Gotlob FREGE Grundgesetze der Arithmetik. Begriffsschriftlich abgeleitet, I-II [all published].

 

Grundgesetze der Arithmetik. Begriffsschriftlich abgeleitet, I-II [all published].

FREGE, Gotlob.

 

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Titre : Grundgesetze der Arithmetik. ...

Éditeur : Hermann Pohle 1893-1903, Jena

Date d'édition : 1893

Edition : First edition

Description :

A fine copy of Frege’s magnum opus, from the library of American philosopher Paul Weiss. "The climax of Frege's career as a philospher should have been the publication of the two volumes of ‘Die Grundgesetze der Arithmetik’ (1893-1903), in which he set out to present in formal manner the logicist construction of arithmetic on the basis of pure logic and set theory. This work was to execute the task which had been sketched in the earlier books on the philosophy of mathematics: it was to enunciate a set of axioms which would be recognizably truths of logic, to propound a set of undoubtedly sound rules of inference, and then to present, one by one, derivations by these rules from these axioms of standard truths of arithmetic. The magnificent project aborted before it was ever completed. The first volume was published in 1893; the second volume did not appear until 1903 and while it was in the press Frege received a letter from Russell pointing out that the fifth of the initial axioms made the whole system inconsistent. This was the axiom which, in Frege's words, allowed 'the transition from a concept to its extension', the transition which was essential if it was to be established that numbers were logical objects. Frege’s system, with this axiom, permitted the formation of the class of all classes that are not members of themselves. But the formation of such a class, Russell pointed out, leads to paradox: if it is a member of itself then it is not a member of itself; if it is not a member of itself, then it is a member of itself. A system which leads to such paradox cannot be logically sound. With good reason, Frege was utterly downcast by this discovery, though he strove to patch his system by weakening the guilty axiom. We now know that his logicist programme cannot ever be successfully carried out. The path from the axioms of logic to the theorems of arithmetic is barred at two points. First, as Russell's paradox showed, the naive set theory which was part of Frege’s logical basis was inconsistent in itself, and the remedies which Frege proposed for this proved ineffective. Thus, the axioms of arithmetic cannot be derived from purely logical axioms in the way he hoped. Secondly, the notion of 'axioms of arithmetic' was itself latter called in question when Gödel showed that it was impossible to give arithmetic a complete and consistent axiomatization. None the less, the concepts and insights developed by Frege in the course of expounding his logicist thesis have a permanent interest which is unimpaired by the defeat of that programme at the hands of Russel and Gödel". (The Oxford Companion to Philosophy). Provenance: with the signature of Paul Weiss to the front free end paper. The American philosopher Paul Weiss (1901-2002) who taught at Bryn Mawr and Yale, co-edited (with Charles Hartshorne) the first six volumes of The Collected Papers of Charles Sanders Peirce (Harvard University Press, 1931-1935), and in 1947 founded the Metaphysical Society of America and its academic journal, Review of Metaphysics, serving as the journal’s editor until 1964. Two volumes. Large 8vo: 246 x 163 mm. The two volumes bound together in early twentieth century dark blue cloth with paper spine label, a fine and clean copy. XXXII, 253, (1); (2:blank),xv, (1), 265, (1) pp. N° de réf. du libraire 2309

 

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Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling. Herausgegeben von Karl Menger. Heft 1-7 GÖDEL, Kurt

 

Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling. Herausgegeben von Karl Menger. Heft 1-7

GÖDEL, Kurt.

 

Description :

An absolutely mint set, in the original wrappers, of these rare proceedings to which Gödel contributed fifteen important papers and remarks on the foundations of logic and mathematics. "By invitation, in October 1929 Gödel began attending Menger’s mathematics colloquium, which was modeled on the Vienna Circle. There in May 1930 he presented his dissertation results, which he had discussed with Alfred Tarski three months earlier, during the latter’s visit to Vienna. From 1932 to 1936 he published numerous short articles in the proceedings of that colloquium (including his only collaborative work) and was coeditor of seven of its volumes. Gödel attended the colloquium quite regularly and participated actively in many discussions, confining his comments to brief remarks that were always stated with the greatest precision." (D.S.B. XVII: 350). The papers are: (1) Ein Spezialfall des Entscheidungsproblems der theoretischen Logik, vol. 2, pp. 27-28; (2) Über Vollständigkeit und Widerspruchsfreiheit, vol. 3, pp. 12-13; (3) Eine Eigenschaft der Realisierungen des Aussagenkalküls, vol. 3, pp. 20-21; (4) Untitled remark following W. T. Parry Ein Axiomensystem für eine neue Art von Implikation (analytische Implikation), vol. 4, p. 6; (5) Über Unabhängigkeitsbeweise im Aussagenkalkül, vol. 4, pp. 9-10; (6) Über die metrische Einbettbarkeit der Quadrupel des R3 in Kugelflächen, vol. 4, pp. 16-17; (7) Über die Waldsche Axiomatik des Zwischenbegriffes, vol. 4), pp. 17-18; (8) Zur Axiomatik der elementargeometrischen Verknüpfungsrelationen, vol. 4, p. 34; (9) Zur intuitionistischen Arithmetik und Zahlentheorie, vol. 4, pp. 34-38; (10) Eine Interpretation des intuitionistischen Aussagenkalküls, vol. 4, pp. 39-40; (11) Reprint of Zum intuitionistischen Aussagenkalkül [Anzeiger der Akademie der Wissenschaften in Wien, vol. 69,1932, pp. 65-66], vol. 4, p. 40; (12) Bemerkung über projektive Abbildungen, vol. 5, p. 1; (13) Diskussion über koordinatenlose Differentialgeometrie (with K. Menger and A. Wald), vol. 5, pp. 25-26; (14) Über die Produktionsgleichungen der ökonomischen Wertlehre, vol. 7, p. 6; (15) Über die Länge von Beweisen, vol. 7, pp. 23-24. John Dawson in his Annotated Bibliography of Gödel has the following summaries of these papers: (1) This undated contribution was not presented to a regular meeting of the colloquium, but appeared among the Gesammelte Mitteilungen for 1929/30. In the context of the first-order predicate calculus without equality, Gödel describes an effective procedure for deciding whether or not a formula with prenex form (3x1.xn)(y1y2)(3z1.zn)A(xi,yi,zi) is satisfiable; the procedure is related to the method used in [his dissertation Die Vollstandigkeit der Axiome des logischen Funktionenkalküls] to establish the completeness theorem; (2) Closely related to [Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, 1931], [this paper] notes extensions of the incompleteness theorems to a wider class of formal systems. The system considered in [his 1931 paper] is based on Principia Mathematica and allows variables of all finite types. Here Gödel observes that any finitely-axiomatizable, omega-consistent formal system S with just substitution and implication (modus ponens) as rules of inference will possess undecidable propositions whenever S extends the theory Z of first-order Peano arithmetic plus the schema of definition by recursion; and indeed, that the same is true of infinite axiomatizations so long as the class of Gödel numbers of axioms, together with the relation of immediate consequence under the rules of inference, is definable and decidable in Z; (3) In answer to a question of Menger, Gödel shows that given an arbitrary realization of the axioms of the propositional calculus in a structure with operations interpreting the connectives ~ and ?, the elements of the structure can always be partitioned into two disjoint classes behaving exactly like the classes of true and false pro. N° de réf. du libraire 2713

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On Computable Numbers, with an Application to the Entscheidungsproblem. TURING, Alan Mathison.

 

On Computable Numbers, with an Application to the Entscheidungsproblem.

TURING, Alan Mathison.

 

Détails bibliographiques

 

Titre : On Computable Numbers, with an Application ...

Éditeur : C.F. Hodgson & Son 1936-1937, London

Date d'édition : 1936

Edition : First edition

Description :

A fine set, not ex-library, of arguably the single most important theoretical work in the history of computing. In this paper Turing introduced the concept of a ‘universal machine’, an imaginary computing device designed to replicate the mathematical ‘states of mind’ and symbol-manipulating abilities of a human computer. Turing conceived of the universal machine as a means of answering the last of the three questions about mathematics posed by David Hilbert in 1928: (1) is mathematics complete; (2) is mathematics consistent; and (3) is mathematics decidable. Hilbert's final question, known as the ‘Entscheidungsproblem’, is concerned with whether there exists a definite method, or ‘mechanical process’, that can be applied to any mathematical assertion, and which is guaranteed to produce a correct decision as to whether that assertion is true or not. The logician Kurt Gödel had already in 1931 shown that arithmetic (and by extension mathematics) could not be both consistent and complete. Turing showed, by means of his universal machine, mathematics is undecidable. To demonstrate this, Turing came up with the concept of ‘computable numbers’, which are numbers defined by some definite rule, and thus calculable on the universal machine. These computable numbers would include every number that could be arrived at through arithmetical operations, finding roots of equations, and using mathematical functions like sines and logarithms - every number that could possibly arise in computational mathematics. Turing then showed that these computable numbers could in turn give rise to uncomputable ones, ones that could not be calculated using a definite rule, and that therefore there could be no ‘mechanical process’ for solving all mathematical questions, since computing an uncomputable number was an example of an unsolvable problem. Turing's idea of a ‘universal machine’ was given the name "Turing machine" by Church. The concept of the Turing machine has become the foundation of modern computer science. Origins of Cyberspace 394. Richard Green Library (Christie's sale 2013, lot 326). Erwin Thomas Library T61 and T62. In: Proceedings of the London Mathematical Society, Vol.42: pp.230-265 and Vol.43: pp.544-546 ("A Correction"). The complete volumes offered in near contemporary cloth with gilt spine lettering, completely clean and fresh throughout - a fine set. N° de réf. du libraire 2091

Luigi Ambrosio/ Yann Brenier/ Giuseppe Buttazzo/ Cedric Villani Optimal Transportation and Applications: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2-8, 2001 (Lecture Notes in Mathematics / Fondazione C.I.M.E., F

Optimal Transportation and Applications: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2-8, 2001 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze)

(ISBN 10: 354040192X / ISBN 13: 9783540401926 )

Luigi Ambrosio/ Yann Brenier/ Giuseppe Buttazzo/ Cedric Villani

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1st edition. 171 pages. 9.00x6.00x0.50 inches. In Stock. N° de réf. du libraire __354040192X

 

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Rezakhanlou, Fraydoun; Villani, Cédric Entropy Methods for the Boltzmann Equation: Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 (Lecture Notes in Mathematics)

Entropy Methods for the Boltzmann Equation: Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 (Lecture Notes in Mathematics)

(ISBN 10: 3540737049 / ISBN 13: 9783540737049 )

Rezakhanlou, Fraydoun; Villani, Cédric

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N° de réf. du libraire GQ30155

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Richard Dedekind et les fondements des mathématiques Dugac, Pierre

 

Richard Dedekind et les fondements des mathématiques

Dugac, Pierre

 

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Book Condition: NEAR FINE, very slight shelf wear, otherwise FINE, clean and unmarked throughout. 334 pp. N° de réf. du libraire 001819

 

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Georg Cantor Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind., Herausgegeben von Ernst Zermelo. Nebst einem Lebenslauf Cantors von Adolf Fraenkel.

Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind., Herausgegeben von Ernst Zermelo. Nebst einem Lebenslauf Cantors von Adolf Fraenkel.

Cantor, Georg.

Description :

VII, 486 S. mit einem Bildnis, Reprografischer Nachdruck der Ausgage Berlin 1932. Sprache: de Gewicht in Gramm: 920 Groß 8°, Original-Leinen (Hardcover), Bibliotheks-Exemplar (ordnungsgemäß entwidmet), Stempel auf Titel, insgesamt sehr gutes und innen sauberes Exemplar, N° de réf. du libraire 62362

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Kurt Gödel The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis" [and] "Consistency-Proof for the Generalized Continuum-Hypothesis" [and] "The Independence of the Continuum Hypothesis, I-II"

 

 

The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis" [and] "Consistency-Proof for the Generalized Continuum-Hypothesis" [and] "The Independence of the Continuum Hypothesis, I-II" (in Proceedings of the National Academy of Sciences, Volume 24 (1938), pp.556-557 and Volume 25 (1939), 220-224. Mack Printing Company

Kurt Gödel

 

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Titre : The Consistency of the Axiom of Choice and ...

Reliure : Hardcover

Etat du livre : Very Good

Edition : 1st Edition

Description :

TWO MILESTONE PAPERS ON THE FOUNDATIONS OF MATHEMATICS. Two volume first edition of Kurt Gödel's proof of the consistency of the axiom of choice and the generalized continuum hypothesis with the axiom of set theory. In 1878, German mathematician Georg Cantor put forth a hypothesis that said any infinite subset of the set of all real numbers can be put into one-to-one correspondence either with the set of integers or with the set of all real numbers ("There is no set whose cardinality is strictly between that of the integers and that of the real numbers"). The continuum problem, as Cantor's problem came to be know, was the first in Hilbert's famous list of mathematical problems, presented in an address in 1900. All attempts to prove or disprove Cantor's conjecture failed until 1938, when Kurt Gödel, in these papers, showed it was impossible to disprove the continuum hypothesis. "Gödel studied the relationship of the continuum hypothesis and the axiom of choice to basic set theory as formulated by the mathematicians Ernst Zermelo and Abraham Fraenkel. In 1940 Gödel showed that both the continuum hypothesis and the axiom of choice are consistent with the axioms of set theory. More precisely, he demonstrated that if the Zermelo-Fraenkel system without the axiom of choice is consistent, then the Zermelo-Fraenkel system with the axiom of choice is consistent, and that the continuum hypothesis is consistent with the Zermelo-Fraenkel system" (Ryan, Thinkers of the Twentieth Century, p. 212f). "Godel's result, joined to [Paul J.] Cohen's (1963-1964), set the stage for a whole new era in the theory of sets in which a host of problems of the consistency or independence of various conjectures in set theory relative to this or that set of axioms are being investigated by constructing models" (Shanker, Godel's Theorem in Focus, 66-67). CONDITION & DETAILS: 4to (10 x 7 inches). Both volumes handsomely rebound in aged brown cloth (identical to original binding). Gilt-lettered and dated at the spine. Solidly and tightly bound, with both volumes set into a gilt-titled brown slipcase. New endpapers. Very good to near fine condition in every way. N° de réf. du libraire 90

 

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LIVRE ANCIEN 1637 Discours de la methode pour bien conduire sa raison, & chercher la verité dans les sciences. Plus la Dioptrique, les Meteores, et la Geometrie. Qui sont des essais de cete Methode. DESCARTES, René.

Discours de la methode pour bien conduire sa raison, & chercher la verité dans les sciences. Plus la Dioptrique, les Meteores, et la Geometrie. Qui sont des essais de cete Methode.

DESCARTES, René.

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Titre : Discours de la methode pour bien conduire sa...

Éditeur : Jan Maire, Leiden

Date d'édition : 1637

Edition : First edition

Description :

A very fine and exceptionally large copy, entirely unrestored, in its original Dutch vellum binding - the birth of analytical or co-ordinate geometry, designated by John Stuart Mill as "the greatest single step ever made in the progress of the exact sciences". PMM 129; Grolier/Horblit 24; Dibner 81; Evans 5; Sparrow 54."It is no exaggeration to say that Descartes was the first of modern philosophers and one of the first modern scientists; in both branches of learning his influence has been vast. . The revolution he caused can be most easily found in his reassertion of the principle (lost in the middle ages) that knowledge, if it is to have any value, must be intelligence and not erudition. His application of modern algebraic arithmetic to ancient geometry created the analytical geometry which is the basis of the post-Euclidean development of that science. His statement of the elementary laws of matter and movement in the physical universe, the theory of vortices, and many other speculations threw light on every branch of science from optics to biology. Not least may be remarked his discussion of Harvey’s discovery of the circulation of blood, the first mention of it by a prominent foreign scholar. All this found its starting point in the ‘Discourse on the Method for Proper Reasoning and Investigating Truth in the Sciences’. Descartes’s purpose is to find the simple indestructible proposition which gives to the universe and thought their order and system. Three points are made: the truth of thought, when thought is true to itself (thus cogito, ergo, sum), the inevitable elevation of its partial state in our finite consciousness to its full state in the infinite existence of God, and the ultimate reduction of the material universe to extension and local movement." (Printing and the Mind of Man). 4to (203 x 158 mm), pp 78; [2] 413 [1]; [34], original Dutch vellum, gilt fillet on the covers, back cover with stains, flat spine decorated with gilt fillets, green fabric ties. A fine and very large copy. N° de réf. du libraire 2849

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Disquisitiones Arithmeticae. GAUSS, Carl Friedrich

 

Disquisitiones Arithmeticae.

GAUSS, Carl Friedrich

 

Description :

An outstanding copy of Gauss’ masterpiece which created a new epoch in the history of mathematics; entirely untouched in the original interim wrappers and the copy of Polish mathematician and astronomer Jan Sniadecki who collaborated with Gauss on the observation of the planetoid Ceres which led Gauss to his discovery of the method of least squares (see below). "Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics" (Printing and the Mind of Man). PMM 257; Evans 11; Horblit 38; Dibner 114. "In the late eighteenth century [number theory] consisted of a large collection of isolated results. In his Disquisitiones Gauss summarized previous work in a systematic way, solved some of the most difficult outstanding questions, and formulated concepts and questions that set the pattern of research for a century and still have significant today. He introduced congruence of integers with respect to a modulus (a = b (mod c) if c divides a-b), the first significant algebraic example of the now ubiquitous concept of equivalence relation. He proved the law of quadratic reciprocity, developed the theory of composition of quadratic forms, and completely analyzed the cyclotomic equation. The Disquisitiones almost instantly won Gauss recognition by mathematicians as their prince" (DSB). "Published when Gauss was just twenty-four, Disquisitiones arithmeticae revolutionized number theory. In this book Gauss standardized the notation; he systemized the existing theory and extended it; and he classified the problems to be studied and the known methods of attack and introduced new methods The Disquisitiones not only began the modern theory of numbers but determined the direction of work in the subject up to the present time. The typesetters of this work were unable to understand Gauss’ new and difficult mathematics, creating numerous elaborate mistakes which Gauss was unable to correct in proof. After the book was printed Gauss insisted that, in addition to an unusually lengthy four-page errata, the worst mistakes be corrected by cancel leaves to be inserted in copies before sale [as in the offered copy]. Gauss’s highly technical work was printed in a small edition, and the difficulty of understanding it was hardly alleviated by the sloppy typesetting. The few mathematicians who were able to read the Disquisitiones immediately hailed Gauss as their prince, but the full understanding required for further development until the publication in 1863 of Dirichlet’s less austere exposition in his Vorelsungen über Zahlentheorie." (Norman). Provenance: Jan Sniadecki (1756-1830) was a Polish mathematician and astronomer, and the director of the astronomical observatories at Kraków and Vilnius. He was deeply involved in the celebrated discovery of the new planetoid Ceres in 1801 and, besides publishing several works himself on this subject, corresponded directly with Gauss on the orbit of Ceres. "In 1801 the creativity of the previous years was reflected in two extraordinary achievements, the Disquisitiones arithmeticae and the calculation of the orbit of the newly discovered planet Ceres In January 1801 G. Piazzi had briefly observed and lost a new planet. During the rest of that year the astronomers vainly tried to relocate it In September, as his Disquisitiones was coming off the press, Gauss decided to take up the challenge. To it he applied both a more accurate orbit theory (based on the ellipse rather than the usual circular approximation) and improved numerical methods (based on least squares). By December the task was done, and Ceres was soon found in the predicated position. This extraordinary feat of locating a tiny, distant heavenly body from seemingly insufficient information appeared to be almost superhuman, especially since Gauss did not reveal his methods. With the Disquisitiones it established his reputation as a mathematical and scientific genius of the first order. The decade that b. N° de réf. du libraire 2941

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Lost Notebook and Other Unpublished Papers: Mathematical Works of Srinivasa Ramanujan

 

Détails bibliographiques

 

Titre : Lost Notebook and Other Unpublished Papers: ...

Éditeur : ALPHA SCIENCE

Date d'édition : 2008

Reliure : Hardcover

Etat du livre : Brand New

Description :

419 pages. 11.75x9.50x1.50 inches. In Stock. N° de réf. du libraire __1842655078

 

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LIVRE ANCIEN Elémens d'Algèbre EULER, Léonard 1795

 

Elémens d'Algèbre

EULER, Léonard

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Titre : Elémens d'Algèbre

Éditeur : Bruyset, Lyon

Date d'édition : 1795

Reliure : Couverture rigide

Etat du livre : Très bon

Description :

Pleine basane racinée de l'époque. Dos lisse, orné et doré, portant les pièces de titre et de tomaison. Roulette dorée sur les coupes. Tranches mouchetées. Deux volumes In-8 (19,5x12,5 cm) de : T1 : 1 ff. (titre), 704 pp. T2 : [9] ff., 668 pp. Reliure frottée. Coiffe de tête du premier tome manquante. Quelques cahiers présentent des rousseurs importantes. Le cahier M (pp.177 à 192) du tome 1 est manquant. N'a pas été relié à l'époque. Le faux titre et le 2° titre du tome 2 ont été relié en fin de volume Ouvrage important d'un des plus grand mathématicien du 18° siècle. Il fut traduit par Bernouilli, directeur de l'Observatoire de Berlin. "Hoefer" : Le premier volume de cet ouvrage important, qui ne porte ni le nom du traducteur, ni celui de l'annoteur, traite de l'analyse indéterminée. Le deuxième volume, consacré à l'analyse indéterminée, intègre pour la première fois, (p.371-662) les additions précieuses de Lagrange, formant un véritable traité de l'analyse l'analyse de Diophante ou Analyse indéterminée". "Second French edition; the substantial additions by Lagrange occur for the first time" (Honeyman). Honeyman [II, 1076] 1282 g. N° de réf. du libraire 147

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Oeuvres de Laplace (7 volumes) & Oeuvres complètes de Laplace (6 volumes = vol. 8-13). LAPLACE, PIERRE SIMON (1749-1827).

Oeuvres de Laplace (7 volumes) & Oeuvres complètes de Laplace (6 volumes = vol. 8-13).

LAPLACE, PIERRE SIMON (1749-1827).

 

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Titre : Oeuvres de Laplace (7 volumes) & Oeuvres ...

Éditeur : Paris, Imprimerie Royale / Gauthier-Villars et Fils, 1843.

Date d'édition : 1843

Reliure : Hardcover

Description :

- 1904. The 7 vols. edition is bound in half leather, top edges gilt and the 6 volumes (volumes 8-13 of the 14 vols. ed.) are in orig. paperbacks. Text in French - (covers of paperbacks worn and sl. dam., sl. browned) Although still very good. See image. Weight is 22 kg. Laplace's works were collected in two editions, the seven volumes of his Oeuvres of 1843-47 and the 14 volumes of his Oeuvres complètes of 1878-1912. Present here are the 7 volumes 1843-47 and volumes 8-13 of the 14 vol. edition. Together 13 volumes sold together. 22000g. N° de réf. du libraire 30431

 

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Théorie Analytique des Probabilités. LAPLACE, Pierre Simon.

 

Théorie Analytique des Probabilités.

LAPLACE, Pierre Simon.

 

Détails bibliographiques

 

Titre : Théorie Analytique des Probabilités.

Éditeur : Courcier, Paris

Date d'édition : 1812

Description :

First edition of "the most influential book on probability and statistics ever written." (Anders Hald). "Laplace’s great treatise on probability appeared in 1812, with later editions in 1814 and 1820. Its picture of probability theory was entirely different from the picture in 1750. On the philosophical side was Laplace’s interpretation of probability as rational belief, with inverse probability as its underpinning. On the mathematical side was the method of generating functions, the central limit theorem, and Laplace’s technique for evaluating posterior probabilities. On the applied side, games of chance were still evidence, but they were dominated by problems of data analysis and Bayesian methods for combining probabilities of judgments, which replaced the earlier non-Bayesian methods of Hooper and Bernoulli." (Grattan-Guiness: History and Philosophy of the Mathematical Sciences, p.1301). "In the Théorie Laplace gave a new level of mathematical foundation and development both to probability theory and to mathematical statistics. [It] emerged from a long series of slow processes and once established, loomed over the landscape for a century or more." (Stephen Stigler: Landmark Writings in Western Mathematics, p.329-30). "It was the first full–scale study completely devoted to a new specialty, [and came] to have the same sort of relation to the later development of probability that, for example, Newton’s Principia Mathematica had to the later science of mechanics." (DSB). Evans, First Editions of Epochal Achievements 12; Landmark Writings in Western Mathematics 24; Honeyman 1923. 4to: 255 x 190 mm. Contemporary half calf. Pp. [VI], 464, [2: errata and blank]. A little browning and spotting throughout (as usual with this book), old owners signature scraped from the lower right corner of the title, in all a very good copy. N° de réf. du libraire 2407

 

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In artem analyticum isagoge: eiusdem, Ad logisticem speciosam notae priores. Francisci Vieta Fontenaeensis ; recensuit, scholiisq; illustravit I.D.B[eaugrand]. VIÈTE, François.

 

In artem analyticum isagoge: eiusdem, Ad logisticem speciosam notae priores. Francisci Vieta Fontenaeensis ; recensuit, scholiisq; illustravit I.D.B[eaugrand].

VIÈTE, François.

 

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Titre : In artem analyticum isagoge: eiusdem, Ad ...

Éditeur : Guillaume Baudry, Paris

Date d'édition : 1631

Edition : First edition

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First printing of Viète’s Ad logisticem speciosam notae priores (one of his main works), together with the second edition of his In artem analyticum isagoge, "the earliest work on symbolic algebra [by] the greatest French mathematician of the sixteenth century" (PMM). The first edition of the Isagoge, published at Tours in 1591, is, together with the Lobachevsky, the rarest mathematical work in PMM, and this second edition is in fact rarer than the first in institutional collections [OCLC lists only copies in France and UK]."The ‘Introduction to the Art of Analysis’ is the earliest work on symbolic algebra. Viète’s greatest innovation in mathematics was the denoting of general or indefinite quantities by letters of the alphabet instead of abbreviations of words as used hitherto. Known quantities were represented by consonants, unknown ones by vowels; squares, cubes, etc., were not represented by new letters but by adding the words quadratus, cubus, etc. Viète also brought the + and – signs into general use. This algebraic symbolism made possible the development of analysis, with its complicated processes, a fundamental element in modern mathematics" (PMM). "This innovation, considered one of the most significant advances in the history of mathematics, prepared the way for the development of algebra" (DSB). "To the treatises of the Isagoge belong Ad logisticen speciosam notae priores and Ad logisticen speciosam notae posteriores, the latter now lost. The first was not published during his lifetime, because Viète believed that the manuscript was not yet suitable for publication. (It was published by Jean Beaugrand in 1631.) It represents a collection of elementary general algebraic formulas that correspond to the arithmetical propositions of the second and ninth books of Euclid’s Elements, as well as some interesting propositions that combine algebra with geometry. In propositions 48-51 Viète derives the formulas for sin 2x; cos 2x; sin 3x; cos 3x; sin 4x; cos 4x; sin 5x; cos 5x expressed in terms of sin x and cos x by applying proposition 46. He remarks, that the coefficients are equal to those in the [binomial] expansion., that the various terms must be ‘homogeneous’ and that the signs are alternately + and –" (DSB). The editor, Jean Beaugrand (ca. 1590-1640) "studied under Viète and became mathematician to Gaston of Orléans in 1630; in that year J. L. Vaulezard dedicated his Cinq livres des Zététiques de FR. Viette to Beaugrand, who had already achieved a certain notoriety from having published Viète’s In artem analyticam isagoge, with scholia and a mathematical compendium, in 1631. Some of the scholia were incorporated into Schooten’s edition of [Viète’s Opera Mathematica of] 1646" (DSB, under Beaugrand). Beaugrand was an early friend of Fermat and became his official Paris correspondent, before being replaced in that role by Carcavi. He also communicated some of Fermat’s results to Castelli, Cavalieri and Galileo, all of whom seem to have been impressed by his mathematical ability. In France he became involved in several polemics: against Desargues, claiming that the main proposition of the Brouillon projet was nothing but a corollary to a proposition in Apollonius; and against Descartes, claiming that his Géométrie was plagiarized from Harriot, and that Viète’s methods were in any case superior. OCLC: BNF and Glasgow only; COPAC adds Oxford, UCL and University of London Senate House (for comparison OCLC lists some 15 copies of the 1591 edition). PMM 103 (1591 edition). 12mo (108 x 57 mm), pp [12] 99 [1:errata]; [2] 99, 200-233 [2] [1:blank], although the pagination jumps from 99 to 200 the signatures are continuous (i.e., i2-i3), fine contemporary limp vellum with gilt decoration to front and rear boards, manuscript paper label to spine, two very small paper flaws to the first title, otherwise very fine and clean throughout. N° de réf. du libraire 2885

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