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Titel: Traité d'Algebre; ou principes generaux pour...
Verlag: Paris, Jean Boudot, 1703
2 vols in one, 4to (247 x 184 mm), pp [xviii] 270 [4, Privilege and cancel leaf Ff2], with two folding engraved plates; [iv] 47 [1, errata]; cancel leaves slightly browned as usual, without front free endpaper, otherwise very nice copies in contemporary French speckled calf.I. First edition. 'Although it was his skill in Diophantine analysis that made Rolle's reputation, his favorite area was the algebra of equations, in which he published Traité d'algèbre (1690), his most famous work . [It] contains interesting considerations on systems of affine equations. Following the techniques established by Bachet de Méziriac (1621), Rolle utilized the Euclidean algorithm for resolving Diophantine linear equations. He employed the same algorithm to find the greatest common divisor of two polynomials, and in 1691 he was able to eliminate one variable between two equations.'The Traité d'algèbre, the language of which is so special, has remained famous, thanks notably to the method of "cascades." Rolle used this method to separate the roots of an algebraic equation' (DSB).Leaves A4, H2, M4, P4-Q2, Q4, R1, 2A2, and Ff1 are all cancels. Cancel Ff1 is mispaginated (267 on the recto, and 266 on the verso). This copy is unusual in that the leaf Ff2, which is lacking in almost all copies (although the remaining text is continuous), is present.II. First edition of Rolle's polemic against infinitesimal analysis. 'L'Hospital was an honorary academician; in 1696 he had published Analyse des infiniment petits. The Academy was very divided over infinitesimal analysis. Rolle - incited, it was said, by influential persons - vigorously attacked infinitesimal analysis and strove to demonstrate that it was not based on solid reasoning and led to errors . Varignon defended the new methods and pointed out the paralogisms that Rolle displayed in discussing these examples. The latter, too plebeian to control himself, created an uproar. A commission established to resolve the matter was unable to come to a decision. The dispute lasted from 1700 to 1701, and then continued in the Journal des sçavans in the form of exchanges between Rolle and a newcomer, Joseph Saurin.'Rolle was a skillful algebraist who broke with Cartesian techniques; and his opposition to infinitesimal methods, in the final analysis, was beneficial' (DSB).I. see D.E. Smith, A source book in mathematics pp 253-260, containing partial translations into English. Buchnummer des Verkäufers 3889
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