‎Mathematics‎

‎"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.‎

Bookseller reference : 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.‎

Bookseller reference : 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.‎

Bookseller reference : 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.‎

Bookseller reference : 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.""‎

Bookseller reference : 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.‎

Bookseller reference : 45984

‎"CAYLEY, (ARTHUR).‎

‎On Tschirnhausen's Transformation. Received November 7, - Read December 5, 1861.‎

‎(London, Taylor and Francis, 1862). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1862 - Vol. 152 - Part I. Pp. 561-578.‎

‎First printing.‎

Bookseller reference : 45985

‎"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.‎

‎First apperance of these two papers in which Cayley obtained the transformed equations for the cubic and quartic equations.‎

Bookseller reference : 49346

‎"CAYLEY, ARTHUR & GIUSEPPE VERONESE.‎

‎Sur quelques théorèmes de la géométrie de position (Cayley) (+) Behandlung der projectivischen Verhältnisse der Räume von verschiedenen Dimensionen durch das Princip des Projicirens und Schneidens. 2 vols. - [THE CAYLEY-VERONESE CLASS OF CONFIGURATIONS.]‎

‎Berlin, G. Reimer, 1846. - Leipzig, B.G. Teubner, 1881. 4to and 8vo. Cayley's paper in ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, Bd. 31: Drittes Heft.1846"". Pp. (179-)268,(2) and 1 plate. The whole issue (Drittes Heft) present with titlepage, stitched without wrappers. Cayley's paper pp. 213-226. - Veronese's paper in ""Mathematische Annalen. In Verbindung mit C. Neumann...hrsg. von Felix Klein und Adolph Meyer. XIX. Band. 2 Heft. 1881."" Pp. (161-)234. The whole issue (2. Heft) present with orig. printed wrappers. No backstrip. Veronese's paper pp. (161-)234.‎

‎Both papers first edition and first apperance in print of these two main papers in the history of projective geometry.""Cayley, in his paper ""Sur quelques théorèmes de la géométrie de position"", (the paper offered) first calls attention to the figures obtained by taking the section, by a plane or 3-dimensional space, of the complete n-point (viz., n points, and the (n/2) lines, (n/3) plans etc. dtermined by them) in a flat spaceof v dimensions. Later Veronese discusses more fully the nature of this class of configurations thus obtained in r dimensions (the second paper offered). Both Cayley and Veronese state that these same configurations can also be obtained as projections of higher-dimensional figures."" (Walter B. Carver). Veronese ""in particular may be considered the main founder of the projective geometry of hyperspaces with n dimensions, which had previously been linear algebra presented geometrically, rather than geometry.""(DSB). - An: Veronese-paper see Sommerville Bibliography of Non-Euclidean Geometry, 1881:3.This issue of ""Crelle's Journal"" contains one more paper of Cayley: ""Problème de géometrie analytique."", pp. 227-230.‎

Bookseller reference : 41240

‎"CAYLEY, ARTHUR.‎

‎An Elementary Treatise on Elliptic Functions.‎

‎Cambridge, Deighton, Bell and Co., 1876. Orig. full brown cloth. Gilt lettering to spine. Spine ends slightly frayed. Some discolouring to endcover. Light wear to extremities. X,(1),384pp. + Publisher's catalogue 16 pp. Internally clean and fine. From the library of the Englsih mathematician F.S. Carey, having his name on upper part of titlepage. ""F.S. Carey/Trin. Coll. Cam.""‎

‎"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.‎

‎On the Theory of Groups, as depending on the Symbolic Equation theta^n=1. - [THE THEORY OF GROUPS]‎

‎London, Taylor & Francis, 1854. 8vo. Bound in contemporary half calf with gilt lettering and five raised bands in gilt to spine. In ""Philosophical Magazine"", Fourth Series, Vol. 7. 1854. Wear to extremities and stamp to title-page. Otherwise fine and clean. Pp. 40-47. (Entire volume: VII, (1), 536 pp. + 4 engraved plates.)‎

‎"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. - A FUNDAMENTAL PAPER ON INVARIANT THEORY.‎

‎An Introductory Memoir upon Quantics. received April 20, - Read may 4, 1854.‎

‎(London, Richard Taylor and William Francis, 1854). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1854, Vol. 144 - Part I. Pp. 245-258.‎

‎"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.‎

‎"CAYLEY, ATHUR.‎

‎Tables des formes quadratiques binaires pour les determinants negatifs depuis D = - 1 jusqu'à D= - 100, pour les déterminants positifs non carrés depuis D = 2 jusqu'à D = 99, et pour les treize déterminants négatifs irréguliers qui se trouvent dans ...‎

‎Berlin, G. Reimer, 1862. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 60. Band, 1862""., without backstrip. Fine and clean. [Cayley:] Pp. 357-372.‎

‎First printing of Cayley's paper including many tables of tables of binary quadratic forms.‎

Bookseller reference : 48049

‎"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)‎

Bookseller reference : 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.‎

Bookseller reference : 59901

‎"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.‎

‎First printing.‎

Bookseller reference : 48064

‎"CHURCH, ALONZO (+) ALAN TURING (+) EMIL POST.‎

‎[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) Review of ""A. M. Turing. On Computable numbers, with an application to the Entscheidungsproblem"" (+) [Post:] Finite combinatory processes-formulation... - [LANDMARK VOLUME IN THE HISTORY OF LOGIC]‎

‎[No place], The Association for Symbolic Logic, 1936 & 1937. Royal8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 1 & 2 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 16 pages. A very fine copy. [Church:] Pp. 40-1" Pp. 101-2. [Post:] Pp. 103-5. [Turing:] Pp. 153-163" 164. [Entire volume: (4), 218, (2), IV, 188 pp.]‎

‎First edition of this collection of seminal papers within mathematical logic, all constituting some of the most important contributions mathematical logic and computional mathematics. A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) CORRECTION TO A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) REVIEW OF ""A. M. TURING. ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM"":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) Church coined in his review of Turing's paper the phrase 'Turing machine'.FINITE COMBINATORY PROCESSES-FORMULATION I: 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 (received on October 7, 1936). Post's paper was intended to fill a conceptual gap in Alonzo Church's paper on 'An unsolvable problem of elementary number theory'. Church had answered in the negative Hilbert's 'Entscheidungsproblem' but failed to provide the assertion that any such definitive method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be one written in the form of instructions to mind-less worker operating on an infinite line of 'boxes' (equivalent to the Turing machines 'tape'). The range of instructions proposed by Post 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 asserting that ""the present article ... although bearing a later date, was written entirely independently of Turing's"". (Hook & Norman: Origins of Cyberspace, 356).COMPUTABILITY AND LAMBDA-DEFINABILITY (+) THE Ø-FUNCTION IN LAMBDA-K-CONVERSION: The volume also contains Turing's influential ""Computability and lambda-definability"" in which he proved that computable functions ""are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene"". (Hook & Norman: Origins of Cyberspace, 395).‎

Bookseller reference : 48376

‎"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.].‎

‎"CHURCH, ALONZO.‎

‎A formulation of the simple theory of types.‎

‎(No place), The Association for Symbolic Logic, 1940. Large 8vo. Bound in blue half cloth with silver lettering to spine. In ""Journal of Symbolic Logic"", Volume 5. Small paper label to lower part of spine and upper inner margin of front board. Stamp to title-page and last leaf, otherwise internally fine. Pp. 56-68. (Entire copy: IV, 188 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) Order-nr.: 48379‎

Bookseller reference : 60429

‎"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)‎

Bookseller reference : 48379

‎"CHURCH, ALONZO.‎

‎Norwood Russell Hanson. A note on the Gödel theorem (+) David Perlman. A milestone in math - professor's new concept (+) Benson Mates. Stoic Logic.‎

‎[No place], The Journal of Symbolic Logic, 1967. 8vo. In the original printed wrappers. In ""Journal of Symbolic Logic"", Vol. 28, Number 4. December, 1963. Entire issue offered. A very fine and clean copy. Pp. 295 [Entire issue: Pp. 273-346, VI. ].‎

‎First printing of three short reviews by Alonzo Church.‎

Bookseller reference : 49084