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2020-03-25 08:03:07
MACLAURIN, Colin
A Treatise of Fluxions. In Two Books
Edinburgh: Printed by T.W. and T. Ruddimans, 1742. First edition of "the earliest logical and systematic publication of the Newtonian [calculus] methods. It stood as a model of rigor until the appearance of Cauchy's Cours d'Analyse in 1821" (DSB). The 'Treatise' was written partly (but only partly, see below) as a response to the attack on the foundations of the method of fluxions and infinitesimal calculus made by George Berkeley in 'The Analyst' (1734). "[Berkeley] showed that many definitions in the infinitesimal calculus are paradoxical and cannot be justified by intuition. He explained the success of the new calculus by a repeated neglect of infinitely small quantities leading through a compensation of errors to a correct answer" (Jahnke, A History of Analysis, p. 127). "MacLaurin provided a rigorous foundation for the method of fluxions based on a limit concept drawn from Archimedean classical geometry. He went on to demonstrate that the method so founded would support the entire received structure of fluxions and the calculus, and to make advances that were taken up by continental analysts . . . The 'Treatise' was generally cited by British fluxionists as the definitive answer to Berkeley's criticism, but Maclaurin had accomplished much more than this. Judith Grabiner has described Maclaurin's influence on the Continental analysts in detail. Maclaurin's work was cited with admiration by Lagrange, Euler, Clairaut, d'Alembert, Laplace, Legendre, Lacroix, and Gauss. The influence of Maclaurin's use of the algebra of inequalities as a basis for his limit arguments can be … [Click Below for Full Description]
Bookseller: Landmarks of Science Books [Richmond, United Kingdom]
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