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Analogy and the Growth of Mathematical Knowledge

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The Growth of Mathematical Knowledge

Part of the book series: Synthese Library ((SYLI,volume 289))

Abstract

High esteem for the mathematical discoveries and rigorous argumentation of the ancient mathematicians like Euclid or Archimedes has always been accompanied by astonished speculation about how after all they had found their results, which were subsequently demonstrated in such an exemplary way that they became paradigms of rigorous argumentation. Thus we find that Kepler as well as Leibniz appealed to Archimedes in the context of justification. What is more, Leibniz justified his differential calculus (LMG 5, 350) by saying that the difference from the style of Archimedes consists only in the expressions (expression), which in his method are more direct and more appropriate to the art of inventing (art d’inventer). His differential calculus is only a new kind of notation, novum notationis genus (Leibniz 1714, 404).

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Authors
  1. Eberhard Knobloch
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Editors and Affiliations

  1. The Pennsylvania State University, USA

    Emily Grosholz

  2. Leibniz Archives, Hannover, Germany

    Herbert Breger

  3. University of Hannover, Germany

    Herbert Breger

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Knobloch, E. (2000). Analogy and the Growth of Mathematical Knowledge. In: Grosholz, E., Breger, H. (eds) The Growth of Mathematical Knowledge. Synthese Library, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9558-2_20

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  • DOI: https://doi.org/10.1007/978-94-015-9558-2_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5391-6

  • Online ISBN: 978-94-015-9558-2

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