‎Mathématiques‎

‎"BERNSTEIN, S. N.‎

‎Sur la meilleure approximation de |x| par des polynomes de degré donné. - [BERNSTEIN'S CONSTANT]‎

‎Berlin, Stockholm, Paris, Beijer, 1914. 4to. Bound in contemporary half cloth. In ""Acta Mathematica Hrsg. von G. Mittag-Leffler."", Bd. 37. Entires issue offered. Fine and clean. Pp. 1-52.. [Entire volume: (4), 387, 20, 33, 22 pp.].‎

‎First printing where Bernstein shows that the limit 2nE_{2n}(|x|) exists, today it is often referred to as the Bernstein's constant. Bernstein's constant, usually denoted by the Greek letter ß (beta), and is approximately equal to 0.2801694990.‎

书商的参考编号 : 49771

‎"BEZOUT, ÉTIENNE.‎

‎Mémoire sur plusieurs Classes d'Équations de tous les Degrés, Qui admettent une Solution algébrique.‎

‎(Paris, L'Imprimerie Royale, 1764.) 4to. Without wrappers. In ""Histoire de L'Academie Royale des Sciences. Année MDCCLXII. Avec les Memoires de Mathematiques & de Physique, pour la même Année."" Pp. 17-52. Clean and fine.‎

‎First printing of a main work on algebraic elimination theory, being Bezout's first paper in this field. This paper provides the method of solution for certain nth-degree equations.‎

书商的参考编号 : 53466

‎"BION, NICOLAI.‎

‎Neu-eröffnete Mathematische Werck-Schule, Oder Gründliche Anweisung, Wie die Mathematische Instrumenten (+) Weitere Eröffnung der neuen Mathematischen Werck-Schule. - [""THE MOST FAMOUS BOOK DEVOTED TO INSTRUMENTS""]‎

‎Franckfurt und Leipzig, Hoffmännischen Buchladen in Nürnberg, 1712 (+) Nürnberg, Conrad Monath, 1717. 4to. In contemporary full vellum with title in contemporary hand to spine. A few dots and mark to extremities and a few annotation to pasted down front end-paper. A very nice copy. (12), 394 pp. + frontispiece and 28 plates"" (8), 48 pp. + 11 plates.‎

‎First German edition of, according to historian of science David M. Knight, ""the most famous book devoted to instruments"". The work is one of the best of that time on scientific instruments, including the compass of proportion, surveying and astronomical instruments, etc. The short work bound withbound is “written by Doppelmayr and illustrates a number of instruments, which, although claiming to be from Bion’s workshop, do not appear in any of Bion’s French editions. The most inventive are optical-binocular and reflecting telescopes”. (Erwin Tomash). The present work was translated from the French original edition, published in 1709, by J. G. Doppelmayr. Erwin Tomash B161 & B162.‎

书商的参考编号 : 60640

‎"BIOT, JEAN BAPTISTE - FOURCROY & VAUQUELIN‎

‎Recherches Sur l'intégration des équations différentielles, partielles, et sur les vibrations des surfaces. Lu le prairial an 8 (1800).‎

‎(Paris, Baudouin, AN XI (1803)). 4to. Without wrappers. Uncut. Extracted from ""Mémoires de L'Institut National des Sciences et Arts"", Tome Quatrieme. Pp. 21-112. Fine and clean, unopened.‎

‎"BOEHM, KARL.‎

‎Axiome der Arithmetik.‎

‎Heidelberg, Carl Winter, 1911. 8vo. Uncut in the original printed wrappers. ""Sitzungsberichte der Heidelberger Akademie der Wissenschaften"", Jahrgang 1911, 13. Abhandlung. Soiling to front wrapper and a few nicks to extremities, otherwise fine. 11 pp.‎

‎"BOHR, HARALD.‎

‎Lösung des absoluten Konvergenzproblems einer allgemeinen Klasse Dirichletscher Reihen.‎

‎[Berlin, Stockholm, Paris, Beijer, 1913] 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 36, pp. 197-240.‎

‎"BOIS-REYMOND, PAUL DAVID GUSTAV DU.‎

‎Über asymptotische Werthe, infinitäre Approximationen und infinitäre Auflösung von Gleichunge. - [ANTICIPATING CANTOR'S ""DIAGONAL ARGUMENT"".]‎

‎Leipzig, B. G. Teubner, 1875. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 8., 1875. 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. Title page missing a small piece of paper to the right margin, not affecting text. Very fine and clean. Pp. 363-414. [Entire volume: IV, 576 pp.].‎

‎"BOLLÉE, LÉON. - THE INVENTION OF ""THE MILLIONAIRE CALCULATOR""‎

‎Sur une nouvelle machine à calculer.‎

‎(Paris, Gauthier-Villars, 1889). 4to. No wrappers. Disbound. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 109, No 20. Pp. (723-) 758 (entire issue offered). Bollée's paper: pp. 737-739. Disbound but clean.‎

‎"BOLTZMANN, LUDWIG. - DEFENDING THE ATOMIC VIEWPOINT.‎

‎Über die Integrale linearer Differentialgleichungen mit periodischen Coëfficienten.‎

‎Wien, Karl Gerold's Sohn, 1868. 8vo. Uncut and unopened in orig. printed wrappers. In: ""Sitzungsberichte der kaiserlichen Akademie der Wissenschaften"", 58. Band, 1. Heft - Juni. Pp. (1-) 155 a. 7 plates.(Entire issue offered). Boltzmann's paper: pp. 54-59. Clean and fine.‎

‎"BOLZANO, BERNARD.‎

‎Versuch einer objectiven Begründung der Lehre von den drei Dimensionen des Raumes. (Aus dem Abhandlungen der k. böhm. Gesellschaft der Wissenschaften (V Folge, Bd. 3).) - [BOLZANO'S FIRST WORK ON SPACE AND TIME]‎

‎Prag [Prague], 1843. 4to. Uncut in the original printed light pink wrappers, with a dicreet new black cloth back-strip. A bit of brownspotting and minor chipping to edges pf wrappers, but overall a very nice copy of this fairly fragile publication. 15, (1) pp.‎

‎The very rare first edition, off-print (separately paginated), of this important treatise on space and time, which constitutes an important part of Bolzano's philosophical-logical theory. The present paper constitutes the first public formulation of these controversial ideas on time and space, with which Bolzano sets out to establish a foundation of mathematics which is non-empirical. By uniting mathematics and philosophy and applying both to the question of space and time, Bolzano here brings both sciences to a higher level of completeness, acknowledging that his theories depart from the those of Hegel, Kant, Schelling, etc. As always, Bolzano grabs the essence of the question and the terms that he is treating and retraces the concepts that must be used, establishing their original inner connection. In the present paper, the question of space, time, and thought are treated in order to establish the precise and full nature of space, a theme which Bolzano had apparently been working on for many years but previously only discussed with a very small number of intimate acquaintances, and now publishes on for the first time. The concept of space plays an important rôle in Bolzano's ontology and is closely linked to his mathematical and philosophical logic, in which the ""space-position"" plays a part in the demarcation of that which is purely mathematical and logical. Furthermore, for Bolzano, truth is constituted by true propositions (which state things as they are), and his canonical form of all propositions entails that ""[a] proposition is true iff the object has the property (the attribute) which belongs to the subject of the proposition. Moreover, empirical propositions must contain determinations of space and time. Without these determinations, the sentence ""It is snowing"" has no truth value, it is just a propositional form which does not correspond to a complete proposition"" ""in order to be true, [such propositions] require the addition of such specifications as to time (and often place as well), 'It is snowing today, in this place'"" (SEP).‎

书商的参考编号 : 41020

‎"BOOLE, GEORG - FOUNDING MODERN DIGITAL COMPUTER SCIENCE.‎

‎The Calculus of Logic.‎

‎Cambridge, Macmillan, Barclay, and Macmillan, 1848. No wrappers as extracted from ""The Cambridge and Dublin Mathematical Journal. Edited by W. Thomson."" Vol. III. Pp. 183-198. Having the titlepage (2) pp. to the entire volume.‎

‎First printing of this major paper in the founding of mathematical logic and pure mathematics. The paper offered here is a continuation of Boole's ""The Mathematical Analysis of Logic""(1847), pioneering the assimilation of logic to mathematics.Boole showed that how mathematical techniques could be applied to the study of logic, and as such he laid the foundations for the axiomatic and deductive treatment og logic, the Boolean algebra, which find imortent applications in both probability theory and computing. This mathematication of logic was undertaken by Frege and brought to a climax by Whitehead and Russell. Boolean algebra was used for this purpose.Boole's work contains what Bertrand Russell called the greatest discovery of the nineteenth century: the nature of pure mathematics.‎

书商的参考编号 : 41705

‎"BOOLE, GEORG. - A PRIZE WINNING PAPER.‎

‎On a General Method in Analysis. Received January 12th,- Read January 18th.‎

‎(London, Richard and John E. Taylor, 1844). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1844 - Part II. Pp. 225-282. Clean and fine.‎

‎First appearance of Boole's main paper on the Calculus.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.In 1843 the schoolmaster Boole finished a lengthy paper on differential equations, combining an exponential substitution and variation of parameters with the separation of symbols method. The paper was too long for the Cambridge Mathematical Journal. Gregory, and later De Morgan, encouraged him to submit it to the Royal Society. The first referee rejected Boole's paper, but the second recommended it for the Gold Medal for the best mathematical paper written in the years 1841 - 1844, and this recommendation was accepted. In 1844 the Royal Society published Boole's paper (the paper offered), and awarded him the Gold Medal, the first Gold Medal awarded by the Society to a mathematician.‎

书商的参考编号 : 42840

‎"BOOLE, GEORG. - THE THEORY OF INVARIANTS INITIATED.‎

‎Exposition of a general Theory of linear Transformations. Part I-II. (November 1841 a. May 1842).‎

‎Cambridge, E. Johnson, 1843. 8vo. Unbound without wrappers. In: ""The Cambridge Mathematical Journal"", Vol. III. IV,292 pp. (Entire volume offered). Boole's paper: pp. 1-20 a. 106-119.‎

‎First appearance of Boole's work on algebraic invariants, the starting point of the theory of invariants.""This was the starting point of the theory of invariants, so rapidly and extensively developed in the second half of the nineteenth century"" Boole himself, however, took no part in this development.""(DSB).The volume contains other papers by Boole ""On the Transformation of definite Integrals"", pp. 277-283 and ""Remarks on a Theorem of M. Catalan"", pp. 277-283. Also 6 papers by Arthur Cayley.‎

书商的参考编号 : 48322

‎"BOOLE, GEORGE.‎

‎Of Propositions Numerically Definite. [Read March 16th], 1868].‎

‎London, Taylor and Francis, 1869. 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 11. Fine and clean. Pp. 395-411, (1) + the pasted on title-page.‎

‎First appearance.‎

书商的参考编号 : 54758

‎"BOOLE, GEORGE.‎

‎On Simultaneous Differential Equations of the First Order in which the Number of the ariables exceeds by more than one the umber of the Equations. 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. A very faint dampstain to upper corners on the last 2 leaves, otherwise clean and fine, wide-margined..‎

‎First appearance of one of Boole's last papers.George Boole is mostly known for his ""An Investigation on the Laws of Thought"" 1854 and his developments of a form of symbolic logik, called Boolean Algebra. But he also did importent work on the Calculus, Differential Equations and the heory of probabilities.‎

书商的参考编号 : 42127

‎"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.‎

书商的参考编号 : 42126

‎"BOOLE, GEORGE.‎

‎Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order (+) On certain theorems in the calculus of variations (+) On the integration of linear differential equatio... - [FIRST PAPERS BY BOOLE]‎

‎Cambridge, Macmillan, Barclay, and Macmillan, 1840-1846. 8vo. Bound in recent brown full cloth with gilt letting to spine. In ""The Cambridge Mathematical Journal, Vol. 1-2, Second edition"". Light writing in pencil to title page and very light miscolouring to borders of pages, otherwise a fine and clean copy. VI, 311, (1), VIII, (2), II, 284 pp. + folded plates.‎

‎First printing of four early papers by the influential British mathematician and philosopher. As the inventor of Boolean logic-the basis of modern digital computer logic-Boole is regarded in hindsight as a founder of the field of computer science. His earliest published paper was the ""Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order."" Printed in the Cambridge Mathematical Journal in February 1840 (Volume 2, no. 8, pp. 64-73), and it led to a friendship between Boole and D.F. Gregory, the editor of the journal, which lasted until the death of the latter in 1844.In 1840 he began to contribute to the recently founded Cambridge Mathematical Journal and also to the Royal Society, which awarded him a Royal Medal in 1844 for his papers on operators in analysis"" he was elected a fellow of the Royal Society in 1857.""In papers in the Cambridge Mathematical Journal in 1841 and 1843 [The present], Boole dealt with linear transformations. The algebraic fact had been partly perceived by Lagrange and by Gauss, but Boole's argument drew attention to the (relative) invariance of the discrimiant ab - h2, and also to the absolute invariants of the transformation. This was the starting point of the theory of invariants, so rapidly and extensively developed in the second half of the nineteenth century."" (DSB)‎

书商的参考编号 : 45091

‎"BOOLE, GEORGE. (+) ARTHUR CAYLEY.‎

‎The Theory of Linear Transformations (+) On The Reduction of the General Equation of the n-th Degree (Sequel to a Memoire on the Theory of Linear Transformations) [Boole] (+) Note on Mr. Cockle's Solution of a Cubic Equation [Cayley]. - [THE VERY FIRST BOOLEAN DETERMINANT]‎

‎Cambridge, Macmillan and Co., 1851. 8vo. Bound with the original front wrapper in contemporary half calf with black and red title labels to spine with gilt lettering. In ""The Cambridge and Dublin Mathematical Journal"", Vol. VI [6], (Being Vol. X [10], of the Cambridge Mathematical Journal), 1851. Bookplate pasted on to pasted down front free end-paper and library code written in hand to lower part of spine. Library cards in the back. First two leaves detached, but present (Title page and index page). Otherwise a fine and clean copy. Pp. 87-106"" Pp. 106-141. [Entire volume: IV, 293 pp.].‎

‎First printing of these two important paper by Boole and Cayley's famous note to include the very first Boolean determinant: ""...the Hessian, or as it ought to be termed, the first Boolean Determinant"" (P. 192).‎

书商的参考编号 : 47440

‎"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.‎

书商的参考编号 : 42985

‎"BOREL, EMILE.‎

‎Sur les zéros des fonctions entieres.‎

‎[Berlin, Stockholm, Paris, Beijer, 1897]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 20. Fine and clean. Pp. 357-396.‎

‎First printing.‎

书商的参考编号 : 45851

‎"BOSSUT, (CHARLES)‎

‎Usages de la Differentiation des Parametres, pour la Solution de plusieurs Problèmes de laa méthode inverse des Tangentes.‎

‎(Paris, Imprimerie Royale, 1755). 4to. Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome II. Pp. 435-451 a. 1 folded engraved plate.‎

‎First printing of Busset's first mathematical paper.""Bossut was one of a very few whom d’Alembert took as students, and as such he was admitted as a correspondant to the Académie des Sciences on 12 May 1753" subsequently, he rose to géométre, mécanicien, and mathématicien. In 1761, 1762, and 1765 he won or shared prizes given by the Academy for memoirs on mechanics applied to the operation of ships and on the resistance of the ether in planetary motions. He won additional prizes for his mechanics memoirs from the academies of Lyons and Toulouse, and was elected to the scientific academies of Bologna, Turin, and St. Petersburg. In 1775 he participated with d’Alembert and Condorcet in a well known series of experiments on fluid resistance. Never more than a minor mathematician or physicist, Bossut is nevertheless one of the important figures in the history of physics and engineering education. (DSB).‎

书商的参考编号 : 45595

‎"BOSSUT, (CHARLES).‎

‎Recherches de Dynamique.‎

‎(Paris, Imprimerie Royale, 1760). 4to. Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome III. Pp. 473-500 a. 3 folded engraved plates.‎

‎First printing of one of Busset's major papers on mathematical physics.""Bossut was one of a very few whom d’Alembert took as students, and as such he was admitted as a correspondant to the Académie des Sciences on 12 May 1753" subsequently, he rose to géométre, mécanicien, and mathématicien. In 1761, 1762, and 1765 he won or shared prizes given by the Academy for memoirs on mechanics applied to the operation of ships and on the resistance of the ether in planetary motions. He won additional prizes for his mechanics memoirs from the academies of Lyons and Toulouse, and was elected to the scientific academies of Bologna, Turin, and St. Petersburg. In 1775 he participated with d’Alembert and Condorcet in a well known series of experiments on fluid resistance. Never more than a minor mathematician or physicist, Bossut is nevertheless one of the important figures in the history of physics and engineering education. (DSB).‎

书商的参考编号 : 45589

‎"BRACONNIER, JEAN.‎

‎L'analyse harmonique dans les groupes abeliens. [Monographies de l""Enseignment mathematique, No 5].‎

‎Geneve, L'Enseignement Mathematique, (1956). 8vo. Original light blue wrappers. 48, (2) pp. Slight miscolouring to wrapper, otherwise a nice and clean copy.‎

书商的参考编号 : 42865

‎"BRILL, ALEXANDER VON (+) MAX NOETHER.‎

‎Ueber die algebraischen Functionen und ihre Anwendung in der Geometrie. - [THE BRILL-NOETHER THEORY]‎

‎Leipzig, B. G. Teubner, 1874. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 7., 1874. 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. Title-page and index-page with nicks and repairs. Otherwise fine and clean. Pp. 269-316. [Entire volume: IV, 638 pp.].‎

‎First printing of this important paper in which the Brill-Noether theory was presented for the first time. In the theory of algebraic curves, Brill-Noether theory, is the study of special divisors, certain divisors on a curve C that determine more compatible functions than would be predicted. In classical language, special divisors move on the curve in a ""larger than expected"" linear system of divisors.‎

书商的参考编号 : 47190

‎"BRILL, ALEXANDER WILHELM VON.‎

‎Ueber die Discriminante (+) Ueber rationale Curven vierter Ordnung. (Mit Zwei Lithographirten).‎

‎Leipzig, B. G. Teubner, 1877. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 12., 1877. 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. Very fine and clean. Pp. 87-89" Pp. 90-122. [Entire volume: IV, 576 pp.].‎

‎First printing of Brill's paper which was of seminal importance in the development of the discriminant of an algebraic number field.The definition of the discriminant of a general algebraic number field, K, was given by Dedekind in 1871. Hermite's theorem predates the general definition of the discriminant with Charles Hermite publishing a proof of it in 1857. In 1877, Alexander von Brill determined the sign of the discriminant.The present volume contain several other papers by influential contemporary mathematicians.‎

书商的参考编号 : 47157