‎Mathématiques‎

‎"CANTOR, G.‎

‎Fondements d'une théorie générale des ensembles (+) Sur divers théorémes de la théorie des ensembles de points situs - dans un espace continu a n dimensions. - [SET THEORY]‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1883]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 2. Fine and clean. Pp. 381-414.‎

‎First French translation (and translation in general) of Cantor's fifth, thus most important, paper in his series of papers which founded set theory. (The first mentioned).It contained Cantor's reply to the criticism of the first four papers and showed how the transfinite numbers were a systematic extension of the natural numbers. It begins by defining well-ordered sets. Ordinal numbers are then introduced as the order types of well-ordered sets. Cantor then defines the addition and multiplication of the cardinal and ordinal numbers. In 1885, Cantor extended his theory of order types so that the ordinal numbers simply became a special case of order types. It was later published as a separate monograph.The concept of the existence of an infinity was an important shared concern within the realms of mathematics, philosophy and religion. Preserving the orthodoxy of the relationship between God and mathematics was long a concern of Cantor's. He directly addressed this relationship between these disciplines in the introduction to the present paper, where he stressed the connection between his view of the infinite and the philosophical one. To Cantor, his mathematical views were closely linked to their philosophical and theological implications-he identified the Absolute Infinite with God and he considered his work on transfinite numbers to have been directly communicated to him by God, who had chosen Cantor to reveal them to the world.‎

書籍販売業者の参照番号 : 45855

‎"CANTOR, G.‎

‎Sur les ensembles infinis et linéaires de points (I-IV).‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1883]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 2. No backstrip. Fine and clean. Pp. 349-380.‎

‎First printing of Poincaré's concluding papers on transfinite numbers.‎

書籍販売業者の参照番号 : 46181

‎"CANTOR, G.‎

‎Sur les séries trigonométriques (transl. of Über trigonometrische Reihen) (+) Extension d'un théoréme de la théorie des séries trigonométriques.‎

‎Berlin, Stockholm, Paris, Beijer, 1883. 4to. As extracted from ""Acta Mathematica, 2. band."", Clean and fine. Pp. 329-348.‎

‎First transation of Cantor's important papers on trigonometric series.‎

書籍販売業者の参照番号 : 46012

‎"CANTOR, G.‎

‎Sur une propriété du systéme de tous les nombres algébriques réels. [Translated from the German: Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen]. - [FIRST CONTRIBUTION TO SET THEORY AND THE BIRTH OF THE THEORY OF THE TRANSFINITE]‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1883]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", Bd. 2. Fine and clean. Pp. 305-328.‎

‎First French [and general] translation of Cantor's famous and exceedingly influential paper which contains the first proof that the set of all real numbers is uncountable"" also contains a proof that the set of algebraic numbers is denumerable. ""This article is Cantor's first published contribution to the theory of sets. The deep and epoch-making result of the paper is not the easy theorem alluded to in the title - the theorem that that the class of real algebraic numbers is countable - but rather the proof, in 2, that the class of real numbers is not countable [...]. And that marks the start of the theory of the transfinite. [Ewald, Pp. 839-40].""The first published writing on set theory [the present paper], contained more than the title indicated, including not only the theorem on algebraic numbers but also the one on real numbers, in Dedekind's simplified version, which differs from the present version in that today we use the ""diagonal process,"" then unknown"" (DSB)‎

書籍販売業者の参照番号 : 45857

‎"CANTOR, GEORG (+) WILHELM KILLING.‎

‎Bemerkung mit Bezug auf den Aufsatz: Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen (+) Die Zusammensetzung der stetigen endlichen Transformationsgruppen.‎

‎Leipzig, B. G. Teubner, 1889. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 33., 1889. 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. P. 476"" Pp. 1-48. [Entire volume: IV, 604 pp.].‎

‎First printing of CANTOR'S important comment to Illigens paper from the same year: ""Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen"". He states that: ""The squareroot of 3 is thus only a symbol for number which has yet to to be found, but is not its definition. The definitions is, however, satisfactorily given by my method as, say (1.7, 1.73, 1.732, ...). [From the present paper]. First publication of KILLING'S important second paper (of a total of four) in which he laid the foundation of a structure theory for Lie algebras.""In particular he classified all the simple Lie algebras. His method was to associate with each simple Lie algebra a geometric structure known as a root system. He used linear transformation, to study and classify root systems, and then derived the structure of the corresponding Lie algebra from that of the root system.""(Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences)Unfortunately for Killing a myth arose that his work was riddled with error, which later has been proved untrue. ""As a result, many key concepts that are actually due to Killing bear names of later mathematicians, including ""Cartan subalgebra"", ""Cartan matrix"" and ""Weyl group"". As mathematician A. J. Coleman says, ""He exhibited the characteristic equation of the Weyl group when Weyl was 3 years old and listed the orders of the Coxeter transformation 19 years before Coxeter was born.""The theory of Lie groups, after the Norwegian mathematician Sophus Lie, is a structure having both algebraic and topological properties, the two being related.‎

書籍販売業者の参照番号 : 47188

‎"CANTOR, GEORG.‎

‎Bemerkung mit Bezug auf den Aufsatz: Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen in Math. Annalen. Bd. XXXIII, p. 154. - [CANTOR ON NUMBER THEORY]‎

‎Leipzig, B.G. Teubner, 1889. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet 1889 durch Rudolf Friedrich Alfred Clebsch. XXXIII.[33] Band. 3. Heft."" Entire issue offered. Internally very fine and clean. [Cantor:] P. 476. [Entire issue: Pp. (1), 318-476, (1)].‎

‎First printing of Cantor's important comment to Illigens paper from the same year: ""Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen"". He states that: ""The squareroot of 3 is thus only a symbol for number which has yet to to be found, but is not its definition. The definitions is, however, satisfactorily given by my method as, say (1.7, 1.73, 1.732, ...). [From the present paper]. Cantor is famous for his work on infinite numbers.‎

書籍販売業者の参照番号 : 44494

‎"CANTOR, GEORG.‎

‎Über unendliche, lineare Punktmannichfaltigkeiten. - [THE THEORY OF SETS AND INFINITE SETS - THE SECOND PAPER]‎

‎Leipzig, B.G. Teubner, 1880. 8vo. Bound in a nice contemporary half calf with five raised gilt bands. Red leather title label with gilt lettering to spine. All edged gilt. In ""Mathematische Annalen"", Band 17, 1880. Entire volume offered. Corners with wear, otherwise a very fine and clean copy. Pp. 355-358. [Entire volume: IV, 576 pp.].‎

‎"CANTOR, GEORG.‎

‎Über unendliche, lineare Punktmannichfaltigkeiten. - [THE THEORY OF SETS AND INFINITE SETS - THE FINAL PAPER]‎

‎Leipzig, B.G. Teubner, 1884. 8vo. Bound in a nice contemporary half calf with five raised gilt bands. Red leather title label with gilt lettering to spine. All edged gilt. In ""Mathematische Annalen"", Band 23, 1884. Entire volume offered. Corners with wear, otherwise a very fine and clean copy. Pp. 453-488. [Entire volume: IV, 598, (2) pp.].‎

‎First printing of Cantor's seminal sixth paper in the landmark series consisting of a total of six papers which together constitute the foundation Theory of Sets (Mengenlehre) and Transfinite Set Theory. Cantor here introduces his new Set Theory with which he created an entirely new field of mathematical research and is widely regarded as being one of the most important mathematical conquests in the 19th century. ""Cantor published a sequel in the following year as a sixth in the series of papers on the Punktmannigfaltigkeitslehre (The present paper). Though it did not bear the title of its predecessor, its sections were continuously numbered, 15 through 19"" it was clearly meant to be taken as a continuation of the earlier 14 sections of the ""Grundlagen"" itself. In searching for a still more comprehensive analysis of continuity, and in the hope of establishing his continuum hypothesis, he focused chiefly upon the properties of perfect sets and introduced as well an accompanying theory of content"" (Dauben, P. 111)Hilbert spread Cantor's ideas in Germany and praised Cantor's transfinite arithmetic as ""the most astonishing product of mathematical thought, one of the most beautiful realizations of human activity in the domain of the purely intelligible"". He is famously quoted for saying ""No one shall expel us from the paradise which Cantor created for us"". Bertrand Russel described Cantor's work as ""probably the greatest of which the age can boast"".""The major achievement of the ""Grundlagen"" was its presentation of the transfinite ordinal numbers as a direct extension of the real numbers. Cantor admitted that his new ideas might seem strange, even controversial, but he had reached a point in his study of the continuum where the new numbers were indispensable for further progress. Cantor had finally come to the realization that his 'infinite symbols' were not just indices for derived sets of the second species, but could be regarded as actual transfinite numbers that were just as real mathematically as the finite natural numbers."" (Grattan-Guinness, Landmark Writings in Western Mathematics, Pp. 604-5).Dauben: (Cantor)1884a.‎

書籍販売業者の参照番号 : 47159

‎"CANTOR, GEORG.‎

‎Über unendliche, lineare Punktmannichfaltigkeiten. - [THE THEORY OF SETS AND INFINITE SETS - THE FIRST PAPER]‎

‎Leipzig, B.G. Teubner, 1879. 8vo. Bound in a nice contemporary half calf with five raised gilt bands. Red leather title label with gilt lettering to spine. All edged gilt. In ""Mathematische Annalen"", Band 15, 1879. Entire volume offered. Corners with wear, otherwise a very fine and clean copy. Pp. 1-7. [Entire volume: IV, 576 pp.].‎

‎First printing of Cantor's seminal exceedingly important first paper in his landmark series of six papers which together constitute the foundation Theory of Sets (Mengenlehre) and Transfinite Set Theory. Cantor here introduces his new Set Theory with which he created an entirely new field of mathematical research and is widely regarded as being one of the most important mathematical conquests in the 19th century. Hilbert spread Cantor's ideas in Germany and praised Cantor's transfinite arithmetic as ""the most astonishing product of mathematical thought, one of the most beautiful realizations of human activity in the domain of the purely intelligible"". He is famously quoted for saying ""No one shall expel us from the paradise which Cantor created for us"". Bertrand Russel described Cantor's work as ""probably the greatest of which the age can boast"".""The major achievement of the ""Grundlagen"" was its presentation of the transfinite ordinal numbers as a direct extension of the real numbers. Cantor admitted that his new ideas might seem strange, even controversial, but he had reached a point in his study of the continuum where the new numbers were indispensable for further progress. Cantor had finally come to the realization that his 'infinite symbols' were not just indices for derived sets of the second species, but could be regarded as actual transfinite numbers that were just as real mathematically as the finite natural numbers."" (Grattan-Guinness, Landmark Writings in Western Mathematics, Pp. 604-5).Dauben: (Cantor)1879b.‎

書籍販売業者の参照番号 : 47161

‎"CAPELLI, ALFREDO.‎

‎Ueber die Zurückführung der Cayley'schen Operation O auf gewöhnliche Polar-Operationen. - [CAPELLI'S IDENTITY]‎

‎Leipzig, B.G. Teubner, 1887. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 29, 1887. 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. 331-338. [Entire volume: IV, 582 pp.].‎

‎"CARNAP, RUDOLF.‎

‎Der Raum. Ein Beitrag zur Wissenschaftslehre. - [SPACE - CARNAP'S FIRST PUBLICATION]‎

‎Berlin, Reuther & Reichard, 1922. 8vo. Uncut in the original grey printed wrappers w. very neat professional repairs to inner hinges and to capitals. Printing on spine nearly fully intact. A very faint waterstaining to upper corner throughout, otherwise a very good, nice and clean copy of a publication, which in itself is quite fragile. 87 pp.‎

‎"CARNAP, RUDOLF.‎

‎Der Raum. Ein Beitrag zur Wissenschaftslehre. - [SPACE - CARNAP'S FIRST PUBLICATION]‎

‎Berlin, Reuther & Reichard, 1922. 8vo. Uncut in the original grey printed wrappers w. very neat professional repairs to inner hinges and to capitals. Printing on spine nearly fully intact. A very faint waterstaining to upper corner throughout, otherwise a very good, nice and clean copy of a publication, which in itself is quite fragile. 87 pp.‎

‎First edition of Carnap's first publication, his doctoral dissertation. Printed in Kant-Studien, Ergänzungshefte, Nr. 56. Issued by H. Vaihinger, M. Frischeisen-Kähler and A Liebert. Rudolf Carnap (born 1891 in Ronsdorf, Germany, died 1970 in Santa Monica, California) was an immensely influential analytic philosopher, who has contributed decisively to the fields of logic, epistemology, semantics, philosophy of science, and philosophy of language. He was one of the leading figures of the Vienna Circle, and a prominent logical positivist. He studied philosophy, physics and mathematics at the universities of Berlin and Freiburg, and worked at the universities of Jena, Vienna and Prague until 1935, when he, due to the war, emigrated to the U.S., where he became an American citizen in 1941. In America he became professor of the University of Chicago. In Jena he was appointed Professor of Mathematics, though his main interest at that time was in physics. By 1913 he planned to write his dissertation on thermionic emission, but this was interrupted by World War I, where he served at the front until 1917. Afterwards he studied the theory of relativity under Einstein in Berlin, and he developed the theory for a new dissertation, namely on an axiomatic system for the physical theory of space and time. He thus ended up writing the important dissertation under the direction of Bouch on the theory of space (Raum) from a philosophical point of view. The dissertation was submitted in 1921, and, due to the clear influence from Kantian philosophy, it was published the following year in this supplement to the ""Kant-Studien"". After the publication of his first work, Carnap's involvement with the Vienna Circle began to develop. He met Reichenbach in 1923 and was introduced to Moritz Schlick in Vienna, where he then moved to become assistant professor at the university. He soon became one of the leading members of the Vienna Circle, and in 1929 he, Neurath, and Hahn wrote the manifest of the Circle.As the title indicates, ""Der Raum"" deals with the philosophy of space. Partly influenced by Husserl, under whom he studied at Freiburg, Carnap poses the question whether our knowledge of space is analytic, synthetic a priori or empirical. His answer is that it depends on what is meant by ""space"", and thus differentiates between three kinds of theories of space: Formal (which is analytic [a priori]), intuitive (which is synthetic a priori), and physical (which is empirical [or synthetic aposteriori]). He compares this division of space with that of geometry into: projective, metric and topological. This, of course, anticipates much of his later philosophy, and some of his theories developed in this paper became the official position of logical empiricism on the philosophy of space. In this work he also develops a formal system for space-time topology, which became quite influential.‎

書籍販売業者の参照番号 : 33482

‎"CARNAP, RUDOLF.‎

‎Foundations of Logic and Mathematics.‎

‎Chicago, The University of Chicago Press, (1939). 8vo. In the original blue printed wrappers. A very nice and clean copy - near mint. VIII, 71 pp.‎

‎"CARNAP, RUDOLF.‎

‎Foundations of Logic and Mathematics.‎

‎Chicago, The University of Chicago Press, (1939). 8vo. In the original blue printed wrappers. A very nice and clean copy - near mint. VIII, 71 pp.‎

‎First printing of Carnap's seminal publication of his semantical period. Here Carnap presents a clear and detailed account of the application of logic and mathematics in empirical science and the central importance of the analytic/synthetic distinction herein.Carnap thought that the logic of science could be fruitfully applied to the problems of quantum theory as well. In particular, the final sections of Foundations of Logic and Mathematics (1939, 24, 25) suggest that the vexed question of the ""interpretation"" of the wave-function can be resolved by appreciating that theories of modern mathematical physics operate with ""abstract"" terms which are implicitly defined, in the manner of Hilbert, in an axiomatic system (and thus require no ""intuitive"" or ""visualizable"" meaning) but which still relate to empirical phenomena (experimental measurements) indirectly. (Cambridge Companion to Carnap).These thoughts anticipate Carnap's later conception of the ""partial interpretation"" of theoretical terms.Rudolf Carnap (born 1891 in Ronsdorf, Germany, died 1970 in Santa Monica, California) was an immensely influential analytic philosopher, who has contributed decisively to the fields of logic, epistemology, semantics, philosophy of science, and philosophy of language. He was one of the leading figures of the Vienna Circle, and a prominent logical positivist. He studied philosophy, physics and mathematics at the universities of Berlin and Freiburg, and worked at the universities of Jena, Vienna and Prague until 1935, when he, due to the war, emigrated to the U.S., where he became an American citizen in 1941. In America he became professor of the University of Chicago.‎

書籍販売業者の参照番号 : 44775

‎"CARTAN, ÉLIE.‎

‎La Géométrie des espaces de Riemann.‎

‎Paris, Gauthier-Villars et Cie, 1925. Uncut in orig. printed wrappers. (Mémorial des Sciences Mathématiques...Fascicule IX). (4),60,(4) pp. Small tears to backstrip, no loss.‎

‎"CAUCHY, AUGUSTIN + I.J. BIENAYMÉ - THE CAUCHY DISTRIBUTION AND THE PROOF OF CLT.‎

‎Mémoire sur l'évaluation d'inconnues déterminées par un grand nombre d'équations approximatives du premier degré. (+) Mémoire sur l'interpolation, ou Renarques sur les remarques de M. Jules Bienaymé. (+) Sur la nouvelles méthode d'interpolat...‎

‎(Paris, Bachelier),1853. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome XXXVI, No. 26 and tome XXXVII. No. 3,4,6,7,9,10 (entire issues offered). The papers: pp. 1114-1122, 64-69, 100-109, 198-206, 264-272, 326-334, 381-385. Some scattered brownspots.‎

‎"CAUCHY, AUGUSTIN. - CAUCHY'S THORY OF EQUIVALENCES.‎

‎Mémoire sur une nouvelle théorie des imaginaires, et sur les racines symboliques des équations et des équivalences.‎

‎(Paris, Bachelier), 1847. 4to. Without wrappers. In ""Comptes rendus hebdomadaires des séances de l’Académie des sciences"", Vol. 24, No 26. Pp. (1117-) 1160. (Entire issue offered). Cauchy's paper: pp. 1120-1130.‎

‎"CAUCHY, AUGUSTIN. - THE CLASSICAL ""SAMPLING THEOREM"" STATED.‎

‎Mémoire sur diverses formules d'analyse.‎

‎(Paris, Bachelier), 1841. 4to. Without wrappers. In ""Comptes rendus hebdomadaires des séances de l’Académie des sciences"", Vol. XII, No 6. Pp. (267-) 316. (Entire issue offered). Cauchy's paper: pp. 283-298. Some scattered brownspots.‎

‎"CAYLEY, (ARTHUR)‎

‎A Memoir on the Theory of Reciprocal Surfaces. Received November 12, 1868, - Read January 14, 1869.‎

‎(London, Taylor and Francis, 1870). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1869 - Vol. 159 - Part I. Pp. 201-229. Clean and fine.‎

‎First printing of the paper which ""contains some extensions of dr. Salmon's theory of Reciprocal Surfaces‎

書籍販売業者の参照番号 : 45118

‎"CAYLEY, (ARTHUR)‎

‎A Memoir on the Transformation of Elliptic Functions. Received November 14, 1873, - Read January 8, 1874.‎

‎(London, Taylor and Francis, 1874). 4to. No wrappers as extracted from ""Philosophical Transactions"", Vol. 164. Pp. 397-456.‎

‎First edition. The subject treated here was the substance of his only published book ""Tretise on Elliptic Functions"", published 1876.‎

書籍販売業者の参照番号 : 46018

‎"CAYLEY, (ARTHUR)‎

‎On the Analytical Theory of the Conic. Received May 8, - Read May 15, 1862.‎

‎(London, Taylor and Francis, 1862). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1862 - Vol. 152 - Part I. Pp. 639-662. Clean and fine.‎

‎First printing of an importent paper in analytical geometry.‎

書籍販売業者の参照番号 : 45121

‎"CAYLEY, (ARTHUR)‎

‎On the Curves which satisfy given Conditions. Received April 18, - Read May 2, 1867. (+) Second Memoir on the Curves...(2 Papers).‎

‎(London, Taylor and Francis, 1869). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1868 - Vol. 158. Pp. 75-143 a. pp. 145-172. Clean and fine.‎

‎First printings on 2 influential memoirs on the analytical geometry of curves.‎

書籍販売業者の参照番号 : 45122

‎"CAYLEY, (ARTHUR)‎

‎On the Double Tangents of a Plane Curve. Received March 17, - Read April 14, 1859.‎

‎(London, Taylor and Francis, 1859). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1859 - Vol. 149 - Part I. Pp. 193-212. Clean and fine.‎

‎First printing of the paper in which Cayley gives a solution to the problem of double tangents.‎

書籍販売業者の参照番号 : 45119

‎"CAYLEY, (ARTHUR).‎

‎A Memoir on Prepotentials. Received April 8, - Read June 10, 1875.‎

‎(London, Taylor and Francis, 1876). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1875 - Part II. Pp. 675-774. Clean and fine.‎

‎First printing of Cayley's importent paper on multiple integrals in which he gives the formula for the potential of certain heterogenous ellipsoids. Clifford called it ""a contribution of great value to the most importent branch of mathematical physics.""‎

書籍販売業者の参照番号 : 45117

‎"CAYLEY, (ARTHUR).‎

‎On the Sextactic Points of a Plane Curve. Received November 5, - Read december 22, 1864.‎

‎(London, Taylor and Francis, 1865). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1865 - Vol. 155 - Part II. Pp. 545-578.‎

‎First printing of an importent paper. Cayley was the to determine the sextic curve.‎

書籍販売業者の参照番号 : 45984