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COURNOT, Augustin.
Recherches sur les principes mathématiques de la théorie des richesses.
Paris, L. Hachette, 1838.
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12500 €
First edition.
Landmark in economic theory.
Cournot is considered a pioneer in mathematical economics. He was among the first to formalize economic theories using mathematical equations.
He proposed basing economic theory not on elementary algebra but on the branch of analysis dealing with arbitrary functions, subject to certain conditions.
His work focused on a theory of price equilibrium in a free market.
Though largely ignored in his time, his research on equilibria between two producers, now known as "Cournot equilibria," would later be generalized under the term "Nash equilibria" or "Nash-Cournot equilibria," earning John Forbes Nash the Nobel Prize in Economics in 1994.
Cournot's work is bound after the following:
URBAIN, Introduction to the Study of Political Economy, Paris, Bossange Père, 1833.
VIETE, François.
Opera mathematica in unum volumen congesta ac recognita, opera atque studio Francisci a Schooten.
Leyde, ex officina Bonaventura Abraham Elzeviriorum, 1646.
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9500 €
First collective edition of the works of François Viète.
François Viète, a 16th-century French mathematician born in Fontenay-le-Comte in 1540 and died in Paris in 1603, is often hailed as the father of modern algebra.
Indeed, Viète was one of the first mathematicians in Europe to note the parameters of an equation using symbols. His innovative approach and contribution to algebraic notation was particularly influential and opened new ways for solving mathematical problems. In recognition of his contributions, Viète is widely considered one of the greatest mathematicians of his time and his legacy endures in the field of modern mathematics to this day.
This first collective edition features sixteen of Viète's works, including his seminal 'Isagoge in artem analyticam', which introduced his innovative algebraic notation.
GALOIS, Évariste.
Oeuvres mathématiques d'Évariste Galois. In Journal de Mathématiques pures et appliquées ou Recueil mensuel de mémoires sur les diverses parties des mathématiques, Année 1846, Tome XI.
Paris, Bachelier, 1846.
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6500 €
First edition of collected mathematical works of Evariste Galois given by Liouville in this volume of the Journal de Mathématiques pures et appliquées .
A brilliant mathematician, misunderstood in his day and with a tragic fate (he died at the age of 20 in a gallant duel), Galois created the notion of group, and his work has inspired generations of mathematicians.
A brilliant student, he was misunderstood by his contemporaries. Poisson rejected the work he wanted to present to the Paris Academy of Sciences.
In 1832, on the eve of his fatal duel, Galois wrote his mathematical will, which he entrusted to a friend.
It was not until 1846 that Liouville published them in this volume of the Journal des mathématiques, and not until 1870 that Jordan recognized their importance.
"When, yielding to the wish of Evariste's friends, I gave myself up, as it were under the eyes of his brother, to the attentive study of all the printed or manuscript pieces he left behind, I therefore thought I had to propose as my sole aim to seek out, to unravel, to then bring out as best I could, what was new in these productions.
My zeal was soon rewarded, and I was delighted when, after filling in a few small gaps, I recognized the complete accuracy of the method by which Galois proves, in particular, this beautiful theorem: For an irreducible equation of prime degree to be solvable by radicals, it is necessary and sufficient that all the roots be rational functions of any two of them.
This method, truly worthy of the attention of geometers, would alone suffice to secure our compatriot a place among the small number of scientists who have earned the title of inventor." (Liouville p.382).
SAVARY, Jacques.
Le Parfait Négociant ou instruction générale pour ce qui regarde le commerce.
Paris, Jean Guignard, 1675.
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3500 €
First edition.
A famous merchant born in 1622 in Doué (Anjou) from a noble family, Savary became a wealthy merchant and retired from business at the age of 36. He was chosen by Colbert to be one of the writers of the commercial code of 1673 which was called "Code Savary". He wrote in 1675 the "Perfect trader" which is the compilation of the knowledge he had gathered for the drafting of the ordinance. The legal solutions are clear, sensible, practical, honest. The book is a business bible whose importance Max Weber underlined. This work became a classic, reprinted many times and translated into German, English and Italian.
MACLAURIN, Colin.
Traité des fluxions.
Paris, Charles-Antoine Jombert, 1749.
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3500 €
First french edition.
Mathematical defense of Newton's work against the Berkeley attacks, Maclaurin also proposes there a particular use of the Taylor theorem which is since called Taylor-Maclaurin formula and the first test of convergence of an infinite series.
MILLIET DECHALES, Claude François.
Cursus seu Mundus Mathematicus.
Lyon, ex officina Anissoniana, 1674.
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3000 €
First edition of the most important work of Milliet Dechalles.
Complete Mathematics course, which also covers other topics sciences (mechanical, architecture, optics, perspective, astronomy, ..).
We usually meet the second edition published in 1690 in four volumes.
This first edition, complete in three volumes is quite rare.
NEWTON, Isaac.
La Méthode des fluxions et des suites infinies.
Paris, De Bure l'ainé, 1740.
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2500 €
First french edition.
Buffon's translation of Method of Fluxions and Infinite Series published a few years earlier. It is one of the last treatises on which Newton worked to explain the method of calculation used in his Principia. The fluxion method is the Newtonian solution of differential calculus problems. It is the counterpart of the method of infinitely small developed by Leibniz.
The fluxion method places Newton among the fathers of infinitesimal calculus.
PASCAL, Blaise.
Oeuvres de Blaise Pascal.
La Haye [Paris], Detune, 1779.
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2500 €
The first and sole ancient collective edition, partially original.
Published by Bossut, this edition is illustrated with a portrait and 14 plates.
Among the unpublished there are many "pensée", writings on Grace, the Treaty of vacuum and and extensive correspondence.
Volumes IV and V contain the scientific works.
We found the second printing of the describing of invention of the computing machine of Descartes (TIV, pages 7-30). The first edition, certainly printed by the author, is unobtainable (only two copies known).
Also of interest here is the reprint of Pascal's 1654 paper introducing his triangle of binominal coefficients (Pascal's Triangle), included in Volume V, pages 1-54. Pascal's invention "predated the concepts of computation of the values of polynomial functions by differences.".
GROLLIER DE SERVIÈRE, Gaspard.
Recueil d'ouvrages curieux de mathématique et de mécanique, ou description du cabinet de Monsieur Grollier de Servière avec des figures en taille douce.
Lyon, David Forey, 1719.
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2200 €
First edition.
Among the mechanical inventions depicted in Grollier de Serviere's Cabinet are those for propelling ships, making elevations, various kinds of clocks, lamps, mechanical figures, mills, optical contrivances and geometrical instruments.
AGNESI, Maria Gaetana.
Traités élémentaires de calcul différentiel et de calcul intégral. Traduits de l'italien de Mademoiselle Agnesi, avec des additions.
Paris, Claude-Antoine Jombert, 1775.
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2000 €
First edition in french.
Agnesi is according to DSB : "the first woman in the Western world who can accurately be called a mathematician".
Rare treatise on algebra and analysis which met a great success.
It was considered as the clearest, the more methodical and the most comprehensive work on the subject.
OZANAM, Jacques.
Récréations Mathématiques et Physiques, qui contiennent plusieurs Problêmes d'Arithmétique, de Géometrie, d'Optique, de Gnomonique, de Cosmographie, de Méchanique, de Pyrotechnique, & de Physique. Avec un Traité nouveau des Horloges Elémentaires.
Paris, Jean Jombert, 1694.
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2000 €
Rare first edition and the first work on "Recreational Mathematics".
NEWTON, Isaac.
La Méthode des fluxions et des suites infinies.
Paris, De Bure l'ainé, 1740.
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2000 €
First french edition.
Buffon's translation of Method of Fluxions and Infinite Series published a few years earlier. It is one of the last treatises on which Newton worked to explain the method of calculation used in his Principia. The fluxion method is the Newtonian solution of differential calculus problems. It is the counterpart of the method of infinitely small developed by Leibniz.
The fluxion method places Newton among the fathers of infinitesimal calculus.
CLAVIUS, Christoph.
Epitome arithmeticae practica.
Roma, Dominici Basae, 1583.
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1800 €
First edition of this work which is known to have influenced Descartes and Leibniz.
POINCARE, Henri || HILBERT, David || HERTZ, Heinrich.
Acta Mathematica.
Stockholm, F et G Beijer, 1887-1900.
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1500 €
First edition.
Set of eleven volumes of the famous Acta mathematica in which the greatest mathematicians published their research in their languages. Among the illustrious contributors we will note 7 articles by Henri Poincaré, 2 articles by David Hilbert, 1 article by Hertz, 3 articles by Tchebycheff and numerous articles from the French school following Emile Borel.
Non-exhaustive list of articles:
POINCARÉ, H. L'oeuvre mathématique de Weierstrass..........
POINCARÉ, H. Sur les propriétés du potentiel et sur les fonctions Abéliennes
POINCARÉ, H. Sur une forme nouvelle des équations du problème des trois corps...
POINCARÉ, H. Sur les rapports de l'analyse pure et de la physique mathématique
POINCARE, H. La méthode de Neumaun et le problème de Dirichlet
POINCARE, H. Sur la polarisation par diffraction
POINCARÉ, H. Sur la polarisation par diffraction. (Seconde
Partie)
HILBERT, DAVID. Ein Beitrag zur Theorie des Legendre'schen Polynoms
HILBERT, D. und HURWITZ, A. Über die diophantischen Gleichungen vom Geschlecht Null
HERTZ, H. Sur les équations fondamentales de l'électrodynamique pour les corps en mouvement
TCHEBYCHEFF, P. Sur deux théorèmes relatifs aux probabilités
TCHEBYCHEFF, P. Sur les résidus intégraux qui donnent des valeurs approchées des intégrales.
TCHEBYCHEW, P. Angenäherte Darstellung der Kvadrat- wurzel einer Veränderlichen mittelst einfacher Brüche. Aus dem Rus sischen übersetzt von O. Backlund....
BOREL, ÉMILE. Sur les séries de Taylor 243 248
d'OCAGNE, MAURICE. Théorie des équations représentables par trois systèmes linéaires de points cotés
COUSIN, PIERRE. Sur les fonctions den variables complexes
GOURSAT, E. Sur une classe d'équations aux dérivées partielles du second ordre, et sur la théorie des intégrales intermédiaires
LECORNU, LÉON. Mémoire sur le pendule de longueur variable
LIOUVILLE, R. Sur les équations de la dynamique
BOREL, EMILE. Sur les zéros des fonctions entières..........
HADAMARD, J. Mémoire sur l'élimination
LIOUVILLE, R. Sur le mouvement d'un corps solide pesant suspendu par l'un de ses points
PINCHERLE, 8. Sur la génération des systèmes récurrents au moyen d'une équation linéaire différentielle.
HADAMARD, J. Sur les caractères de convergence des séries à termes positifs et sur les fonctions indéfiniment croissantes
HADAMARD, J. Note additionnelle à l'article Sur les caractères de convergence des séries à termes positifs et sur les fonctions indéfiniment croissantess
PICARD, E. Sur une classe de transcendantes nouvelles. (Pre- mier mémoire)........
GOURSAT, É. Sur un mode de transformation des surfaces minima
GOURSAT, É. Sur un mode de transformation des surfaces mi- nima (second mémoire)
PICARD, É. Démonstration d'un théorème générale sur les fonctions uniformes liées par une relation algébrique...
PICARD, E. Sur une classe d'équations linéaires aux dérivées partielles du second ordre..
PICARD, EMILE. Sur une classe de transcendantes nouvelles (second mémoire).
CAUCHY, Augustin Louis.
Résumés analytiques.
Turin, Imprimerie royale, 1833.
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1500 €
First edition.
Publication of Cauchy while he was in exile in Turin, his opposition to the July Monarchy having in effect closed him access to teaching posts in France.
He summarizes here his courses in algebraic analysis.
LA HIRE, Philippe De.
Nouveaux élémens des sections coniques, les lieux géométriques, la construction, ou effection des équations.
Paris, André Pralard, 1679.
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1500 €
First edition.
Philippe de La Hire (1640-1718) is a French mathematician, he is the successor of Desargues and Pascal in the geometry of conics, in that he deduces the properties of conics from the properties of the circle.
La Hire innovates compared to his two predecessors, in that he exploits to the maximum the properties of invariance of harmonic division, which allows him to reason almost exclusively in the plane (and not in space).
This approach leads him to develop the notions of poles and polars, homology, orthoptic locus, etc.
MONTUCLA, Jean Etienne.
Histoire des Mathématiques, dans laquelle on rend compte de leur progrès depuis leur origine jusqu'à nos jours; où l'on expose le tableau et le développement des principales découvertes dans toutes les parties des Mathématiques, les contestations qui se sont élevées entre les Mathématiciens, et les principaux traits de la vie des plus célèbres.
Paris, Henri Agasse, 1799-1802.
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1500 €
Most complete edition in 4 volumes.
The first edition was published in 2 volumes, Montucla was to complete it with a third but died before its publication. It is Jérôme De La Lande who will finally publish the last two volumes according to Montucla's notes.
A reference on the history of mathematics.
PASCAL, Blaise.
Oeuvres de Blaise Pascal.
La Haye [Paris], Detune, 1779.
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1500 €
First and only old collective edition,
Published by Bossut, this edition is illustrated with a portrait and 14 plates.
Among the unpublished there are many "pensée", writings on Grace, the Treaty of vacuum and and extensive correspondence.
Volumes IV and V contain the scientific works.
We found the second printing of the describing of invention of the computing machine of Descartes (TIV, pages 7-30). The first edition, certainly printed by the author, is unobtainable (only two copies known).
Also of interest here is the reprint of Pascal's 1654 paper introducing his triangle of binominal coefficients (Pascal's Triangle), included in Volume V, pages 1-54. Pascal's invention "predated the concepts of computation of the values of polynomial functions by differences.".
GAUTHIER, Mr.
Collections mathématiques.
s.l., s.n., 1806-1807.
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1500 €
Fine copy.
LEURECHON, Jean.
Récréation mathématicque composée de plusieurs problèmes plaisants et facétieux en faict d'Arithméticque, Géometrie, Méchanicque, Opticque, et autres parties de ces belles sciences.
Lyon, Claude Rigaud & Claude Obert, 1627.
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1450 €
The very rare first Lyons edition of this work on physics
récréation which was published for the first time at Pont-à-Mousson in 1624 and reprinted several times.
PRESTET, Jean.
Nouveaux elemens des mathematiques ou principes generaux de toutes les sciences qui ont les grandeurs pour objet.
Paris, André Pralard, 1689.
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1200 €
Second enlarged edition.
This edition is important because Prestet gives (Volume 1 p.140 to p.150) for the first time his some early work on the fundamental theorem of arithmetic.
L’HOSPITAL, Guillaume (Marquis de).
Traité analytique des sections coniques et de leur usage pour la résolution des équations dans les problèmes tant déterminez qu’indéterminez.
Paris, Jean Boudot, 1707.
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1200 €
First edition.
Treatise on conic sections, which he treats both by geometric and analytical methods (equations of the form ax2 bx2 cxy dx ey f = 0) and which was very successful. Finalized in 1699, it was not published until after his death at the request of Fontenelle, then secretary of the Royal Academy.
MÖBIUS, August Ferdinand.
Der barycentrische Calcul, ein neues Hülfsmittel zur analytischen Behandlung der Geometrie.
Leibzig, Barth, 1827.
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1200 €
First edition of the most important work of Möbius.
LACROIX, Sylvestre Francois.
Traité du calcul differentiel et du calcul integral.
Paris, J.B.M. Duprat, 1797-1798-1800.
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Sold
First edition.
Rare with the third volume, published separatly, under the title "Traité des différences et des séries" and that will be included in the second edition of the "Traité du calcul differentiel et du calcul integral".
LOBACHEVSKY, Nikolai Ivanovich.
Nouveaux principes de la géométrie avec une théorie complète des parallèles.
Bruxelles, Hayez, 1901.
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1200 €
First edition in french of this the "New Foundations of Geometry with a Complete Theory ol Parallels".
CORIOLIS, Gustave Gaspard.
Théorie mathématique des effets du jeu de Billard.
Paris, Carilian-Goeury, 1835.
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1200 €
Coriolis, devoted his energies to the applications of the laws of mechanics and was responsible for the terms "work" and "kinetic energy." He is best known for "his theorem relating the various components of acceleration in rotating systems, one of which rise to the so-called Coriolis force. (Bibliotheca mecanica).
First edition of the first mathematical analysis of the complex kinetics of billiards.
OZANAM, Jacques.
Cours de Mathématiques qui comprend toutes les parties de cette Science les plus utiles & les plus nécessaires à un homme de Guerre, & à tous ceux qui se veulent perfectionner dans les Mathématiques.
Paris, Jean Jombert, 1693.
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1150 €
First edition.
Full course of 5 volumes and impressive iconographic support in 204 plates.
Beyond purely mathematical treatises on geometry, arithmetic and trigonometry we find a treatise on gnonomics, a treatise on fortification, the sine and logarithm tables.
DUPIN, Charles.
Développements de géométrie, avec des applications à la stabilité des vaisseaux, aux déblais et remblais, au défilement, à l'optique, etc. pour faire suite a la géométrie descriptive et a la géométrie analytique de M. Monge. Théorie.
ET
Applications de géométrie et de méchanique, à la Marine, aux Ponts et Chaussées, etc. Pour faire suite aux développements de Géométrie.
Paris, Vve Coucier & Bachelier, 1813-1822.
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950 €
First edition of the two books of the mathematical works of Dupin.
Dupin is known for it's theorem and for the cyclides of Dupin.
Today, Dupin cylides are used in computer-aided design (CAD), because cyclide patches have rational representations and are suitable for blending canal surfaces (cylinder, cones, tori, and others).
MONGE, Gaspard.
Géométrie descriptive. Leçons données aux écoles normales, l'An 3 de la république.
Paris, Baudouin, An VII [1799].
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950 €
First edition, first issue with the errata at the verso of page vii.
"Monge is regarded as the creator of descriptive geometry, for 'it ws he who elegantly and methodically converted the group of graphical procedures used by practionners into a general uniform technique based on simple an rigorous reasoning and methods ...Monge's systematic use of cylindrical projection and, more discreetly, that of central projection, opened the way to the parallel creation of projective and modern geometry' (DSB). It was primarily through Monge's teachings, both at the ephemeral École de l'an III and the École Polytechnique, that descriptive geometry, analytical geometry and differential geometry were established as special fields".(Norman).
LEVY, Paul.
Calcul des probabilités.
Paris, Gauthier-Villars, 1925.
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950 €
First edition.
Paul Lévy (1886-1971) French mathematician is among the founders of modern probability theory. We also owe him important considerations on the stable stochastic laws which bear his name as well as on martingales. In 1920, he was appointed professor of analysis at the École Polytechnique and on this occasion discovered the discipline that would leave his mark the most: the calculation of probabilities. It can be said that most of the essential concepts of probability theory derive from him.
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