudes generally. Volterra gives an elaborate mathematical analysis of these yearly fluxtuations.‎

书商的参考编号 : 49640