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John Landen: First Attempt for the Algebrization of Infinitesimal Calculus

  • Christine Phili
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 151)

Abstract

The conceptualization and codification of infinitesimal calculus during the 17th century were not able to elucidate their fundamental notions. The criticisms and controversies surrounding the foundation of calculus finally led to important scientific activity which gave rise to the rigorous foundation of analysis. Nevertheless, before the final period of its arithmetization in the 19th century, there was a turning point in the 18th century when algebrization transformed the metaphysical face of analysis.

Keywords

Algebraic Expression Differential Calculus Residual Analysis Monthly Review Binomial Theorem 
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Notes

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    “It may sometimes be of use to observe, that, when y is very large number, the Log of 1+ÿ will be = ÿ nearly the value of the series -2- — - + etc. being there so very small that is may be neglected”. Idem p. 33.Google Scholar
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    Cf. his paper on fluxions, cf. note 23; moreover, from his former publications we can establish that Landen never returned to his theory. Cf. Mathematical Memoirs, Vol. I, II, London 1780.Google Scholar
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    Lagrange also had abandoned his own theory, seeing that his paper in 1772, made no impression and he had followed Leibniz’s conception in his Mécanique Analitique. Google Scholar
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    Cf. Landen’s foreword; cf also “I can also mention a method which Landen gave in 1758 to avoid consideration of infinity, of motion or of fluxions... he is perhaps the only English mathematician, who has acknowledged in inconvenience of the method of fluxions”, Review of Lacroix’s Calcul différentiel. Monthly Review, London 1800, p. 497.Google Scholar
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    “Landen, I believe, first considered and proposed to the treat of fluxionary calculus merely as a branch of Algebra.” R. Woodhouse, Principles of Analytical Calculation, Cambridge 1803, p. xviii. His homogeneous method was also appreciated by the philosophers Compte, Hegel, Cohen etc. Marx in his Mathematical Manuscrits stresses the importance of Landen’s uniformity, cf. The Mathematical Manuscrits of Karl Marx, New Park Publication, New York 1983, pp. 33, 75, 113, 139.Google Scholar
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    Moritz Cantor in his History of Mathematics criticizes severly Landen’s Residual Analysis: “die residual Division, geschieht aber selbstverständlich durch Grenzübergang, so dass die Landenschen Methode nichts wesentlich Neues darbietet”, M. Cantor, Vorlesungen über Geschichte der Mathematik, Band III, Leipsig, 1894, p. 661.Google Scholar
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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Christine Phili
    • 1
  1. 1.National Technical UniversityAthensGreece

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