‎Mathématiques‎

‎"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)].‎

‎"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. - THE FUNDAMENTAL PAPERS ON SET-THEORY, TRANSFINITE NUMBERS, THE CONTINUUM ETC.‎

‎Collection of 13 fundamental papers by Cantor (of which 12 are the first translations into French). 1. Sur une propriété du systeme de tous les nombrés algébriques réels (translation of ""Über eine Eigenschaft des Inbegriffes aller reellen algebraisc...‎

‎Stockholm, F. & G. Beijer, 1883, 1884, 1885. 4to. Contained in 3 issues from ""Acta Mathematica"", Vol. 2:4, vol. 4:4 a. vol. 7:2. All 3 issues with orig. printed wrappers, no backstrip.Vol. 2:4: pp. 305-310, 311-328, 329-335, 336-348, 349-380, 381-408, 409-414. - Vol. 4:4: pp. 381-392 - Vol. 7:2: pp.105-124.‎

‎"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.‎

‎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.‎

‎"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. - 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.‎

‎"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.‎

‎"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.‎

‎"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.‎

‎"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.‎

‎"CAYLEY, A.‎

‎Note sur la transformation de Tschirnhausen (+) Deuxième sur la transformation de Tschirnhausen.‎

‎Berlin, Georg Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 1861, band 58. Without backstrip. Fine and clean. Pp. 259-69.‎

‎"CAYLEY, ARTHUR.‎

‎A Theorem on Groups. - [CAYLEY'S GROUP THEOREM]‎

‎Leipzig, B. G. Teubner, 1879. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 13., 1878. 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. 561-65. [Entire volume: IV, 576 pp.].‎

‎"CAYLEY, ARTHUR.‎

‎Note on a Family of Curves of the Fourth Order.‎

‎Cambridge, Macmillan and Co., 1850. 8vo. Bound in contemporary half calf with black and red title labels to spine with gilt lettering. In ""The Cambridge and Dublin Mathematical Journal"", Vol. V [5], (Being Vol. IX [9], of the Cambridge Mathematical Jorunal), 1850. Bookplate pasted on to pasted down front free end-paper and library code written in hand to lower part of spine. Library cards in the back. A fine and clean copy. Pp. 148-59. [Entire volume: IV, 288 pp.].‎

‎"CAYLEY, ARTHUR.‎

‎Sur quelques propriétés des déterminants gauches.‎

‎Berlin, Georg Reimer, 1846. 4to. In ""Journal für die reine und angewandte Mathematik, 32. Band, 2 Heft, 1846"". In the original printed wrappers, without backstrip. Front wrapper with a brown mark to top left corner, otherwise fine and clean. [Cayley:] Pp. 119-23. [Entire issue: Pp. 93-180, (2)].‎

‎"CAYLEY, ARTHUR. - THE CAYLEY-HAMILTON THEOREM ANNOUNCED - THE MATHEMATICS OF QUANTUM MECHANICS.‎

‎A Memoir on the Theory of Matrices. Received December 10, 1857, - Read January 14, 1858. (+) A Supplementary Memoir on the Theory of Matrices. Received October 24, - Read December 7, 1865.‎

‎(London, Richard Taylor and William Francis, 1858 and Taylor and Francis, 1866. 4to. No wrappers as extracted from ""Philosophical Transactions"" Vol. 148 - Part I. Pp. 17-37, and Vol. 156 - Part I, Pp. 25-35. Clean and fine.‎

‎"CAYLEY, ARTHUR. - THE THEORY OF FORMS (QUANTICS) - A NEW ASPECT OF NON-EUCLIDEAN GEOMETRY.‎

‎A Sixth Memoir upon Quantics. Received November 18, 1858, - Read anuary 6, 1859.‎

‎(London, Richard Taylor and William Francis, 1859). 4to. No wrappers as extracted from ""Philosophical Transactions"" Vol. 149 - Part I. Pp. 61-90. Clean and fine.‎

‎"CHURCH, ALONZO (+) EMIL L. POST.‎

‎[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) [Post:] Finite combinatory processes-formulation I. [In ""Journal of Symbolic Logic"", Volume 1, number 1 + 3, 1936] - [THE FOUNDATION FOR MODERN COMPUTER LOGIC]‎

‎Wisconsin, The Association for Symbolic Logic, 1936. Lev8vo. Entire volume one of ""Journal of Symbolic Logic"" (i.e. number 1-4), March, June, September, December 1936) BOUND WITH ALL THE ORIGINAL WRAPPERS in a blue half cloth with gilt lettering to spine. Crossed-out library paper-label to lower part of spine and top left corner of front board. Two library stamps (in Chinese) to back of front free end-paper. Chinese library-stamp (red) and stamped inventory-number lower part of all four front wrappers. Minor bumping to lower corner of nr. 4, otherwise internally a very fine and clean copy of the entire volume. [Church:] Pp. 40-1"" 101-2. [Post:] Pp. 103-5. [Entire volume: 218 pp.].‎

‎First publication of Church's seminal paper in which he proved the solution to David Hilbert's ""Entscheidungsproblem"" from 1928, namely that it is impossible to decide algorithmically whether statements within arithmetic are true or false. In showing that there is no general algorithm for determining whether or not a given statement is true or false, he not only solved Hilbert's ""Entscheidungsproblem"" but also laid the foundation for modern computer logic. This conclusion is now known as Church's Theorem or the Church-Turing Theorem (not to be mistaken with the Church-Turing Thesis). The present paper anticipates Turing's famous ""On Computable Numbers"" by a few months. ""Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus', [...] Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis."" (Hook & Norman: Origins of Cyberspace, 250) The volume also contains 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, 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, independently 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).Even though Post's work to some degree has been outshined by Turing's, the present paper is of seminal importance in the history of the foundation for modern computer logic and the ideological basis for the modern computer.The volume also contains the following important papers by W. V. Quine:1. Toward a Calculus of Concepts. Pp. 2-25.2. Set-theoretic Foundations for Logic. Pp. 45-57.Hook & Norman, Origins of Cyberspace, 2002: 250 + 356 Charles & Ray Eames, A Computer Perspective, 1973: 125.‎

书商的参考编号 : 43552

‎"CHURCH, ALONZO.‎

‎A formulation of the simple theory of types. - [CHURCH'S TYPE THEORY]‎

‎(No place), The Association for Symbolic Logic, 1940 & 1941. Lev8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 5 & 6. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. A very fine copy. Pp. 56-68. [Entire copy: IV, 188, IV, 184 pp.).‎

‎First printing of Church's seminal paper in which he introduced his Type Theory: A simpler and more general Type Theory than the one introduced by Bertrand Russell in 1908 and Whitehead & Russell in 1927.""Church's type theory is a formal logical language which includes first-order logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory. It is particularly well suited to the formalization of mathematics and other disciplines and to specifying and verifying hardware and software. A great wealth of technical knowledge can be expressed very naturally in it. With possible enhancements, Church's type theory constitutes an excellent formal language for representing the knowledge in automated information systems, sophisticated automated reasoning systems, systems for verifying the correctness of mathematical proofs, and certain projects involving logic and artificial intelligence."" (SEP)‎

书商的参考编号 : 48379

‎"CHASLES, MICHEL.‎

‎Histoire de l'arithmétique - Règles de l'Abacus.‎

‎(Paris, Bachelier), 1843. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome XVI, Pp. 218-46. (Entire issue offered: Pp. 215-80 ).‎

‎First appearance of Chasles' famous paper in which he via the tenth century wrintings on the abacus by the monk Gerbert (later Pope Sylvester II) argued for a Pythagorean rather than a Hindu origin for our numeral system.""Gerbert's abacus was not a standard table abacus, but had columns in which special counters were placed. It is thought that Gerbert, disguised as an Arab, made his way into Spain and learned of the Hindu-Arabic numerals there. The Gerbert abacus was not convenient to use and was soon abandoned."" (Erwin Tomash Library C70).""Chasles wrote two historical works elaborating points in the Aperçu historique (notes 12 and 3 respectively) which had given rise to controversy. The histoire d'arithmétique (1843) argued for a Pythagorean rather than a Hindu origin for our numeral system. Chasles based his claim on the description of a certain type of abacus, which he found in the writings of Boethius and Gerbert. The second work was a reconstruction of the lost book of Prisms of Euclid (1860). Chasles felt that the porisms were essentially the equations of curves and that many of the results utilized the concept of the cross ratio. Neither of these works is accepted by contemporary scholars."" (DSB).(Erwin Tomash Library C70)‎

书商的参考编号 : 50603

‎"CHAUM, DAVID L.‎

‎Untraceable Electronic Mail, Return Addresses, and Digital Pseudonyms. - [THE BIRTH OF THE CYPHERPUNK MOVEMENT]‎

‎(New York), 1981. Large8vo. Bound with the original front wrapper in recent brown cloth with gilt lettering to spine. In: ""Communications of the ACM"", January 1981, Vol. 24. Entire volume offered. Margins closely shaved, otherwise fine and clean. Pp. 84-88. [Entire volume: 858 pp.].‎

‎First appearance of Chaum’s seminal contributions to digital privacy and invention of digital cash which led to the creation of the Cypherpunk movement, which advocated for widespread use of cryptography as a route to progressive social change. Among the notable cypherpunks are Julian Assange, founder of WikiLeaks, Wei Dai, the creator of the b-money system, cited by Satoshi Nakamoto in the bitcoin white paper, and smart contracts inventor Nick Szabo. In 1981, in the present paper, Chaum proposed the idea of an anonymous communication network. His proposal, called mix networks, allows a group of senders to submit an encryption of a message and its recipient to a server. Once the server has a batch of messages, it will reorder and obfuscate the messages so that only this server knows which message came from which sender. The batch is then forwarded to another server who does the same process. Eventually, the messages reach the final server where they are fully decrypted and delivered to the recipient. A mechanism to allow return messages is also proposed. Mix networks are the basis of some remailers and are the conceptual ancestor to modern anonymous web browsing tools like Tor (based on onion routing). Chaum has advocated that every router be made, effectively, a Tor node.‎

书商的参考编号 : 59901

‎"CHASLES, MICHEL.‎

‎Histoire de l'arithmétique - Règles de l'Abacus.‎

‎(Paris, Bachelier), 1843. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome XVI, Pp. 218-46. (Entire issue offered: Pp. 215-80 ).‎

‎"CHRISTOFFEL, E. B.‎

‎Über die Gaußsche Quadratur und eine Verallgemainerung derselben.‎

‎Berlin, G. Reimer, 1858. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 55. Band, 1858""., without backstrip. Fine and clean. [Christoffel:] Pp. 61-82.‎

‎"CHURCH, ALONZO (+) ALAN TURING.‎

‎[Church:] Review of ""A. M. Turing. On Computable numbers, with an application to the Entscheidungsproblem"" (+) [Turing:] Computability and lambda-definability (+) The Ø-Function in lambda-K-Conversion. [In Volume 2, number 1-4, 1937 of ""Journal of Sym... - [COINING THE PHRASE ""TURING MACHINE""]‎

‎Wisconsin, The Association for Symbolic Logic, 1937. Lev8vo. Entire volume 2 offered. Bound in half cloth with marbled boards. Gilt title to spine. Library stamp pasted on to lower part of spine and top left corner of front board. Two stamps (in Chinese) to verso of title-page and final page of index. A fine and clean copy. [Church:] Pp. 42-3" 101-2. [Turing:] Pp. 153-163 " 164. [Entire volume: iv, 188 pp.].‎

‎"CHURCH, ALONZO.‎

‎A formulation of the simple theory of types. - [CHURCH'S TYPE THEORY]‎

‎(No place), The Association for Symbolic Logic, 1940 & 1941. Lev8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 5 & 6. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. A very fine copy. Pp. 56-68. [Entire copy: IV, 188, IV, 184 pp.).‎