‎Mathematics‎

‎BLANC-LAPIERE, A. et ROBERT FORTET.‎

‎Theorie des Fonctions Alétoires. Applications a divers Phénomènes de Fluctuation.‎

‎Paris, 1953. Orig. cloth. XVI, 693 pp.‎

Bookseller reference : 4137

‎"PEIRCE, C(HARLES) S(ANDERS).‎

‎On the Algebra of Logic [In: American Journal of Mathematics. Volume III. Number I.]. - [INTRODUCING MODERN SEMANTICS]‎

‎Cambridge, 1880. 4to, entire issue present (Vol. III, no. 1). With the original printed wrappers. Uncut. Wrappers detached and with tears and loss to extremities. Backtrip gone. Stitching a bit loose. Internally nice and clean. Pp. (15)-57. [Entire issue 96 pp. + 2 plates]‎

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

Bookseller reference : 41486

‎CONFORTO, FABIO‎

‎Abelsche Funktionen und Algebraische Geometrie. Aus dem nachlass bearbeitet und herausgegeben von W. Gröner, A. Andreotti und M. Rosati.‎

‎Berlin Heidelberg New York, Springer, 1956. 8vo. Original yellow full cloth with the original wrappers. Wrappers with a few tears, otherwise a nice and clean copy. XI, (1), 276 pp.‎

Bookseller reference : 41576

‎"GAUSS, CARL FRIEDRICH & NIELS HENRIK ABEL - ANNOUNCING ""THE PRINCIPLE OF LEAST CONSTRAINT"".‎

‎Über ein neues allgemeines Grundgesetz der Mechanik (Gauss) + (Abel:) Précis d'une théorie des fonctions elliptiques + Précis dúne théorie des fonctions elliptiques. (Suite du mémoire 19. cah. dern.). 3 Memoirs.‎

‎(Berlin, G. Reimer, 1829). 4to. No wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 4. - Gauss' paper: pp. 232-35. - Abel's papers: pp. 236-278 and pp. 309-348.‎

‎First printing of probably Gauss' most importent work in physics by presenting his ""Principle of Least Action"" , which states that the motion of a system of points which are influenced both by each other and by outside conditions is such as to maximize the agreement with free motion, given the existent constraint. The work is based on his Potential Theory.""In it (the present paper) Gauss stated that the law of least constraint: the motion of a system departs a little as possible from free motion, where departure, or constraint, is measured by the sum of products of masses times the squares of their deviations from the path of free motion. He presented it merely as a new formulation equivalent to the well-known principle of d'Alembert. This work seems obviously related to the old meditations on least aquares, but Gauss wrote to Olbers on 31 January 1829 thai it was inspired by studies of capillarity and other physical problems."" (Kenneth O. May in DSB).The two papers (first printings) by Abel (book-lenghts memoirs) are his last works - he died 1829 and they were published after his death - on the theory of ""elliptic functions"", the discovery of which he shared with Jacobi. In these papers he mentions also the great discoveries published in his memoir 1826 (Memoire sur une proprieté générale d'un classe très-etendu de fonctions transcendentes), which was not published until 1841.Together with these 3 memoirs is found a paper by Alexander von Humboldt: ""Über die bei verschiedenen Völkern üblichen Systeme von Zahlzeichen und über den Ursprung des Stellenwerthes in den indischen Zahlen"", 1829. Pp. 205-231.‎

Bookseller reference : 41607

‎"HILBERT, DAVID. - WARING'S PROBLEM SOLVED.‎

‎Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl nter Potenzen (Waringische Problem).‎

‎Leipzig, B.G. Teubner, 1909. Orig. printed wrappers. No backstrip. In. ""Mathematische Annalen. Hrsg. von Felix Klein, Walther v. Dyck, David Hilbert, Otto Rosenthal"", 67. Bd., 3. Heft. Pp. 281-432 (=3. Heft). Hilbert's paper: pp. 281-300.‎

‎First printing of a groundbreaking work in Number Theory. Edward Waring (1734-98) stated, in his ""Meditationes Algebraicae"" (1770), the theorem known now as ""Waring's Theorem"", that every integer is either a cube or the sum of at most nine cubes"" also every integer is either a fourth power of the sum of at most 19 fourth powers. He conjectured also that every positive integer can be expressed as the sum of at most r kth powers, the r depending on k. These theoremes were not proven by him, but by David Hilbert in the paper offered.Hilbert proves that for every integer n, there exists an integer m such that every integer is the sum of m nth powers. This expands upon the hypotheis of Edward Waring that each positive integer is a sum of 9 cubes (n=3, m=9) and of 19 fourth powers (n= 4, m=19).This issue also contains F. Hausdorff's ""Zur Hilbertschen Lösung des Waringschen Problems"", pp. 301-305.(Se Kline p. 609).‎

Bookseller reference : 41656

‎"KIRCHHOFF, GUSTAVE ROBERT - KIRCHHOFF'S HYDRODYNAMICS.‎

‎Ueber die Bewegung eines Rotationskörpers in einer Flüssigkeit. + Ueber die Kräfte. welche zwei unendlich dünne, starre Ringe in einer Flüssigkeit scheinbar auf einander ausüben können. (2 Papers).‎

‎Berlin, G. Reimer, 1870. 4to. Without wrappers. In: ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 71. Bd., Heft 3, pp. (2),201-304. Entire issue offered with titlepage. Kirchhoff's papers: pp. 237-262 and pp. 263-273. Light browning to titlepage. A few scattered brownspots to margins.‎

‎First printing of these two importent papers, forming the substance of Kirchhoff's hydrodynamics.Kirchhoff was the first to show how the differential equations as used on rigid bodies, could elegantly be used on ideal fluid bodies, to. (The Kirchhoff-Clebsch equations).The issue contains further R. Lipschitz: Entwicklung einiger Eigenschaften der quadratischen Formen von n Differentialen. 1.-2. Mittheilung. Pp. 274-287 and 288-304.‎

Bookseller reference : 41673

‎"THOMÉ, LUDVIG G.‎

‎13 papers on ""Linearen Differentialgleichungen"" und ""Differentialgleichungen mitt algebraischen Koeffizienten"" etc.‎

‎Berlin, G. Reimer, 1887-1901. 4to. All 13 offprints from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bde. 100-123. Some of the offprints with traces after having been folded.‎

‎All first printing.‎

Bookseller reference : 41691

‎"EULER, LEONHARD - THE PRINCIPLE OF LEAST ACTION‎

‎Harmonie entre les Principes generaux de repos et de Mouvement de M. de Maupertuis.‎

‎(Berlin, Haude et Spener, 1753). 4to. No wrappers, as extracted from ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome VII, pp. (167-)198.and 2 folded engraved plates.‎

‎First printing of this memoir in which Euler tries to show that the ""harmony"" between Maupertuis' Law of rest, which he formulated for any system of bodies attracted by forces, is a generalization of his own Principle of least Action.‎

Bookseller reference : 41693

‎"EULER, LEONHARD.‎

‎Solution d'une Question tres difficile dansl le Calcul des Probabilités.‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome XXV, pp. 285-302. Fine and clean.‎

‎First printing of one of Euler's papers in probabilistic analysis, dealing with an analysis of a lottery for which there are several classes and a guarateed payment.The Genoise lottery was the first number lottery. It and its variants were discussed by many mathematicians because such lotteries were perceived to be unfair and because they gave rise to many interesting problems. Usually it took the form of choosing 5 from 100 with various payoffs depending upon the wager made. - Enestroem E 412.‎

Bookseller reference : 41875

‎"PLÜCKER, JULIUS.‎

‎Über ein neues Princip der Geometrie und den Gebrauch allgemeiner Symbole und unbestimmter Ciëfficienten‎

‎(Berlin, G. Reimer, 1830). 4to. No wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 5. - Plücker's paper pp. 268-286.‎

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

Bookseller reference : 41886

‎"EUCLID (EUKLID) OF ALEXANDRIA. - FIRST DANISH EDITION OF ""EUCLID"".‎

‎Euclidis Elementa Geometriæ, Det er, Første Grund Til Geometrien, I det Danske Sprog oversat af Ernst Gotlieb Ziegenbalg.‎

‎Kjøbenhavn, Ernst Henrik Berling, 1744. 4to. Samt. hldrbd. over træ. Ryg lidt slidt Overtrækspapiret på permer med mangler.(12),20,311 pp. samt 5 foldede kobberstukne plancher, i teksten talrige geometriske figurer. De første blade og de 5 plancher med en svag vandskjold. Svag skjold på de sidste ca 20 blade. En del blade med brunplet i øvre margin.4to. Contemporary half calf over wooden boards. Spine a bit worn and lacing some of the paper over boards. Faint damp stain to first leaves, to plates, and to the last ab. 20 leaves. Some leaves with a brown spot to upper margin. (12), 20, 311 pp + 5 folded engraved plates. Numerous geometrical figures in the text.‎

‎Første udgave på dansk af Euclids ""Elementer"", omfattende Bog 1-6 og 11-12. J.F. Ramus have allerede nogle år tidligere udgivet Euclid, men disse var mindre lærebøger i uddrag og på latin. Oversættelsen indeholder en lang introduktion af Ramus ""Betænkning om Euclidis Elementer og om deres Oversættelse i det Danske Sprog.""Ziegenbalg var teologisk kandidat, men havde studeret matematik i flere år, både i Jena og i England. Han blev udnævnt til professor i matematik ved Københavns Universitet efter Ramus, og havde i nogle år forinden fungeret som dennes assistent. Hans oversættelse er dedikeret Christian den VI, og i forordet introducerer han den således ""offereres (oversættelsen) Deres Kongelige Majestæt...disse udi det Danske Sprog oversatte Elementa Geometriæ, som ere Hoved=Kilden til alle Mathematiske Videnskaber og have nu i 2000 Aar været i saa stor Estime, at alle de største og erfarne Mathematici have grundet deres Skrifter paa dem og at de til almindelig Nytte og Brug ere bekientgiorte næsten udi alle Europæiske, men ey tilforn i dette Sprog.""First edition of the first Euclid-translation into Danish, comprising Book 1-6 and 11-12. Bound in cont. hcalf. Rebacked in old style. A good copy. - Riccardi, Bibl. Euclideana, Parte 4, p. 47. - Bibl. Danica IV:96.‎

Bookseller reference : 41890

‎"POINCARÉ, HENRI.‎

‎Sur les Groupes des Equations linèaires.‎

‎(Stockholm, F.& G. Beier), 1885. 4to. Orig. printed wrappers (to Acta Mathematica 4:3). Extracted from ""Acta Mathematica"", Vol. 4. Pp. 201-312. Clean and fine.‎

‎First appearance of a major paper on differential equations of the first order""...the whole theory of automorphic functions was from the start guided by the idea of integrating linear differential equations with algebraic coefficients. Poincaré simultaneously investigated the local problem of linear differential equation in the neighborhood of an ""irregular"" singular point, showing for the first time how asymptotic developments could be obtained for the integrals. A little later (1884, the paper offered) he took up the question, also started by I.L. Fuchs, of the determination of all differential equations of the first order (in the complex domain) algebraic in y and y' and having fixed singular points"" his rechearches was to be extended by Picard for equations of the second order, and to lead to the spectacular results of Painlevé and his school at the beginning of the tweentieth century.""(DSB).‎

Bookseller reference : 41900

‎"MINKOWSKI, HERMANN. - THE MINKOWSKI PROBLEM.‎

‎Volumen und Oberfläche.‎

‎Leipzig, B.G. Teubner, 1903. Orig. printed wrappers. No backstrip. In: ""Mathematische Annalen begründet durch Georg Clebsch und Carl Neumann"", 57. Bd., 4. Heft. The whole issue offered (=4.heft). Pp. 425-572. Minkowski's paper: pp. 447-495.‎

‎First appearance of the formulation of the Minkowski Problem.The Minkowski problem deals with existence, uniqueness, regularity, and stability of closed convex hypersurfaces whose Gauss curvature (as a function of the outer normals) is preassigned. Major contributions to this problem were made by Minkowski in the offered paper.‎

Bookseller reference : 41974

‎APPOLLONIUS - (CARL JOHAN DANIELSSON HILL).‎

‎Försök til en Theoretisk och Practisk Lära om Apollonii Parabel.‎

‎Lund, 1832. Samtidigt hldrbd. Rig rygforgyldning, men ryg slidt og lang revne i forreste fals. Kobberstukket titelblad med vignet, som viser kanonskuddets parabel. VIII,228 pp. 3 kobberstukne plancher, den ene adskilt i to. Gennemstukket med hvide blade, hvorpå talrige tilføjelser i gl. hånd, ligeledes en del løst indlagte blade med formler og beregninger. Tekstblade rene.‎

‎Hill var professor i matematik og rektor ved Lunds Universitet.‎

Bookseller reference : 41992

‎"BOOLE, GEORGE.‎

‎On the Theory of Probabilities. Received June 19, - Read June 19, 1862.‎

‎London, Taylor and Francis, 1862. 4to. No wrappers as extracted from ""Philosophical Transactions"" 1862. Vol. 152 - Part I. Pp. 225-252. Clean and fine, wide-margined..‎

‎First appearance of one of Boole's last papers. - ""This paper has for its object the investigation of the general analytical condition of a Method for the solution of Questions in the Theory of Probabilities, which was proposed by me in a work entitled ""An Investigation of the Laws of Thought, 1854."" (Foreword to the paper).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 : 42126

‎"BABBAGE, C. (CHARLES). - CREATING A NEW BRANCH OF MATHEMATICS.‎

‎An Essay towards the calculus of functions. Communicated by W.H. Wollaston. Read June 15, 1815. (+) An essay towards the calculus of functions. Part II. Communicated by W.H.Wollaston. Read March 14, 1816. (2 Papers).‎

‎(London, W. Bulmer and Co., 1815 and 1816). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1815 - Part I. and 1816 - Part II. Having both titlepages to the parts. Pp. (2),389-446 and (2),179-256. First titlepage with a stamp on verso. Otherwise fine and clean.‎

‎First printings of Babbage's main mathematical contributions.""Babbage's major Contribution to mathematics was his calculus of functions, which he became interested in as early as 1809 and continued to develop during his years at Cambridge. Babbage presents his major ideas on the subject in the above two papers, published in the ""Philosophical Transactions"" in 1815 and 1816. ""It can be said with some assurance that no mathematician prior to Babbage had treated the calculus of functions in such systematic way...Babbage must be given full credit as the inventor of a distinct and importent branch of mathematics"" (Dubbey 1978, 90). Elsewhere Dubby states that his new scheme would serve as a generalized calculus to include all problems capable of analytical formulation, and it is possible to see here a hint of the inspiration for his concept of THE ANALYTICAL ENGINE. While the work on the engines and his other scientific, social and political activities caused him virtually to abandon mathematical research at the age of thirty, the calculus of functions was the area he often yearned to continue. In fact the calculus of functions was not taken up by other workers, and it is the aspect of Babbage's mathematical work that modern mathematicians find most fascinating (Dubbey 1989, 18-19)."" (Hook a. Norman No. 19).Charles Babbage, William Herschel and George Peacock founded in 1810 in Cambridge the ""Analytical Society"", at Trinity College in order to reform the notation and the teaching of mathematics in England, introducing Leibniz' differential notation instead of Newton's fluxions. The continental texts and papers then became accessible to English students.‎

Bookseller reference : 42184

‎TARSKI, ALFRED and BJARNI JÓNSSON.‎

‎Direct Decompositions of Finite Algrebraic Systems.[Notre Dame Mathematical Lectures. Number 5]. - [THE STARTING POINT OF JÓNSSON-TARSKI ALGEBRAS]‎

‎(Michigan), 1947. 8vo. Ogiginal printed wrappers, black cloth back-strip. A nice and clean copy of this lithoprinted publication. (6), 64 pp. + 2 leaves of maschine-written (probably mimeographed) corrections laid in loose.‎

‎First printing of Tarski and Jónsson's important first joint publication, which constitutes the starting point of the influential Jónsson-Tarski algebras and the Jónsson-Tarski duality. The important Icelandic mathematician and logician Bjarni Jónsson (born 1920) received his PhD the year before the present publication at the University of Berkely, under the supervision of Alfred Tarski, the great Polish-American who has contributed seminally to the fields of mathematics and logic in a number of ways, and who together with Frege, Russell and Gödel now ranks as the most important contributor to the field of logic. He is thus considered one of the four greatest logicians of all times.‎

Bookseller reference : 42323

‎OSGOOD, WILLIAM FOGG.‎

‎Functions of a Complex Variable.‎

‎N.Y., G.E. Stechert & Co., 1942. Orig. full cloth. VIII,257 pp.‎

Bookseller reference : 42356

‎DETTMAN, JOHN W.‎

‎Applied Complex Variables.‎

‎N.Y., Dover Publ., (1965). Orig. wrappers. 481 pp.‎

Bookseller reference : 42360

‎BOURBAKI, N.‎

‎Éléments deMathématique. XV + XVIII + XIX. Livre V: Espaces Vectoriels Topologiques Chapitre I-V + (Fascicule de Résultats). 3 vols.‎

‎Paris, Hermann & Cie, 1953-55. Bound in one contemp. full cloth. 123,(10)(2),19139 pp., tables and 1 plate. Clean and fine.‎

‎First edition. Actualités Scientifiques et Industrielle 1189, 1229 and 1230.‎

Bookseller reference : 42438

‎"PEARSON, KARL. - ESTABLISHING MODERN MATHEMATICAL STATISTICS AND BIOMETRICS.‎

‎Contributions to the Mathematical Theory of Evolution. (I-) VI. (I. Contributions to...Received October 18, - Read November 18, 1893. - II. Skew Variation in Homogenous Material. Received December 19, 1894 - Read January 24, 1895. - III. Regression, H...‎

‎(London, Harrison and Sons, 1894, 1895, 1897, 1898, 1899 a. 1899. 4to. No wrappers as extracted from ""Philosophical Transactions"", Vol. 185 - Series A, pp. 71-110, textfigs. a. 5 plates. - Vol. 186 - Series A, pp. 343-414 a. 10 plates. - Vol. 187 - Series A, pp. 253-318 - Vol. 191 - Series A, pp. 229-311 - Vol. 192-Series A, pp. 169-244 a. 2 plates. - Vol. 192, Series A, pp. 257-330. All clean and fine.‎

‎First appearance of the founding papers of modern mathematical statistics, out of which grew Pearson's creation of Biometrics.""Founder of biometrics, Karl Pearson was one of the principal architects of the modern mathematical statistics. He was a polymath whose interests ranges from astronomy, mechanics, meteorology and physics, to biological sciences in particular, including...eugenics, evolotionary biology,heredity......Largly owing to his interests in evolutionary biology, Person created, almost single-handedly, the modern theory of statistics in his Biometric School at University College London.... In his creation of biometrics, out of which the discipline of mathematical statistics had develoiped by the end of the nineteenth century, Person introduced a new vernacular for statistics (including such termss as the standard deviation, mode, homoscedasticity, heteroscedasticity, kurtosis and the producct-moment correlation coefficient."" (Heyde in Statisticians of the Centuries).In the first paper offered here Person introduced the method of moments as a mean curve fitting assymetrical distributions (""point-binominals"") and he applies the theory to crabs and prawns. This is a general method for determining the values of the parameters of a frequency distribution.In the second paper offered here, Pearson develpoed the general formula to use for subsets of six types of frequency curves, now known as ""Pearson Type Curves"".In his seminal paper ""Regressin, Heredity and Panmixia"", the third papers offered here, Pearson introduced matrix algebra into statistical theory and also introducing 'eta' as a measure for curvilinear relationship, the standard error of an estimate, multiple regression and multiple and partial correlation, and devises the coefficient of variation as a measure of the ratio of a standard deviation to the corresponding mean expressed as a percentage.In the fourth paper he deals with the theory of probable erros and of correlations of errors...In the fifth paper he deals with the theory as involving multiple correlations...stature in biology is shown to be best reconstructed from measurements of long bones.The last paper offered deals with a variety of biological correlations, inheritance of characters etc. etc.G.M. Morant: A Bibliography ofthe Statistical and other writings of Karl Pearson Nos 2, 4, 6, 16, 17 and 20. - Eiasenhart in DSB, pp. 449-453.‎

Bookseller reference : 42461

‎"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