‎Mathematics‎

‎"POINCARÉ, H.‎

‎Sur les rapports de l'analyse pure et de la physique mathématique.‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1897]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 21. No backstrip. Fine and clean. Pp. 331-341.‎

‎First printing of Poincaré's principal address at the first International Congress of Mathematicians held in Zürich in 1897.‎

Bookseller reference : 46182

‎"KLEIN, FELIX‎

‎Beweis für die Nichtauflösbarkeit der Ikosaedergleichung durch Wurzelzeichen.‎

‎Leipzig, B.G. Teubner, 1905. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. 61. Band. 3. Heft."" Entire issue offered. Internally very fine and clean. Pp. 369-371. [Entire issue: Pp. 289-452].‎

‎First printing of Klein's paper on the Icosahedron.""One of the leading mathematicians of his age, Klein made many stimulating and fruitful contributions to almost all branches of mathematics, including applied mathematics and mathematical physics. Moreover, his extensive activity contributed greatly to making Göttingen the chief center of the exact sciences in Germany. An opponent of one sided approaches, he possessed an extraordinary ability to discover quickly relationships between different areas of research and to exploit them fruitfully."" (DSB).‎

Bookseller reference : 46191

‎"LEBESGUE, HENRI.‎

‎Recherches sur la Convergence des Séries de Fourier.‎

‎Leipzig, B. G. Teubner, 1905. 8vo. In the original printed wrappers, without backstrip. In ""Mathematische Annalen, 61. Band, 2. Heft, 1905"". Fine and clean. [Lebesgue:] Pp. 251-280. [Entire issue: 161-288 pp].‎

‎First printing of Lebesque's paper in which he extended and accepted Fourier's work that stated that any arbitrary function, defined in a finite interval, can be expressed as a sum of sine and cosine functions: ""In 1905 Lebesgue gave a new sufficient condition for the convergence of the Fourier series to a function f(x) that include all previously known conditions"". (Kleine, P. 1047)‎

Bookseller reference : 46200

‎"TCHEBYCHEFF, P. [PAFNUTY LVOVICH CHEBYSHEV]‎

‎Sur la représentation des valeurs limites des intégrales par des résidus intégraux.‎

‎Berlin, Stockholm, Paris, Beijer, 1886. 4to. With the original wrappers in ""Acta Mathematica, 9:1. Band]. No backstrip. Fine and clean. Pp. 35-56. [Entire issue: 104 pp. ].‎

‎First translation of Tchebycheff's paper on Moments - a quantitative measure of the shape of a set of points. Tchebycheff is known for his work in the field of probability, statistics and number theory.‎

Bookseller reference : 46202

‎"TORTOLINI, BARNABA.‎

‎Sur les transformations et les valeur de plusieurs intégrales définies qui se rapportent aux surfaces et aux solidités des volumes.‎

‎Berlin, G. Reimer, 1843. 4to. In ""Journal für die reine und angewandte Mathematik, 26. Band, 4 Heft, 1843"". In the original printed wrappers, without backstrip. Fine and clean. [Tortolini:] Pp. 277-310. [Entire issue: Pp. 277-368, (2) + 1 plate.].‎

‎First printing of Italian Mathematician's paper on definit integrals relating to surfaces. Barnaba Tortolini was a 19th-century Italian priest and mathematician who played an early active role in advancing the scientific unification of the Italian states. He founded the first Italian scientific journal with an international presence, Annali di scienze matematiche e fisiche, and functioned a professor of mathematics at the University of Rome for 30 years.‎

Bookseller reference : 46280

‎"GÖDEL, KURT.‎

‎Ein Spezialfall des Entscheidungsproblems der theoretischen Logik. - [INCOMPLETENESS FROM THE STANDPOINT OF FIRST-ORDER LOGIC]‎

‎Leipzig & Berlin, B.G. Teubner, 1932. 8vo. A mint copy, in the original wrappers, still contained in the original plastic protection. In ""Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Manger, Heft 2"". Pp. 27-28. [Entire volume: 38 pp].‎

‎First edition of Gödel's important paper, which constitutes a supplement to his ""Die Vollständigkeit der Axiome des logischen Funktionskalküls"" (1930). In the present paper, Gödel seminally formulates his earlier incompleteness results from the standpoint of first-order logic, thereby contributing substantially to modern mathematical logic.""In 1932 Godel published his formulation of the incompleteness results from the standpoint of first order logic. If number theory is regarded as a formal system in first-order logic, then the above results about incompleteness and unprovability of consistency apply to S. If, however, S is extended by variables for sets of numbers, for sets of sets of numbers, and so on (together with the corresponding comprehension axioms), then we obtain a sequence of systems S"" the consistency of each system is provable in all subsequent systems. But in each subsequent system there are undecidable propositions. Going up in type in this way, he noted, corresponds in a type-free system of set theory to adding axioms that postulate the existence of larger and larger infinite cardinalities. This was the beginning of Gödel's interest in large cardinal axioms, an interest that he elaborated in 1947 in regard to the continuum problem."" (DSB).The issue contains several papers by Karl Menger.‎

Bookseller reference : 46285

‎"[MENCKE, FRIEDRICH OTTO [EDT.]].‎

‎Actorum Eruditorum, Supplementa. Tomus X.‎

‎Leipzig, Grosse & Gleditsch, 1734. 4to. Contemp. full vellum. Faint handwritten title on spine. A small stamp to title page and pasted library label to pasted down front free end-paper. In: ""Actorum Eruditorum Anno MDCCXXXIV"". The entire volume offered.(4), 560, (27) pp. + 1 plate‎

‎The offered volume contain many papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 46343

‎[MENCKE, FRIEDRICH OTTO [EDT.]].‎

‎Nova Acta Eruditorum Anno MDCCXXXVIII.‎

‎Leipzig, Grosse & Gleditsch, 1738. 4to. 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. (6), 710, (42) pp + 6 plates.‎

‎The offered volume contain many papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 46346

‎[BEL, KARL ANDREAS. [EDT.]].‎

‎Nova Acta Eruditorum Anno MDCCLV [1755].‎

‎Leipzig, Gleditsch & Lanckisiii, 1755. 4to. 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. A fine copy. (4), 720, (24) pp + 6 plates.‎

‎First issue of Nova Acta Eruditorum with Karl Andreas Bel as editor.The offered volume contain many reviews and original contributions by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 46348

‎[MENCKE, FRIEDRICH OTTO [EDT.]].‎

‎Nova Acta Eruditorum Anno MDCCXXXII. [1732].‎

‎Leipzig, Gleditsch & Martini, 1732. 4to. 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 brownspotting. (6), 594, (32) pp + 6 plates.‎

‎First issue of Nova Acta Eruditorum with Friedrich Otto Mencke as editor, the grandson of the founder of the journal, Otto Mencke. The offered volume contain many reviews by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 46350

‎[BEL, KARL ANDREAS. [EDT.]].‎

‎Nova Acta Eruditorum. Anno MDCCLIX.‎

‎Leipzig, Gleditsch & Lanckisiii, 1759. 4to. 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 brownspotting. (4), 720, (30) pp + 1 plates.‎

‎The offered volume contain many reviews by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 46352

‎"JACOBI, C.G.J.‎

‎Über die unmittelbare verification einer Fundamentalformel der Theorie der elliptischen Functionen (+) Über die partielle Differentialgleichung, welcher die Zähler und Nenner der elliptischen Functionen.‎

‎Berlin, G. Reimer, 1848. 4to. In the original wrappers, no backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 36. Band, Erstes [1] Heft"". Entire issue offered. A fine and clean copy. Pp. 75-89. [Entire volume: IV, (2), 96, (2) pp.].‎

‎First printing of these two papers influential papers by Jacobi published in the epoch-making year 1848.""In the revolutionary year of 1848 Jacobi became involved in a political discussion in the Constitutional Club. During an impromptu speech he made some imprudent remarks which brought him under fire from monarchists and republicans alike. Hardly two years before, in the dedication of volume I of his Opuscula mathematica to Friedrich Wilhelm IV, he had expressed his royalist attitude"" now he had become an object of suspicion to the government. A petition of Jacobi’s to become officially associated with the University of Berlin, and thus to obtain a secure status, was denied by the ministry of education. Moreover, in June 1849 the bonus on his salary was retracted. Jacobi, who had lost his inherited fortune in a bankruptcy years before, had to give up his Berlin home. He moved into an inn and his wife and children took up residence in the small town of Gotha, where life was considerably less expensive."" (DSB).‎

Bookseller reference : 46355

‎[MENCKE, OTTO [EDT.]].‎

‎Actorum Eruditorum. Supplementa, tomus II [2].‎

‎Leipzig, Grosse & Fritschium, 1696. 4to. 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. (2), 603 pp. + 10 engraved folded plates.‎

‎The offered volume contain many papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 46396

‎"TSCHIRNHAUS, EHRENFRIED W. V. [FIRST PUBLICATION OF THE ""TSCHIRNHAUS TRANSFORMATION"".]‎

‎Methodus datae figurae, rectis lineis & curva Geometrica terminate, aut Quadraturam, aut impossibilitatem ejusdem Quadraturae determinandi. (+) Nova Methodus determinandi Maxima & Minima (+) Aufrendi omnes terminos intermedios ex data aequatione. - [FORCED LEIBNIZ TO PUBLISH THE CALCULUS]‎

‎Leipzig, Grosse & Gleditsch, 1683. 4to. Contemporary full vellum. Handwritten title on spine. Library label to pasted down front free end-paper and a small stamps on titlepage. In: ""Acta Eruditorum Anno MDCLXXXIII"". As usual with various browning to leaves and plates. Tschirnhaus' paper: pp. 122-124" Pp. 204-207" Pp. 433-437. [Entire volume: (8), 561, (7) pp + 13 plates].‎

‎First appearance of Tschirnhaus's three exceedingly important papers which were to to initiate one of the most famous mathematical discoveries. In the papers he used infinitisimal methods which were very close to Leibniz's method and where he tried to lay down criteria for rational quadratures in the case of conic, cubic and quadratic curves, papers that led Leibniz to publish his first paper on the differential calculus, the ""Nova Methoda"" in the Acta for 1684 in order to secure his priority over Tschirnhaus concerning the calculus. Leibniz discovered, when he read Tschirnhaus' papers, that Tschirnhaus had here published results showing similarity with Leibniz's invention of the calculus as he had confided to Tschirnhaus earlier, during their Parisian stay, and this without references to Leibniz.The present volume of Acta also contain the first edition of Tschirnhaus' ""Tschirnhaus Tranformation"". Tschirnhaus work intensively on finding a general method for solving equations of higher of higher degree. ""His transformations constituted the most promising contribution to the solution of equations during the seventeenth century" but his elimination of the second and third coefficients by means of such transformation was far from adequate for the solution of the quintic.(Boyer. A History of Mathematics, 1968, 472 p.).Tschirnhaus (1651-1708) , a Saxon nobleman, had as wide interest as acquaintances: He studied in Leyden, served in the Dutch army, visited England and Paris several times. He set up a glassworks in Italy and is said to have introduced Porcelain to Europe. He wrote about philosophy and mathematics and was a close friend of Leibniz.‎

Bookseller reference : 46399

‎"HERMITE, C.‎

‎Note sur la réduction des fonctions homogénes á coefficients entiers et á deux indéterminées.‎

‎Berlin, G. Reimer, 1848. 4to. In ""Journal für die reine und angewandte Mathematik, 1848. Band, 4 Heft"". In the original printed wrappers, without backstrip. Fine and clean. [Hermite:] Pp. 357-364. [Entire volume: Pp. 275-364 + 3 folded plate.].‎

‎First printing.Charles Hermite (1822-1901), French mathematician, made significant contributions to pure mathematics, and especially to number theory and algebra. In 1858 he solved the equation of the fifth degree by elliptic functions, and in 1873 he proved that e (the base of natural logarithms) is transcendental. The legacy of his work can be shown in the large number of mathematical terms which bear the adjective 'Hermitian'.‎

Bookseller reference : 46404

‎"JACOBI, C. G. J.‎

‎Elementarer Beweis einer merkwürdigen analytischen Formel, nebst einigen aus ihr folgenden Zahlensätzen.‎

‎Berlin, G. Reimer, 1840. 4to. In ""Journal für die reine und angewandte Mathematik, 1848."". Without backstrip. Fine and clean. Pp.: 13-32 [Entire volume: 13-100 pp.].‎

‎First printing of Jacobi's proof an analytical formula. ""Most of Jacobi's fundamental research articles in the theory of elliptic functions, mathematical analysis, number theory, geometry, and me-chanics were published in Crelle's Journal fue die reine and angewandte Mathematik. With an average of three articles per volume, Jacobi was one of its most active contributors and quickly helped to establish its international fame."" (DSB)‎

Bookseller reference : 46406

‎"RICHELOT, F.‎

‎De integralibus quibusdam definitis, quorum summa ad quadraturam divisionemque circuli revocatur.‎

‎Berlin, G. Reimer, 1840. 4to. In ""Journal für die reine und angewandte Mathematik, 21. band, 4. heft."". Entire issue offered in the original printed wrappers, without backstrip. Fine and clean. Pp. 293-327 [Entire volume: Pp. 293-380, (2) + 1 folded plate.].‎

‎First printing.Richelot was a student of Jacobi. Richelot authored numerous publications among them - with his 1832 dissertation - the first known guide to the Euclidean construction of the regular 257-gon with compass and straightedge.‎

Bookseller reference : 46408

‎"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.‎

Bookseller reference : 46465

‎"HURWITZ, A.‎

‎Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt. - [HURWITZ DETERMINANT]‎

‎Leipzig, B. G. Teubner, 1895. 8vo. In the original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch and Carl Neumann. 46. Band. 2. Heft."" Entire issue offered. Internally very fine and clean. Pp. 273-285. [Entire volume: Pp. 161-320].‎

‎First printing of Hurwitz's important paper in which he presented the ""Hurwitz determinant"" for the first time. They are used to give a criterion for all roots of a polynomial to have negative real part.‎

Bookseller reference : 46504

‎[CLEBSCH, ALFRED (+) CARL NEUMANN. EDT.].‎

‎Mathematische Annalen. Begründet durch Alfred Clebsch and Carl Neumann. 51. Band. 2. Heft. 1898.‎

‎Leipzig, B. G. Teubner, 1898. 8vo. In the original printed wrappers, no backstrip. Entire issue offered. Internally very fine and clean. Pp. 161-480‎

‎First printing.‎

Bookseller reference : 46506

‎"LIPSCHITZ, R.‎

‎Beiträge zur Theorie der Variation der einfachen Integrale.‎

‎Berlin, G. Reimer, 1865. 4to. In the original printed wrappers, without backstrip. In ""Journal für die reine und angewandte Mathematik, 65 Band, 1. Heft, 1865"". Minor browning, otherwise fine. Pp. 24-41. [Entire volume: IV, 96, (2) pp..].‎

‎First printing of Lipschitz's paper on integrals. ""At the age of fifteen he began the study of mathematics at the University of Königsberg, where Franz Neumann was teaching. He then went to Dirichlet in Berlin, and he always considered himself Dirichlet’s student. After interrupting his studies for a year because of illness, he received his doctorate from the University of Berlin on 9 August 1853. After a period of taining and teaching at the Gymnasiums in Königsberg and Elbing, Lipschitz became a Privatdozent in mathematics at the University of Berlin in 1857. In the same year he married Ida Pascha, the daughter of a neighboring landowner. In 1862 he became an associate professor at Breslau, and in 1864 a full professor at Bonn, where he was examiner for the dissertation of nineteen-year-old Felix Klein in 1868. He rejected an offer to succeed Clebsch at Göttingen in 1873. Lipschitz was a corresponding member of the academies of Paris, Berlin, Göttingen, and Rome.Lipschitz distinguished himself through the unusual breadth of his research. He carried out many important and fruitful investigations in number theory, in the theory of Bessel functions and of Fourier series, in ordinary and partial differential equations, and in analytical mechanics and potential theory."" (DSB)‎

Bookseller reference : 46521

‎"CAMUS, CHARLES ÈTIENNE LOUIS. - THE GEAR OF TIMEKEEPERS.‎

‎Sur la Figure des Dents des Roues, et des Aisles des Pignons, pour rendre les Horloges plus parfaites.‎

‎(Paris, L'Imprimerie Royale, 1735). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1733"". Pp. 117-140 and 4 folded engraved plates. Fine and clean.‎

‎By this paper Camus was the first to work out the mathematical theory of gearteeth into a systematical and general theory of the mechanism.‎

Bookseller reference : 46584

‎"OZANAM, (JACQUES).‎

‎L'Usage du Compas de Proportion, expliqué et demontré d'une maniere courte & facile, & augmenté d'un Traité de la division des Champs. Derniere édition, corrigée & augmentée.‎

‎Paris, Charles-Antoine Jombert, 1736. 8vo. Contemp. full vellum. 150,(2) pp. and 1 folded engraved plate, many textdiagrams. Leaves somewhat browned.‎

‎Ozanam's work on the proportional compas - first printed in 1688 - became very popular and successfull and it was lastly printed in 1794.""By almost any criterion Ozanam cannot be regarded as a first-rate mathematician, even of his own time. But he had a flair for writing and during his career wrote a number of books, some of which were very popular, passing through many editions.""(DSB).‎

Bookseller reference : 46755

‎KARSTEN, WENCESL. JOHANN GUSTAV.‎

‎Auszug aus den Anfangsgründen und dem Lehrbegriffe der Mathematischen Wissenschaften. Die zweyte Auflage. 2 Bde.‎

‎Greifswald, Anton Ferdinand Röse, 1785. Small8vo. 2 contemp. hcalf. Gilt spines and titlelabels with gilt lettering. Spines slightly rubbed. XVIII,(3),456(6),445,(19) pp. and 25 folded engraved plates. 2 plates with a small hole, taped. Some scattered brownspots.‎

‎Deals with Arithmetics, Geometry, Trigonometry, Algebra, Statics, Hydraulics, Perspective, Machine theory, Artillery, Optics, Dioptrics, Catroptics, Astronomy, Gnomonics, Civil- and military Architecture. - Karsten was a pupil of Leonhard Euler.‎

Bookseller reference : 46847

‎HAMILTON, WILLIAM ROWAN.‎

‎On Quaternions" or on a new System of Imaginaries in Algebra. - [MAKING THE GENERAL THEORY OF RELATIVITY POSSIBLE]‎

‎London, Richard and John Taylor, 1844. Contemp. hcalf. Gilt lettering to spine ""Philosophical Magazine"" - Vol. XXV. In: ""The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. Conducted by David Brewster et al."". Vol. XXV. A stamp to titlepage and a few other pages. Entire volume offered (July-December 1844). VIII,552 pp., textillustr. Hamilton's paper: pp. 10-13, 141-145 and 241-246.‎

‎First printing of this landmark paper in which Hamilton published his creation of a new algebra of quaternions (a noncommunicative algebra), a turning point in the development of mathematics and a discovery which made possible the creation of the general theory of relativity. His algebra was later to form the basis of quantum mechanics and for the proper understanding of the atom.""Gauss had treated imaginary numbers in combination with real ones as representing points on a plane and showed the methods by which such complex numbers could be manipulated. Hamilton tried to extend this to threee dimensions and found himself unable to work out a self-consistent method of multiplication, until it occurred to him that the cummutative law of multiplication need not necessarily hold. It is taken for granted that A times B is equal to B times A... and this is an example of what seems to be an eternal and inescapable truth. Hamilton, however, showed that he could built up a logical algebra for his quaternions only when B times A was not made to equal - A times B. This seems against common sense but, like Lobachevski, Hamilton showed that the truth is relative and depends on the axioms you choose to accept.""(Asimov).The creation of quaternions is one of the famous moments in the history of mathematics. ""The quaternions came to Hamilton in one of those flashes of understanding that occasionally occur after long deliberation on a problem. He was walking into Dublin on 16 October 1843 along the Royal Canal to preside at a meeting of the Royal Irish Academy, when the discovery came to him. As he described it, ""An electric circuit seemed to close.""18 He immediately scratched the formula for quaternion multiplication on the stone of a bridge over the canal. His reaction must have been in part a desire to commemorate a discovery of capital importance, but it was also a reflection of his working habits. Hamilton was an inveterate scribbler. His manuscripts are full of jottings made on walks and in carriages. He carried books, pencils, and paper everywhere he went. According to his son he would scribble on his fingernails and even on his hard-boiled egg at breakfast if there was no paper handy.""(DSB).Hamilton later developed his invention in his book from 1853 ""Lectures on Quaternions"" - see PMM: 334 and Grattan-Guiness ""Landmark Writings in Western Mathematics 1640-1940"", pp. 460 ff.In this volume other importent papers by Gassiot, Sylvester, Joule, Draper.‎

Bookseller reference : 46875