‎Mathématiques‎

‎"ABEL, NIELS HENRIK - C.G.J. JACOBI - ON ELLIPTIC FUNCTIONS.‎

‎Sur de notices sur les fonctions elliptiques (Jacobi). (+ Abel:) Théorèmes sur les fonctions elliptiques. (+ Abel:) Démonstration d'une proprieté générale d'une certaine classe de fonctions transcendentes.‎

‎Berlin, G. Reimer, 1829. 4to. Without wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 4. Bd., Heft 2. - Jacobi's paper PP. 185-193. Abel's papers pp. 194-199 a. 200-214.‎

‎"ABEL, NIELS HENRIK.‎

‎(7 papers in ""Crelle's Journal"":) 1. Untersuchung der Functionen zweier unabhängig veränderlichen Grössen x und y, wie f(x,y), welche die Eigenschaft haben, dass f(z, f(x,y)) eine symmetrische Function von z,x und y ist. - 2. Beweis der Unmöglichkeit ...‎

‎Berlin, Duncker und Humblot, 1826. 4to. Contemp. hcalf. Part of spine lacks, some of spine loose. IV,387,(1) pp. and 5 folded engraved plates. Wide margins, on good paper, light marginal browning, a few scattered brownspots. The whole volume of ""Journal für die reine und angewandte Mathematik. Herausgegeben von A.L. Crelle"" Erster Band. In 4 Heften. Mit 5 Kupfern. Abel's papers: pp. 11-15, pp. 65-84, pp. 159-60, pp. 185-221, pp. 311-339, pp. 153-160, pp. 117-136.‎

‎"ABEL, NIELS HENRIK.‎

‎Mathematische Bruchstücke aus Herrn N. H. Abels Briefen.‎

‎(Berlin, G. Reimer, 1830). 4to. No wrappers. Extracted from""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 5, Fine and clean. Pp. 336-343. [Offered pages: Pp. 319-418.].‎

‎"ABEL, NIELS HENRIK.‎

‎Recherches sur les fonctions elliptique.‎

‎Berlin, G. Reimer, 1827. 4to. No wrappers. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. II, Heft 2, pp. 101-196 (the whole Issue, Heft 2). Abel's paper: (2= titlepage to vol. II) + pp.101-181.‎

‎"ABEL, NIELS HENRIK. - ""A MONUMENT MORE LASTING THAN BRONCE"" (LEGENDRE).‎

‎Mémoire sur une propriété générale d'une classe trés-étendue de fonctions transcendantes. - [ABEL'S THEOREM]‎

‎Paris, Académie des Sciences, 1841 (submitted 1826). 4to. (257x197mm). Extract from: 'Mém. Acad. d. Sciences de Paris', 1841, pp.176-264. Contemporary half calf with gilt spine lettering. Spine with a little wear. Some light brown spotting throughout. Otherwise fine and clean.‎

‎"ACKERMANN, WILHELM.‎

‎Begründung des ""tertium non datur"" mittels der Hilbertschen Theorie der Widerspruchsfreiheit. - [ACKERMANN'S DISSERTATION]‎

‎Berlin, Julius Springer, 1925. In: 'Mathematische Annalen', volume 93, pp.1-36. Entire volume offered here (314 pp.) Bound in modern full cloth. Ex-library stamp on title page.‎

‎"ACKERMANN, WILHELM.‎

‎Zum Hilbertschen Aufbau der reellen Zahlen. - [THE ACKERMANN FUNCTION - THE FIRST TOTAL COMPUTABLE FUNCTION]‎

‎Berlin, Julius Springer, 1928. 8vo. Without wrappers as extracted from ""Mathematische Annalen, 99. Band. 1928"". Pasted on backstrip in marbled paper. Internally fine and clean. Pp. 118-33‎

‎"ADAMS, GEORGE.‎

‎Geometrische und Graphische Versuche, oder Beschreibung der mathematischen Instrumente, deren man sich in der Geometrie, der Civil= und Militär= Vermessung, beim Nivelliren und in der Perspektive bedient, nebst verschiedenen neuen Aufgaben zur nähern ...‎

‎Leipzig, Siegfried Lebrecht Crusius, 1795. Contemp. hcalf. Gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on top of spine. Stamps on title-page. Engraved frontispiece. XXX,652,91 pp. 1 folded table and 41 large folded engraved plates (Plate 35 bis, 36 bis and 37 bis). Occassional light browning to leaves and plates.‎

‎"ALEXANDROFF, P.‎

‎Dimensionstheorie. Ein Beitrag zur Geometrie der abgeschlossenen Mengen. [In ""Mathematische Annalen"", 106. band. 1932].‎

‎Berlin, Julius Springer, 1932. Large8vo. Uncut unopened in the original printed wrappers. In ""Mathematische Annalen"", 106. band. 1932. Entire volume offered. Wear to spine, lacking upper part of spine. Otherwise fine. Pp. 161-238. [Entire volume: IV, 795 pp.].‎

‎"ARCHIMEDES & FEDERICO COMMANDINO.‎

‎(Archimedes:) Opera non nulla à Federico Commandino Urbinate. Nuper in latinum conversa, et commentariis illustrata. Quorum nomina in sequenti pagina leguntur. + (Commandino:) Commentarii in Opera non nulla. - [THE ARCHIMEDEAN RENAISSANCE - THE FIRST COMMANDINO-EDITION]‎

‎Venice, Paulus Manutius, Aldi F., 1558. Small folio. Bound in a contemporary simple full limp vellum binding. Neatly rebacked (hardly noticeable) and binding with toning, a bit of soiling, and light spotting. Verso of last leaf browned, otherwise internally unusually nice, clean, and fresh, possibly washed. With the book-plate of Mr de la place de Mont-Evray to inside of front board and old ownership-inscription (August Biturie ?) to title-page. pp. 1v and 2r with elaborate marginal annotations and calculations in 16th century hand. (4), 55, (1) ff. + (2), 63, (1) ff. Large Aldus printer's device (dolphin and anchor - Cataldi Palau, Delfino 16) to both title-pages and to final leaf of both works. Lovely woodcut illustrated initials and many woodcut text-diagrams throughout.‎

‎"ARCHIMEDES OF SYRACUSE.‎

‎Archimedous ta sozomena meta ton Eutokiou Askaloniton hypomnematon (Greek). Archimedis quae supersunt Omnia cum Eutocii Ascalonitae Commentariis. Ex Josephi Torelli, Veronensis, cum nova Versione Latina. Accedunt Lextiones variantes ex Codd. Mediceo e...‎

‎Oxford, Clarendoniano, 1792. Folio. Bound to style in a nice recent full brown morocco, gilt title on spine. Kept in a matching protective slipcase. Engraved frontispiece. Engraved title-vignette (Archimedes). (2),V,XXIX,471,(1) pp. One engraved plate. Many textdiagrams. Mild browning to upper part of title-page. Greek and Latin text. The last 20 leaves with browning in upper right corner. A few corners repaired (no loss). A few scattered brownspots, otherwise clean and fine, wide-margined.‎

‎First edition of Torelli's remarkable edition of Archimedes' Opera Omnia. ""Of the many editions prior to the modern edition of Heiberg, the most important was that of Joseph Torelli (Oxford, 1792). By this time, of course, Archimedes’ works had been almost completely absorbed into European mathematics and had exerted their substantial and enduring influence on early modern science.""(DSB).Archimedes was called ""the God of mathematics"" by Plinius, and he is without doubt the greatest mathematician, physicist and engineer of ancient times and one of the greatest geniuses of all times. ""There is no one individual whose work epitomizes the character of the Alexandrian age so well as Archimedes (287-212 B.C.), the greatest mathematician in antiquity"" (Morris Kline). ""He gave birth to the calculus of the infinite conceived and brought to perfection successively by Kepler, Cavalieri, Fermat, Leibnitz and Newton."" (Chasles). Lowndes I,61-62: ""The most complete and magnificent edition of this authors works."" - Brunet I,384.‎

書籍販売業者の参照番号 : 50349

‎"ARCHIMEDES OF SYRACUSE.‎

‎Des Unvergleichlichen Archimedis Kunst=Bücher Oder Heutigs Tags befindliche Schrifften, Aus dem Griechischen in das Hoch-Deutsche übersetzt, und mit nothwendigen Anmerkungen durch und durch erläutert von Johanne Christophoro Sturmio. + Des Unvergle... - [FIRST GERMAN ARCHIMEDES]‎

‎Nürnberg, Paulus Fürsten, 1670 + (Sand=Rechnung) 1667. Folio. Contemporary full calf, rebacked in old style with 5 raised bands. Corners neatly restored. Extremities slightly rubbed. Engraved frontispiece with globes, world-systems, and Archimedean figures. Title in red and black. (18), 427, (1) pp. + (8), 32 pp. Numerous diagrams in the text. Occasional light browning, a few brownspots. Some leaves in the ""Sand-Rechnung"" with a dampstain. Ovcerall fine and clean, printed on good paper.‎

‎The highly important first edition of the first German translation of Archimedes' main mathematical works, marking a milestone in the reception of the science of Antiquity. The translation was based on David Rivault's Latin-Greek edition of 1615 and has the famous commentaries by the editor Johann Christoph Sturm (1635-1703), professor of mathematics and Physics at the university of Altdorf from 1669. This seminal work contains the first German translations of the following main works by Archimedes: Sphere & Cylinder (2 Books) Measurement of the Circle. Equilibrium of planes. Quadrature of the parabola. Conoids & spheroids. Spirals. As well as The Sand Reckoner (Psammites, Arenarius), which was separately published, in 1667, and is sometimes withbound as an appendix, as here, but which is often missing. This seminal work, the Sand Reckoner, introduced an extremely large number in arithmetics, (""How many grains of sand could the whole universe hold?"") and also contained the first printed statement of the heliostatic world-picture, a theory first put forward by ARISTARCHUS in a lost work and here referred by Archimedes: ""Dann er fetzet (Aristarchus) die Fix-oder Haft-Sterne, samt der Sonne als unbeweglich in einem Kreiss umb die Sonne, welche das Mittel solches Kreises besitze. Der Fix-oder Haft-Sternen aber ihren umb der Sonnen Mittelpunct ausgespannten, Himmel beschreibet er in solcher Grösse, dass der Erden Lauffkreiss, auf welchem sie umb die Sonne bewegt werden solle, gegen derer Haft-Sternen fernen Entlegenheit, sich nicht anderst verhalte, als einer Kugel Mittel-punct gegen deroselben Umbkreiss."" (pp. 2 -3 in Sand=Rechnung""). Called ""the God of Mathematics"" by Plinius, Archimedes is arguably the greatest mathematician, physicist, and engineer of ancient times. Without the background of the works of Archimedes the development of mathematics in Europe during the 16th end 17th centuries is inconceivable. ""There is no one individual whose work epitomizes the character of the Alexandrian age so well as Archimedes (287-212 B.C.), the greatest mathematician in antiquity."" (Morris Kline). ""He gave birth to the calculus of the infinite conceived and brought to perfection successively by Kepler, Cavalieri, Fermat, Leibnitz and Newton."" (Chasles) The first German edition of the works of Archimedes was foundational in the spreading of the Aristotelian teachings in Northern Europe, making them accessible to a much wider, learned audience. Sturm was a highly important German mathematician, whose fame was not only national. He was closely connected with the Royal Society in London, where his portrait was presumably the first of a German scientist. In 1672, he gained wide acknowledgement for his “Collegium Experimentale” and became a pioneer in the introduction of experiments in scientific teaching in Germany. He is responsible for several important inventions, like the differential thermometer, and his many mathematical works greatly improved the teachings of mathematics in German schools. His magnum opus is no doubt his monumental first German edition of Archimedes’ works. Poggendorff II:1043.‎

書籍販売業者の参照番号 : 62952

‎"ARCHIMEDES.‎

‎De iis quae vehuntur in Aqua Libri Duo. A’ Federico Commandino Urbinate in pristinum nitorem restituti, et commentariis illustrati. - [THE FOUNDING WORK ON HYDROSTATICS]‎

‎Bologna, Alessandreo Benacci, 1565. 4to. In contemporary blank cardboards with marbled paper back-strip. Ff 8-12 with small brown dot to lower outer margin, not affecting text. A fine copy. [4], 43 ff. + 1 blank. (Erroneously paginated f. 33 as 25 and f. 44 as 43).‎

‎First edition of Commandino's translation, and accompanying mathematical additions, of Archimedes' work on floating bodies, being the foundational work of hydrostatics. Commandino's own mathematical additions include the very first attempt to fill the gap in the incomplete proof of propositions 2 in book II of the Latin translation made by the Flemish Willem Moerbeke in 1269. ""This edition of Commandino remained the reference until the early twentieth century and the work of Heiberg after the discovery of the Archimedes palimpsest"". (D.B.I).""In hydrostatics [Archimedes] described the equilibrium of floating bodies and stated the famous proposition - known by his name - that, if a solid floats in a fluid, the weight of the solid is equal to that of the fluid displaced and, if a solid heavier than a fluid is weighed in it, it will be lighter than its true weight by the weight of the fluid displaced. We owe to Archimedes the full exposition of the doctrine of levers and pulleys."" (PMM, p. 44)The work consists of two parts: The first is to the effect that the pressure excerted by any part of a fluid on the fluid is downward. The second postulate states that the pressure of the fluid on a body placed in it is exerted upward along the perpendicular through the center of the body.However, Book II contained many sophisticated ideas and complex geometric constructions and did not have the appeal of Book I. Only after Greek geometry was combined with algebra, trigonometry, and analytical geometry, the present work being one of the earliest attempts to do this, and the field of mechanics reached the maturity to handle the concepts of equilibrium and stability that Archimedes introduced was Book II seriously studied. It then became the standard starting point for scientists and naval architects examining the stability of ships and other floating bodies.""Archimedes left to posterity his famous treatise ""On Floating Bodies"", which establishes the physical foundations for the floatability and stability of ships and other maritime objects. Yet since this treatise was long lost and also simply ignored by practitioners, it took many centuries before Archimedes' brilliant insights were actually applied in ship design and ship safety assessment."" (Nowacki, The Heritage of Archimedes in Ship Hydrostatics: 2000 Years from Theories to Applications).A Greek manuscript dating from about the ninth century and containing both books of On Floating Bodies was translated into Latin by the Flemish Dominican William of Moerbeke in 1269, along with other works of Archimedes from other manuscripts. The tracks of the Greek manuscript were lost in the fourteenth century, but Moerbeke's holograph remains intact in the Vatican library (Codex Ottobonianus Latinus 1850) [5, 8]. Moerbeke's Latin translation was the source of all versions of On Floating Bodies from his time until the twentieth century.""In 1543 Tartaglia [...] the Moerbeke translations of On the Equilibrium of Planes and Book I of On Floating Bodies (leaving the erroneous impression that he had made these translations from a Greek manuscript, which he had not since he merely repeated the texts of the Madrid manuscript with virtually all their errors). Incidentally, Curtius Trioianus published from the legacy of Tartaglia both books of On Floating Bodies in Moerbeke's translation (Venice, 1565). The key event, however, in the further spread of Archimedes was the aforementioned editio princeps of the Greek text with the accompanying Latin translation of James of Cremona at Basel in 1544. Since the Greek text rested ultimately on manuscript A,On Floating Bodies was not included. A further Latin translation of the Archimedean texts was published by the perceptive mathematician Federigo Commandino [...], which the translator supplemented with a skillful mathematical emendation of Moerbeke's translation of On Floating Bodies (Bologna,1565) but without any knowledge of the long lost Greek text."" (DSB)Adams, 1533 Riccardi, I, 42- 5Honeyman 131" Macclesfield 183D.B.I., XXVII, p. 604.Bibliotheca Mechanica 78Graesse I, 180.BM 000105842‎

書籍販売業者の参照番号 : 52966

‎"ARONHOLD, S.‎

‎Theorie der homogenen Functionen dritten Grades von drei Veränderlichen.‎

‎Berlin, G. Reimer, 1858. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 55. Band, 1858""., without backstrip. Fine and clean. [Aronhold:] Pp. 97-191.‎

‎First printing of Aronhold's important paper on the theory of invariants: Aronhold was particularly attracted by the theory of invariants, which was then the center of mathematical interest, and was the first German to do research in this area. The theory of invariants is not, however, connected with Aronhold alone - others who worked on it were Sylvester, Cayley, and Hesse - but he developed a special method that proved to be extremely successful. Aronhold stresses that he arrived at his principles as early as 1851, citing his doctoral dissertation and the treatise ""Theorie der homogenen Funktionen dritten Grades... (1858). Since the subsequent theory and terminology did not yet exist, he claimed priority."" (DSB).‎

書籍販売業者の参照番号 : 48067

‎"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.‎

書籍販売業者の参照番号 : 42184

‎"BABBAGE, CHARLES‎

‎An examination of some questions connected with games of chance (+) On the Application of Analysis to the Discovery of Local Theorems and Porisms. - [BABBAGE'S ONLY PAPER ON PROBABILITY]‎

‎Edinburgh, William & Charles Tait / London, Longman, etc, 1823. 4to. In recent marbled paper wrappers. Extracted from ""Trans. Roy. Soc. Edinburgh"" 9, pt. 1 (1821). Leaves reinforced in margin. Pp. (6), 153-177, 337-352.‎

‎First Edition of Babbage's only paper on probability. ""In this paper [Babbage's] concern was primarily mathematical, and we will find considerable skill in the manipulation of functions and polynomials. [...] The major interest in this particular paper [is] the ingenious use of algebra to solve probability problems, especially the devices using the coefficients of polynomials and the roots of unity"" (Dubbey, The Mathematical Work of Charles Babbage, pp. 141-42).Erwin Tomash B22‎

書籍販売業者の参照番号 : 56997

‎"BABBAGE, CHARLES‎

‎Observations on the Notation employed in the Calculus of Functions. (Read May 1. 1820).‎

‎London, Cambridge University Press, 1822. 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In ""Transactions of the Cambridge Philosophical Society"", Volume 1. Fine and clean. Pp. (63)-76‎

‎"BABBAGE, CHARLES‎

‎Observations on the Notation employed in the Calculus of Functions. (Read May 1. 1820).‎

‎London, Cambridge University Press, 1822. 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In ""Transactions of the Cambridge Philosophical Society"", Volume 1. Fine and clean. Pp. (63)-76‎

‎First appearance of Babbage paper on the notation employed in the Calculus of Functions.""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).Erwin Tomash B47‎

書籍販売業者の参照番号 : 54754

‎"BABBAGE, CHARLES.‎

‎MÉCANIQUE APPLIQUÉE. Note sur la machine suédoise de MM. Schutz pour calculer les Tables mathématique par la méthode des différences, et en imprimer les résultats sur des planches stéréotypes. - [BABBAGE'S REPORT ON THE SCHEUTZ-ENGINE]‎

‎Paris, Mallet-Bachelier, 1855. 4to. Extract, bound in new full blue cloth with gilt lettering to spine. A bit of brownspotting, otherwise a fine. [Babbage:] Pp. 557-560. [Entire issue: (3), 538-63 pp.].‎

‎Scarce first publication of Babbage's early report on the difference engine, which had been built by the Swedish printer Georg Scheutz and his son Edvard, based upon Babbage's own designs. ""In 1854 Babbage's ideas came to the attention of George and Edvard Scheutz, a father and son from Sweden. After reading a description of the Difference Engine (by Babbage), they designed and built their own version. This machine was smaller and lighter than the engine conceived by Babbage. They used gears and levers that would have been suitable for the mechanism of a clock. In contrast, Babbage used technology that would have been appropriate for a steam engine. Babbage's engine, if completed, would have filled a room. The Scheutz engine sat nicely on a table and looked like a complicated music box. Babbage was pleased with Scheutz's engine and praised it publicly [In the present paper]. (DSB).""Georg Scheutz's interest in calculating machines had begun twenty-five years earlier, when he first heard about Babbage's Difference Engine no. 1. In 1834, after reading Dionysius Lardner's technical article about the Difference Engine, Scheutz and his son began building their own engine, completing a crude prototype model in 1843 (Scheutz Engine no. 1) and an improved and more highly finished example in the 1850s (Schultz Engine no. 2.). As part of his effort to promote the Scheutz Engine, Babbage gave a talk on it before the Académie des Sciences, illustrated with drawings by his son Henry, in which Babbage's system of mechanical notation was used to describe the machine's construction and functions. This talk was published without illustrations in the Académie's Comptes rendus [the present paper]. (OOC).See Hook & Norman. Origins of Cyberspace 73.‎

書籍販売業者の参照番号 : 44733

‎"BABBAGE, CHARLES.‎

‎On some new Methods of investigating the Sums of several Classes of infinite Series. Read April 1, 1819.‎

‎(London, W. Bulmer & Co.), 1819. 4to. No wrappers as issued in ""Philosophical Transactions of the Royal Society of London for the Year MDCCCXIX."", pp. 249-282.‎

‎"BABBAGE, CHARLES.‎

‎On some new Methods of investigating the Sums of several Classes of infinite Series. Read April 1, 1819.‎

‎(London, W. Bulmer & Co.), 1819. 4to. No wrappers as issued in ""Philosophical Transactions of the Royal Society of London for the Year MDCCCXIX."", pp. 249-282.‎

‎First edition, the journal printing, of one of the importent works in pure mathematics, which occupied Babbage from 1815-20. The item offered is the authors 5th work.""Babbage brings his great powers of inventiveness to this subject (i.e. infinite series) but like many of his contemporaries, appeared insensitive to problems arising out of convergence, and accepted unquestionably several absurd results."" (Dubbey 1979, pp. 135-36). - Hook and Norman No 24.‎

書籍販売業者の参照番号 : 46465

‎"BABBAGE, CHARLES.‎

‎On the Determination of the General Term of a New Class of Infinite Series. [Read May 3, 1824].‎

‎London, Taylor and Francis, 1826 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In ""Transactions of the Cambridge Philosophical Society"", Volume 2, part 1. . Fine and clean. Pp. (217)-225 + the pasted on title-page.‎

‎First printing of the early mathematical paper. Erwin Tomash B14.‎

書籍販売業者の参照番号 : 54757

‎"BABBAGE, CHARLES. - THE LANGUAGE OF THE COMPUTER INVENTED.‎

‎On a Method of expressing by signs the action of machinery. Read March 16, 1826.‎

‎(London, W.Nicol, 1826). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1826 - Part III. Pp. 250-265 and 4 engraved plates. Some faint dampstains to plates. One plate with a small tear, no loss. the same plate some creasing at upper part, verso of plate somewhat soiled. Page 261 with some marginal brownspots and some soiling. The other leaves clean and fine.‎

‎"BACHARACH, I.‎

‎Ueber den Cayley'schen Schnittpunktsatz. - [THE CAYLEY-BACHARACH THEOREM]‎

‎Leipzig, B. G. Teubner, 1886. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 26., 1886. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. With a marginal tear affecting pp. 275-282 and 2 cm of the text, otherwise very fine and clean. Pp. 275-299. [Entire volume: IV, 606 pp.].‎

‎First printing of Bacharach's paper which gave the final solution to what later was to be known as the Cayley-Bacharach Theorem: That when a plane curve of degree r is drawn through the mn points common to two curves of degrees m and n (both less than r), these do not count for mn conditions in the determination of the curve but for mn reduced by (m + n - r - 1) (m + n - r - 2).""Cayley wrote copiously on analytical geometry, touching on almost every topic then under discussion. Although, as explained elsewhere, he never wrote a textbook on the subject, substantial parts of Salmon’s Higher Plane Curves are due to him"" and without his work many texts of the period, such as those by Clebsch and Frost, would have been considerably reduced in size. One of Cayley’s earliest papers contains evidence of his great talent for the analytical geometry of curves and surfaces, in the form of what was often known as Cayley’s intersection theorem (C. M. P., I, no. 5 [1843], 25-27). There Cayley gave an almost complete proof (to be supplemented by Bacharach, in Mathematische Annalen, 26 [1886], 275-299)"" (DSB).‎

書籍販売業者の参照番号 : 47134

‎"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.‎

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