‎Mathématiques‎

‎"PASCH, MORITZ.‎

‎Mathematik am Ursprung. Gesammelte Abhandlungen über Grundfragen der Mathematik.‎

‎Leipzig, Felix Meiner, 1927. Orig. printed wrappers. Frontwrapper loose. Small loss to top of backstrip. (4),149 pp. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on frontwrapper.‎

‎First edition of this collection of 7 of Pasch's most importent work on axiomatics and geometry.""Pasch initiated the axiomatic method, although the foundational developments of his time were against this point of view. Thus Cantor's striking discoveries were based, from an axiomatic point of view, on nothing... As late as 1903 Frege poked fun of at the axiomatic method as presented in Hilbert's ""Grundlagen der Geometrie....particularly Peano continued Pasch's work. In 1889 Peano published both his exposition of geometry, following Pasch, and his treatment of number...Pasch played a crucial role in the innovation of the axiomatic methode. This method, with contributions from logic and algebra, is a central feature of twentieth-century mathematics."" (DSB).‎

书商的参考编号 : 47944

‎"PASCH, MORITZ.‎

‎Vorlesungen über Neuere Geometrie. - [THE INNOVATION OF THE AXIOMATIC METHOD]‎

‎Leipzig, B.G. Teubner, 1882. Contemp. hcloth. IV,201,(1) pp., textfigs. At end inserted ""Anfangsgründe der beschreibende Geometrie nebst einem Anhang über Kartenprojection. Ein Leitfaden beim Unterricht an höheren Lehranstalten von Wilhelm Mink."" Orig. printed wrappers. 47 pp. textfigs. Internally fine and clean.‎

‎Scarce first edition of this groundbreaking work. ""The work on non-Euclidean geometry had brought the realization that geometries are man-made constructions bearing upon physical space but not necessarely exact idealization of it. This fact implied that several major changes had to be incorporated in any axiomatic approach to geometry. These were recognized and stressed by Moritz Pasch (1843-1930), who was the first to make major contributions to the foundations of geometry. His ""Vorlesungen über neuere Geometrie"", (the offered item) is a groundbreaking work."" (Morris Kline).""Pasch initiated the axiomatic method, although the foundational developments of his time were against this point of view. Thus Cantor's striking discoveries were based, from an axiomatic point of view, on nothing...As late as 1903 Frege poked fun of at the axiomatic method as presented in Hilbert's ""rundlagen der Geometrie....particularly Peano continued Pasch's work. In 1889 Peano published both his exposition of geometry, following Pasch, and his treatment of number...Pasch played a crucial role in the innovation of the axiomatic methode. This method, with contributions from logic and algebra, is a central feature of twentieth-century mathematics."" (DSB). - Sommerville ""Bibliography of Non-Euclidean Geometry"", p. 67 (1882).‎

书商的参考编号 : 39290

‎"PEANO, G. (GUISEPPE). - THE ""FORMULARIO-PROJECT""‎

‎Formulaire de Mathématiques.‎

‎Paris, Georges Carré et C. Naud, 1901. Royal8vo. Contemp. hcalf. Spine gilt and with gilt lettering. Small stamp at foot of titlepage and last leaf. VIII,230,(2) pp. With the ownership-signature of the noted Danish logician Jørgen Jørgensen to front free endpaper. Clean and fine.‎

‎First edition of Peano's third version - the third volume - of his Formulario-project aiming at presenting all mathematical axioms and results in a clear form always using his five axioms and thereby rewrites all known mathematics in a symbolic form and thus provide a key to a satisfactory solution to the questions of the foundations of mathematics. The logical notations used by Peano were used and developed by Whitehead and Russell in their ""Principia Mathematica"" of 1910.""In 1892 he announced in the Rivista the Formulario project, which was to take much of his mathematical and editorial energies for the next sixteen years. He hoped that the result of this project would be the publication of a collection of all known theorems in the various branches of mathematics. The notations of his mathematical logic were to be used, and proofs of the theorems were to be given. There were five editions of the Formulario (the offered item being the third). The first appeared in 1895"" the last was completed in 1908, and contained some 4,200 theorems (the item offered). But Peano was less interested in logic as a science per se than in logic as used in mathematics. (For this reason he called his system ""mathematical logic."") Thus the last two editions of the Formulario introduce sections on logic only as it is needed in the proofs of mathematical theorems."" (DSB).The famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano (1858 -1932) studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting this to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. In 1890 Peano became extraordinary professor, and in 1895 ordinary professor, of infinitesimal calculus at the Unversity of Turin.‎

书商的参考编号 : 48350

‎"PEANO, G. (GUISEPPE). - THE ""FORMULARIO-PROJECT""‎

‎Formulaire de Mathématiques. Publié par le ""Rivista di Mathematica"". Tome I, Tome II and Édition de L'An 1901 (= Tome III).‎

‎Turin, Bocca Freres, 1895, 1899 a. 1901. One contemp. hcalf. Spine lacks. VII,144 - 198,(1) - VIII,230,(1) pp. Internally fine.‎

‎"PEANO, GIUSEPPE.‎

‎Demonstration de l’intégrabilité des équations différentielles ordinaires. - [PEANO EXISTENCE THEOREM]‎

‎Leipzig, B.G. Teubner, 1890. 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.].‎

‎"PEANO, GIUSEPPE.‎

‎Démonstration de l'intégrabilité des équations différentielles ordinaires. - [THE PROOF OF THE EXISTENCE THEOREM - INTRODUCING THE AXIOM OF CHOICE]‎

‎Leipzig, B.G. Teubner, 1890. Orig. printed wrappers, no backstrip. A small offsetting to upper left corner of frontwrapper. A small tear to endwrapper repaired. In ""Mathematische Annalen. Gegenwärtig hrsg. von Felix Klein, Walter Dyck, Adolph Mayer, 36. Band, 2. Heft."" Pp. (153-)320. The whole issue (Heft 2) with orig.wrappers. Peano's paper: pp. 182-288.‎

‎"PEANO, GIUSEPPE.‎

‎Generalizzazione della formola di Simpson.‎

‎Torino, Fratelli Bocca, 1891-1892. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXVII, Disp. 10a, 1891-92. Small paper label pasted on to lower left part of front wrapper. A very fine and clean copy. Pp. 608-612. [Entire issue: Pp. 597-655].‎

‎"PEANO, GIUSEPPE.‎

‎La Geometria basata sulle idee di punto e distanza.‎

‎Torino, Carlo Clausen, 1903. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXXVIII, Disp. 1a e 2a, 1902-1903. Small paper label pasted on to lower left part of front wrapper and stamp to top of front wrapper and title page. Wrappers with nicks, miscolouring and traces after having been bended. Title page with a browning. Internally fine. Pp. 6-10. [Entire issue: 53 pp].‎

‎"PEANO, GIUSEPPE.‎

‎La numerazione binaria applicata alla stenografia.‎

‎Torino, Carlo Clausen, 1898. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXXIV, Disp. 1a, 1894-95. Small paper label pasted on to lower left part of front wrapper. Wrappers with nicks and lacking lower right corner of front wrapper. Internally with occassional brown spots. Fine. Pp. 20-41. [Entire issue: 78 pp].‎

‎"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.‎

‎Sulla formola di Taylor.‎

‎Torino, Carlo Clausen, 1891-1892. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXVII, Disp. 1a, 1891-92. Small paper label pasted on to lower left part of front wrapper. A very fine and clean copy. Pp. 40-46. [Entire issue: 154 pp].‎

‎"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.‎

‎Two rare and important first editions by the famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano, uniting his first publication in logic with his introduction of the basic elements of geometric calculus. The present ""Calcolo geometrico secondo l'Ausdehningslehre de H. Grassmann"" contains a twenty-page long preliminary section on the operations of deductive logic, which constitutes Peano' s very first publication on the subject for which he is most famous, namely logic. This work appeared the year before his seminal ""Arithmetices Principia..."", in which he further improves his logical symbolism, which is introduced in the preliminary section of the present work. ""This section, which has almost no connection with the rest of the text, is a synthesis of, and improvement on, some of the work of Boole, Schröder, Peirce, and McColl."" (D.S.B. X:442).In the other present work, ""Applicazioni geometriche del calcolo infinitesimale"", Peano introduces the basic elements of geometric calculus and gives new definitions for the length of an arc and for the area of a curved surface. This important work (in which not only his geometrical calculus is introduced, but in which he also presented several new geometrical discoveries) is based on his lectures on infinitesimal calculus and its application to geometry from 1885. ""The treatise ""Applicazioni geometriche del calcolo infinitesimal"" (1887) was based on a course Peano began teaching at the University of Turin in 1885 and contains the beginnings of his ""geometrical calculus"" (here still influenced by Bellavitis' method of equipolences), new forms of remainders in quadrature formulas, new definitions of length of an arc of a curve and of area of a surface, the notion of a figure tangent to a curve, a determination of the error term in Simpson's formula, and the notion of the limit of a variable figure. There is also a discussion of the measure of a point set, of additive functions of sets, and of integration applied to sets. Peano here generalized the notion of measure that he had introduced in 1883."" (D.S.B. X:443). Peano (1858 -1932) studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting this to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. In 1890 Peano became extraordinary professor, and in 1895 ordinary professor, of infinitesimal calculus at the Unversity of Turin. Cellerino (Guiseppe Peano e la sua scuola. Catalogo monografico): Nr. 2 + 3. 2: ""Il più alto raggiunto dai matematici del XIX secolo nell'elaborazione della teoria delle funzioni di insiemi, è il V capitolo del libro di Peano..."" F.A. Medvedev.""‎

书商的参考编号 : 39042

‎"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 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.‎

‎"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.‎

‎In this fundamental paper in statistics, Pearson introduced his chi-squared test, the statistical procedure whose results are evaluated by reference to the chi-squared distribution, or the formula yielding a measure of how well a set of observations fits a theoretical hypothesis, the test of goodness of fit. A founding seminal paper in statistical testing theory.""Pearson’s many contributions to statistical theory and practice, many contributions to statistical theory and practice, this X2 text for goodness of fit is certainly one of his greatest"" and in its original and extended forms it has remained one of the most useful of all statistical tests."" (DSB).Parkinson ""Breakthroughs"" 1900 M.‎

书商的参考编号 : 47148

‎"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]‎

‎Scarce first printings of these seminal papers, the first of which introduces Peirce's quincunical projection, the second of which documents his discovery of hitherto unknown diffraction phenomena called ""ghosts"".The Peirce quincuncial projection (published here for the first time) is a conformal map projection that presents the sphere as a square, which allowed for the displaying of the entire sphere with most areas being recognizable . Peirce called his projection quincuncial, after the arrangement of five items in a quincunx. ""For meteorological, magnetological and other purposes, it is convenient to have a projection of the sphere which shall show the connections of all parts of the surface."" Peirce himself wrote. (American Journal of Mathematics. Volume II. Number 4, 394 pp.)In ""On the Ghosts in Rutherfurd's Diffraction-Spectra"" Peirce documented his discovery of hitherto unknown diffraction phenomena called ""ghosts."" In his spectrum meter experiments, Peirce compared wave-lengths of light with the breadth of a diffraction plate. He used a machine called a comparator, a spectrometer he himself designed, and a diffraction plate designed by Lewis M. Rutherfurd.‎

书商的参考编号 : 41487

‎"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]‎

‎The scarce first printing of Peirce's important paper ""On the Algebra of Logic"", in which he broke with the Aristotelian semantics of classes and introduced modern semantics, allowing a class symbol to be empty (as well as to be the universe), and stated the truth values of the categorical propositions that we use today.""This article holds a place of some importance in the history of formal logic and mathematics. In what is published here from the first chapter Peirce discusses that relationship between thinking and cerebration (or logic and physiology)."" (The Essential Peirce: 1867-1893 v. 1: Selected Philosophical Writings, Indiana University Press, 1992, 200 pp.‎

书商的参考编号 : 41486

‎"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].‎

‎First printing of Perron's important paper on positive matrices which profoundly influenced several fields of science. ""Today the Perron-Frobenius mathematics of nonnegative matrices enjoys wide applications, the most sensational perhaps being its implicit use by millions of internet surfers, who routinely activate Google's PageRank algorithm every day. Such a remarkable worldwide application in an electronic search engine is a far cry from the original theoretical articles, written more than a century ago, by Perron and Frobenius. These two German scholars preferred to concentrate on pure mathematics. Especially Frobenius in Berlin considered applications as inferior subjects that should be relegated to technical schools"" (PARYS, How pioneers of linear economics overlooked Perron-Frobenius mathematics).The volume also contain Hjelmslev's important paper: ""Neue Begründung der ebenen Geometrie"" and Brill's paper on three-dimensional algebraic curves: ""Ueber algebraische Raumkurven"".‎

书商的参考编号 : 47453

‎"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

‎"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).‎

书商的参考编号 : 40444

‎"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.‎

‎First appearance of a paper which relates to Plücker's ""New Geometry"".‎

书商的参考编号 : 41886

‎"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.‎