‎Mathematics‎

‎"POST, EMIL LEON.‎

‎Finite Combinatory Processes-Formulation 1. [In: The Journal of Symbolic Logic, Vol. 1, Number 3, Sept. 1936]. - [A SIMULTANEOUS VERSION OF THE ""TURING MACHINE""]‎

‎[No place], 1936. 8vo. Extract, unbound, unstapled. Pp. 103-105.‎

‎The uncommon 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 (same year as the present paper), 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, indepently 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).Hook & Norman, Origins of Cyberspace, 2002: 355.Charles & Ray Eames, A Computer Perspective, 1973: 125.‎

Bookseller reference : 42609

‎"IVORY, JAMES.‎

‎On the development of the disturbing Function, upon which depend the inequalities of the motions of the Planets, caused by their mutual attraction. Received May 30, - Read June 20, 1833.‎

‎(London, Richard Taylor, 1833). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1833 - Part II. Pp. 559-592. Clean and fine.‎

‎First printing of a major paper by James Ivory.""Ivory's scientific reputation, for which he was awarded many honours during his lifetime, including knighthood of the Order of the Guelphs, Civil Division (1831), was founded on the ability to understand and comment the work of the French analysts rather than any great originality of his own...Ivory's work, conducted with great industry over a long period, helped to foster in England a new interest in the application of analysis to physical problems."" (DSB VII. p. 37).‎

Bookseller reference : 42623

‎"BAILEY, W. N.‎

‎Some Identities in Combinatory Analysis. [Received 12 November, 1943. - Read 16 December, 1943.] [In: Proceedings of the London Mathematical Society. Second Series. Volume 49]. - [FIRST PUBLICATION OF ""BAILEY PAIRS"".]‎

‎London, Hodgson & Son, 1947. Royal 8vo. Bound with all the six original front-wrappers for all six parts of the volume (bound in at rear) in a very nice contemporary blue full cloth binding with gilt lettering and gilt ex-libris (""Belford College. Univ. London"") to spine. Very minor bumping to extremities. Binding tight, and in excellent, very nice, clean, and fresh condition, in- as well as ex-ternally. Small circle-stamp to pasted-down front free end-papers and to title-page (""Bedford College for Women""). Discreet library-markings to upper margin of pasted-down front free end-paper and book-plate stating that the book was presented to the Library of Bedford College by ""Professor H. Simpson./ 1946-47."" Pp. 421-435. [Entire volume: (4), 481pp.].‎

‎First publication of Bailey's seminal work on what is later known as a Bailey pair.While studying the second proof of the Rogers-Ramanujan identities, Bailey discovered how to find a pair of sequences satisfying certain relations. In 1984 George E. Andrews introduced the Bailey chain, a series of Bailey pairs.‎

Bookseller reference : 42641

‎"LINDENFELS, I.B.‎

‎Den hemmelige Skrivekonst eller: Chiffrer= og Dechiffrer=Konsten, isærdeleshed practiskt oplyst ved et nyt Transpositionschiffre, der formedelst dets utallige Afvexlinger, i Forening med den største Simpelhed og Lethed, kan gjøres aldeles uopløseligt,... - [THE VIGENÈRE CIPHER CORRECTLY DESCRIBED FOR THE FIRST TIME]‎

‎Kjøvenhavn [Copenhagen], Brummers Forlag, 1819. 8vo. In the fragile and rare original engraved paper-binding with wear and bumping to capitals and corners, but overall fine. Spine a bit soiled and some minor ink-spotting to front board. Internally some occasional brownspotting, but overall nice and clean. Half-title, engraved title-page, (being pp. 1-4), XL pp. + pp. (5) - 294 + 1 leaf errata + 9 engraved plates (numbered I-IX, though the title-page states ""eight engraved plates"") + 5 folded tables (in all there are 7 tables that are numbered, namely A(a-c)-E, of which Ab+c,C,D,E are folded, Aa-B are in the text and are 3/4 and almost full-page respectively. Table D has a tear, no loss).Printed on good, heavy paper. Orig. koberstukket kartonnage, hvor ryggen dog er slidt. Hjørner stødte. Kobberstukket titelblad, XL,294, pp. + 1 blad errata + talrige foldetabeller og 9 kobberstukne foldeplancher. Trykt på skrivepapir, men her og der noget brunplettet.‎

‎The rare first printing of this highly important work of cryptography, which is the very first work to correctly describe Vigenère's cipher. ""Lindenfels, so far as I can ascertain, is the only writer who accurately presents both the tables and the directions of Vigenère."" (Charles J. Mendelsohn, 1940). The present work also constitutes the first Danish cryptographical work.""All European countries have a larger or smaller collection of crytographical works in their languages, whereas we in Denmark, as far as the author is aware, do not own a single letter thereof in the mother tongue. The author has therefore endeavoured, also in a scientific sense, not to be entirely unworthy in filling out this lacuna in the national literature. Both of these purposes unite in the ""pium desiderum"": to enable our young officials - in particular the military - to match also in this respect those of our neighbouring nations. It is necessary in times such as ours, not to lag behind foreigners, especially in these things, if we do not wish at all hours to succumb to them."" (from the ""Prereminder"" - translated from Danish in Franksen). ""In 1918, Charles J. Mendelsohn was made a captain in the Military Intelligence Division of the General Staff of the U.S. Army, in charge of decipherment of German codes. A classic scholar and faculty member of the history department in the College of the City of New York, he was launched by his experience into a lifelong study of historical ciphers and their originators. Among other things, this research resulted in two fundamental papers on Cardano and de Vigenère, respectively... With this background in mind we are hard put to find a more authoritative source on the history of the Vigenère cipher than the article by Mendelsohn. It is therefore noteworthy to read in Mendelsohn's abstract, that ""In all the literature of cipher, I know of only one writer who has correctly described Vigenère's cipher, and that was well over one hundred years ago."" In the body of the article Mendelsohn, referring to ""I.B. Lindenfels, Den hemmelige Skrivekonst (Copenhagen, 1819)"", expands on this remark... (see first quotation above). On this authority I have often relied on Lindenfels' work for factual information in past discussions. Yet, I have withheld his story which, lying dormant in the Danish Army Archives and some contemporary bibliographical accounts, is perhaps as fascinating as the topic he describes... Its title page was engraved, so Lindenfels proudly tells us, together with nine other illustrations by a young artist, H.C. Klingsey, employed as a map-maker by the Danish navy. It reveals that Lindenfels was a major of the artillery and a teacher of the Royal Pageans (cadets training for general staff and military engineering), at the Land Cadet Academy (infantry and horse), and at the Artillery Cadet Institute... In the ""prereminder"", Lindenfels assures the reader that he has done everything in his power to make the book as entertaining as possible. Simultaneously, however, he emphasizes that his choice of motto ""Ei blot til lyst"" (not only for pleasure) on the title-page, is made on purpose (see quotation from the Prereminder above)..."" (Franksen, pp. 215-17).Lindenfels does not invent or introduce an entirely new cipher, he does, however, in the present work, introduce a new practice that is to replace the simple substitution cipher or traditional nomenclature, and in fact he becomes the first to describe the seminal Vigenère cipher correctly. The work is divided into three parts, namely Simple substitution ciphers and nomenclatures" the Vigenère cipher" and a Supplement, all of about the same length. The supplement not only describes the history of ciphers and codes but also covers sign languages, both of thieves and deaf and mutes. Being the first such work in the Danish language, of course it arose some curiosity and excitement. It is evident from the subscription list that Kind Fredrik VI himself purchased 10 copies alone. For curiosity it can be mentioned that Lindenfels here mentions ""the newest galvanic and electric discoveries"" and ""the incredible bordering progress in physics and chemistry"", referring to Ørsted and inferring how Ørsted gradually worked towards his discovery of electromagnetism in 1820, about a year after Lindenfels had published his work. For a long and thorough description of the work and of Lindenfels, see:Franksen, Mr. Babbage's Secret. The Tale of a Cypher - and APL. (IBM).‎

Bookseller reference : 42688

‎"HEAWOOD, P. J.‎

‎Map-colour theorem. [Received 27 January, 1947. - Read 20 February, 1947.] [In: Proceedings of the London Mathematical Society. Second Series. Volume 51].‎

‎London, Hodgson & Son, 1950. Royal 8vo. Volume 51 of ""Proceedings of the London Mathematical Society. Second Series"" Bound with all the six original front-wrappers for all six parts of the volume (bound in at rear) in a very nice contemporary blue full cloth binding with gilt lettering and gilt ex-libris (""Belford College. Univ. London"") to spine. Minor bumping to extremities. Binding tight, and in excellent, very nice, clean, and fresh condition, in- as well as ex-ternally. Small circle-stamp to title-page (""Bedford College for Women""). Discrete library-markings and book-plate stating that the book was presented to the Library of Bedford College by ""Professor H. Simpson./ 1949-50"" to pasted-down front free end-paper. Library-label tipped in at front free end-paper. Pp. 161-175. [Entire volume: (4), 483 pp.].‎

‎First edition of one of the last articles by a key figure in Map-colour theory. Percy John Heawood, proved in 1890 that Alfred Kempe's Four-colour theorem was flawed and established his own five-colour theory. ""Heawood was, however, able to salvage an important idea, that of Kempe chains, from Kempe's proof. Using Kempe's work, Heawood was able to prove that every map is 5-colorable."" (Hilton, Mathematical vistas: from a room with many windows, 2002, p. 148 ). ""It is not known how Heawood became aware of the Four-Color problem. However, his life's work in mathematics was centered on it. After his first paper, 1890, he published seven more papers on the same subject, the last in 1949 at the age of 88."", his biographer Gabor Dirac wrote. (Fritsch, Rudolf. The four color theorem: history, topological foundations, and idea of proof, 1998, 24 p).‎

Bookseller reference : 42736

‎"BEGUELIN, (N.).‎

‎Sur L'Usage du Principe de la Raison suffisante dans le Calcul des Probabilités.‎

‎(Berlin, Haude et Spener, 1769). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XVIII, pp. 297-363 and 3 folded engraved plates.‎

‎First printing of one of Beguelin's influential papers on probability theory.In 1747 Beguelin became a fellow of the Berlin Academy of Sciences, in the period 1786-89 the Director of the section for Philosophy. He wrote memorials on mathematics (probability), physics and metaphysics. He incensed the displeasure of Frederick the Great in 1764, but won again the grace of Friedrich's successor Friedrich Wilhelm II (reg. 1786-1796), his former disciple, in 1768 who gave him the estate Lichterfelde.‎

Bookseller reference : 42835

‎SVERDRUP, ERLING.‎

‎Sverdrup: Hypoteseprøvning. Advanced Statistical Inference. Math. Stat. G8203x-G8204y. Fall Term 1963 and Spring Term 1964. Review of Results Proved and Problems.‎

‎(No place), 1963-64. Xerox-copies (A4) inserted in brown folder with author's inscription to top right corner of title page. (1), 7, 5, 11, 13, 7, 10, 6, (2), 10 pp. Minor corrections throughout the text. A very nice and clean manuscript.‎

‎Erling Svendrup's own copies of his teaching-papers for the Fall Term 1963 and Spring Term 1964. They give a unique insight into how Svendrup taught and how his ideas were developed. Erling Sverdrup was a founding father of mathematical statistics and modern actuarial science in Norway. He exercised profound influence on how statistical studies were formed and executed in Norway. The Norwegian edition of his statistics textbook Laws and chance variations had a great impact on a generation of Norwegian actuaries and statisticians, and his lecture notes in actuarial mathematics were decades ahead of contemporary textbooks. Unfortunately, these lecture notes were never translated and widely publicized.He has made important contributions to life-insurance mathematics, survival analysis and event history analysis, where he, at an early stage, advocated the use of Markov chain models for studying disability. a number of important contributions have only appeared in lecture notes or technical reports.‎

Bookseller reference : 42862

‎HINTIKKA, JAAKKO.‎

‎The Principles of Mathematics Revisited.‎

‎USA, Cambridge University Press, 1996. 8vo. Original full blue cloth with original wrappers. (2), XII, 288 pp. A very fresh and clean copy.‎

Bookseller reference : 42868

‎"SYLVESTER, J.J. (JAMES JOSEPH). - THE PROOF OF NEWTON'S RULE.‎

‎Algebraic Researches, containing a disquisition on Newton's Rule for the Discovery of Imaginary Roots, and an allied Rule applicable to a particular class of Equations, together with a complete invariantive determination of the character of the Roots ...‎

‎(London, Taylor and Francis, 1865). 4to. No wrappers as extracted from ""Philosophical Transactions"", Vol. 154 - Part III, pp. 579-666 and 2 lithographed plates. Some faint brownspots to theplates. Otherwise clean and fine.‎

‎First printing of a main paper of the founder (together with Cayley) of the theory of algebraic invariants, in which Sylvester investigates the roots of quintic equations and the proof of Newton's rule.""Another problem of great importence investigated in two long memoirs of 1853 and 1864 (the paper offered) concerns the nature of the roots of quintic equation. Sylvester took the functions of the coefficients that serve to decide the reality of the roots, and treated them as coordinates of a point in n-dimensional space. A point is or is not ""facultative"" according to whether there correspons, or fail to correspond, an equation with real coefficients. The character of the roots depends on the bounding surface or surfaces of the facultative regions, and on a single surface depending on the ""discriminant.""(DSB XIII, p. 219).‎

Bookseller reference : 42883

‎"EULER, LEONHARD.‎

‎Variae Demonstrationes Geometriae. (Various geometric demonstrations).‎

‎(Petropoli (St. Petersbourg), 1750). 4to. Uncut, without wrappers. Extracted from ""Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tom. I. ad Annum 1747 et 1748. Pp. 49-66 a. 1 engraved plate. Clean and fine.‎

‎First printing of an importent paper in geometry in which ""Euler says that a proof of a theorem by Fermat can be done from a strictly Euclidean way. He also presents relations about triangles and quadrilaterals, relating products of side lengths, squares of side lengths, and areas."" - Enestroem No. 135.‎

Bookseller reference : 42897

‎"BOOLE, GEORGE. - BOOLE'S LAST WORK.‎

‎On the Differential Equations which determine the form of the Roots of Algebraic Equations. Received April 27, - Read May 26, 1864.‎

‎(London, Taylor and Francis, 1865). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1864. Vol. 154 - Part III. Pp. 733-755. Clean and fine.‎

‎First printing of Boole's last paper, - Boole, the founder of Computer science.George Boole is mostly known for his ""An Investigation on the Laws of Thought"" 1854 and his developments of a form of symbolic logic, called Boolean Algebra. But he also did importent work on the Calculus, Differential Equations and the Theory of probabilities.‎

Bookseller reference : 42985

‎"MEALY, GEORGE H.‎

‎A Method for Synthesizing Sequential Circuits. - [FIRST PUBLICATION OF THE MEALY MACHINE]‎

‎New York, American Telephone and Telegraph Company, 1955. 8vo. Original full green cloth. Volume XXXIV, 1955 of ""The Bell System Technical Journal"". Library stamp to front free end-paper and title page. Minor bumping to extremities. A nice and clean copy. Pp. 1045-1079. [Entire volume: 13, (3), 1330 pp.].‎

‎First publication of the highly influential Mealy machine: a finite-state machine whose output values are determined both by its current state and by the values of its inputs. Mealy machines are useful to describe how an output is associated with the transition. A full-adder changes state to reflect the carry-in and outputs the sum as the transition takes place. Vending machines can be set up as Mealy machines.Other papers of interest contained in the present volume: 1. Uhlir, A., The Potentials of Infinite Systems of Sources and Numerical Solutions of Problems in Semiconductors Engineering. Pp. 105-1282. Hohn, Franz E." Schissler, L. Robert. Boolean Matrices and the Design of Combinational Relay Switching Circuits. Pp. 177-202.3. Herring, Conyers. Transport Properties of a Many-Valley Semiconductor. Pp. 237-290. 4. Brewer, S.T. Hecht, G.. A Telephone Switching Network and Its Electronic Controls. Pp. 361-402. 5. Doba, Stephen Jr. Kolding, A. Robert. A New Local Video Transmission System. Pp. 677-712. 6. Fox, A.G. Wave Coupling by Warped Normal Modes. Pp. 823-852. 7. Louisell, W.H.. Analysis of the Single Tapered Mode Coupler. Pp. 853-870. 8. Lee, C.Y. Analysis of Switching Networks. Pp. 1287-1315.And many other.‎

Bookseller reference : 43021

‎"RICE, S. O.‎

‎Mathematical Analysis of Random Noise. - [THE RICE DISTRIBUTION]‎

‎New York, American Telephone and Telegraph Company, 1945. 8vo. Original full green cloth. Volume XXIV, 1945 of ""The Bell System Technical Journal"". Library stamp to free front end-paper and title-page. Minor bumping to extremities. A nice and clean copy. [Mentioned article:] Pp: 46-156. [Entire issue: V, (3), 467].‎

‎First publication of the Rice Distribution, or Rician distribution. Today the paper is widely recognized as a classic within the field of statistics and probability theory. The Rice distribution is an extension of the Rayleigh distribution that adds a coherent signal to the backscattered signal that underlies the Rayleigh distribution.The model is named after Stephen O. Rice who worked at Bell Labs for nearly forty years. His most famous and influential publication is the present article" in 1983 he was awarded the IEEE Alexander Graham Bell Medal.‎

Bookseller reference : 43073

‎ORE, OYSTEIN.‎

‎Theory of Graphs, American Mathematical Society Colloquium publications, Vol. XXXVIII.‎

‎Rhode Island, American Mathematical Society, (1967). 8vo. Original full blue cloth with gilt title to spine and front board. Two small library stamps to pasted down front free end-paper. XI, (1), 270 pp. A fine and clean copy.‎

‎Third printing.‎

Bookseller reference : 43106

‎"SHANNON, CLAUDE, E.‎

‎The Synthesis of Two-Terminal Switching Circuits. - [SHANNON'S EXPANSION]‎

‎New York, American Telephone and Telegraph Company, 1949. 8vo. Volume XXVIII, 1949, No. 1 of ""The Bell System Technical Journal"". In the original printed blue wrappers. Wear and tears to spine. Inner front hinge loosening. Previous owner's name to front wrapper. Internally fine and clean. Pp. 59-98 [Entire issue: 163 pp].‎

‎First publication of Shannon's paper on how a Boolean function can be represented by the sum of two sub-functions of the original. The function was later named Shannon's Expansion or the Shannon Decomposition. ""The area of switching circuits design and optimization was a focus of considerable attention. Boolean algebra provided the basic mathematical foundation for switching circuit design. Shannon provided a basis for the The Synthesis of Two-Terminal Switching Circuits in 1949"". (Ashar, Sequential logic synthesis, 1992, p. 1).Claude Shannon is widely regarded as being the father of information theory and cryptography. Other papers contained in the present issue:1. Albersheim, W.J.Propagation of TE01 Waves in Curved Wave Guides. Pp. 1-32.2. Pierce, J.R." Hebenstreit, W.B. A New Type of High-Frequency Amplifier. Pp. 33-51.3. Hollenberg, A.V.Experimental Observation of Amplification by Interaction Between Two Electron Streams. Pp. 52-58.4. Robertson, Sloan D. A Method of Measuring Phase at Microwave Frequencies. Pp. 99-103.5. Rice, S.O.Reflection from Corners in Rectangular Wave Guides - Conformal Transformation. Pp. 104-135.6. Rice, S.O.A Set of Second-Order Differential Equations Accociated with Reflections in Rectangular Wave Guides - Application to Guide Connected to Horn. Pp. 136-156.‎

Bookseller reference : 43340

‎"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.‎

‎First printing of the first paper in Cayley's famous memoirs on 'quantics', a term he coined for algebraic forms. In this paper Cayley throughout remodelled the whole basis for Invariant Theory.""In addition to his part in founding the theory of abstract groups, Cayley has a number of important theorems to his credit: perhaps the best known is that every finite group whatsoever is isomorphic with a suitable group of permutations (see the first paper of 1854). This is often reckoned to be one of the three most important theorems of the subject, the others being the theorems of Lagrange and Sylow. But perhaps still more significant was his early appreciation of the way in which the theory of groups was capable of drawing together many different domains of mathematics: his own illustrations, for instance, were drawn from the theories of elliptic functions, matrices, quantics, quaternions, homographic transformations, and the theory of equations. If Cayley failed to pursue his abstract approach, this fact is perhaps best explained in terms of the enormous progress he was making in these subjects taken individually.""(DSB)‎

Bookseller reference : 49410

‎"CLIFFORD, W.K.‎

‎On Mr. Spottiswoode's Contact Problems.‎

‎(London, Harrison and Sons, 1874). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1874 - Vol. 164 - Part II. Pp. 705-717.‎

‎First printing of one of Clifford's papers in geometry.""William Clifford (1845-1879) was an important mathematician of his day. He is most remembered today for his invention of Clifford algebras, which are fundamental in modern differential geometry and mathematical physics. His ideas on the connection between energy and matter and the curvature of space were important in the eventual formulation of general relativity. Clifford was particularly interested in non-Euclidean geometry. However, in his relatively brief career, he made contributions to diverse fields of mathematics: elliptic functions, Riemann surfaces, biquaternions, motion in Euclidean and non-Euclidean space, spaces of constant curvature, syzygies, and so on.""‎

Bookseller reference : 49411

‎"MACWILLIAMS, JESSIE.‎

‎Permutation Decoding of Systematic Codes. - [FIRST PUBLICATION OF PERMUTATION DECODING]‎

‎New York, American Telephone and Telegraph Company, 1964. 8vo. Volume XLIII (63), January, Number 1, part 2, 1964 of ""The Bell System Technical Journal"". In the original blue printed wrappers. Previous owner's stamps to front wrapper. A part from minor light spotting to front wrapper, a very nice and clean copy. Pp. 485-505. [Entire issue: Pp. 339-563].‎

‎First publication of MacWilliam's important paper on permutation decoding.""MacWilliams (1917-1990) was a mathematician who contributed to the field of coding theory. She was born in Stoke-on-Trent, England and studied at the University of Cambridge, receiving her BA in 1938 and her MA in the following year. She spent most of her career at Bell Labs, where she worked on error-correcting codes and co-wrote 'The Theory of Error-Correcting Code with Neil Sloane'."" (Codings: Webster's Quotations, 42 p.)The issue contains the following papers.1. Darlington, Sidney. Demodulation of Wideband, Low-Power FM Signals. Pp. 339-374.2. Froehlich, F.E." Anderson, R.R. Data Transmission over a Self-Contained Error Detection and Retransmission Channel. Pp. 375-398.3. Sunde, E.D. Intermodulation Distortion in Analog FM Troposcatter Systems. Pp. 399-435.4. Harris, S.E. DeGrasse, R.W. Schulz-Dubois, E.O. Cutoff Frequencies of the Dielectrically Loaded Comb Structure as Used in Traveling-Wave Masers. Pp. 437-484.5. MacWilliams, Jessie. Permutation Decoding of Systematic Codes. Pp. 485-505.6. Gordon, Eugene I. Optical Maser Oscillators and Noise. Pp. 507-539.7. Wood, Elizabeth A. The 80 Diperiodic Groups in Three Dimensions. Pp. 541-559.‎

Bookseller reference : 43550

‎"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.‎

Bookseller reference : 43552

‎"(LEIBNITZ, GOTTFRIED WILHELM).‎

‎De linee super linea incessu, ejusque tribus speciebus motu radent motu provolutionis et composito ex ambobus (+) Excerptum ex epistola G.G.L. pro hypothesi physica motus planetarii olim (Febr.1689) hic Actis inserta, ad Amicum scripsit.‎

‎Leipzig, Grosse & Gleditsch, 1706. 4to. Contemp. full vellum. Faint hand-written title to spine. Two small stamps to title-page and one stamp to front free end-paper. Library label pasted on to pasted down front free end-paper. As usual with various browning to leaves and plates. The entire volume of ""Actorum Eruditorum Anno MDCCVI"" offered. [Leibniz's paper:] Pp. 10-15 + 1 engraved plate" 446-51 pp. [Entire volume: (2), 590 pp.].‎

‎First publication of two Leibniz papers. In the first paper, Leibniz's calculates the curve for a rolling without sliding body (Pura provolutio). The second paper is a correction to Leibniz's 1689-paper.Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume.‎

Bookseller reference : 43900

‎"BERNOULLI, JACOBI (JACOB).‎

‎Analysis magni problematis Isoperimetrici. - [BERNOULLI'S SOLUTION TO THE ISOPERIMETRIC PROBLEM]‎

‎Leipzig, Gross & Fritsch, 1701. 4to. Contemporary full vellum. Handwritten title on spine. A small stamp to title page and page . Pasted library label to pasted down front free end-paper. In: ""Nova Actorum Eruditorum Anno MDCCI"". Pp 213-228 + 1 engraved plate. [Entire volume: (2), 581 pp. + 8 engraved plates].‎

‎First publication of Jacob Bernoulli influential dissertation in which he published the first correct solution to the isoperimetric problem both Johann Bernoulli and Leibniz had been seeking without success. The paper influenced both Leonhard Euler in writing his first research paper and British mathematician Brook Taylor to begin a dispute which has later been referred to as Taylor versus Continental mathematicians. ""It [the dissertation] was considered as a prodigy of sagacity and invention: and indeed, if the time be considered, it will not be too much to assert, that a more difficult problem never was solved."" (Bossut. A general history of mathematics. 341 p.).The isoperimetric problem is an ancient problem which dates back to antiquity and can be described as which curve, if any, maximizes or minimizes the area of its enclosed region?Euler, who had been taught by Johann Bernoulli, published his first paper in 1726 which was a note on the construction of isochronous curves in a resistant medium.DSB II, 48b.The following papers by Johann Bernoulli are also contained in the present volume:1. Disquisitio Catoptrico-Dioptrica exhibens Reflexionis et Refractionis naturam ex aequilibrii fundamento deductam. Pp 19-26.2. Novaratio construendi radios osculi seu curvanturae in Curvis quibusvis etc. Pp. 136-40.3. Multisectio Anguli vel Arcus, duplici aequatione universali exhibita. Pp. 170-75.‎

Bookseller reference : 44002

‎"LACHLAN, R.‎

‎On Systems of Circles and Spheres. Communicated by A. Cayley. Received February 23, - Read March 11, 1886.‎

‎(London, Harrison and Sons, 1887). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1886 - Vol. 177 - Part II. Pp. 481-625. Clean and fine.‎

‎First edition of an importent study on the geometry of circles, treating circles as vectors and using basic ideas from linear algebra.‎

Bookseller reference : 44042

‎"BERNOULLI, JOHANN.‎

‎Perfectio regulae suae editae in Libro Gall. Analyse des infiniment petits art. 163. pro determinando valore fractionis, cujus Numerator et Denominator certo casu evanescunt‎

‎Leipzig, Grosse & Gleditsch, 1704. 4to. In: ""Acta Eruditorum Anno MDCCIV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 375-80. [Entire volume: (2), 592 pp. + six engraved plates.].‎

‎First printing of Bernoulli's paper on infiniti series. Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume.‎

Bookseller reference : 44107

‎"BERNOULLI, JOHANN.‎

‎Methodus commoda et naturalis reducendi Quadraturas transcendentes cujusvis gradus ad Longitudines Curvarum algebraicarum.‎

‎Leipzig, Grosse & Gleditsch, 1724. 4to. In: ""Acta Eruditorum Anno MDCCXXIV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 356-66. [Entire volume: (2), 543, (43) pp. + five engraved plates.].‎

‎First printing of one of the famous Swizz mathematician Johann Bernoulli's papers. He is known for his contributions to the infinitesimal calculus and educated Leonhard Euler in his youth.The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 44109

‎"BERNOULLI, NICLAUS.‎

‎De trajectoriis curvas ordinatim positione datas ad angulos rectos vel alia date lege secantibus.‎

‎Leipzig, Grosse & Gleditsch, 1718. 4to. In: ""Acta Eruditorum Anno MDCCXVIII"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 248-262. [Entire volume: Pp. (4), 564, (40) + five engraved plates.].‎

‎First printing of Bernoulli's paper on trajectories. The volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 44195