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Article ID: CBB637465302

Le rôle des notations dans la découverte de l’analogie des puissances et des différences de Leibniz (2023)

Waszek, David (Author)

Almagest
Volume: 14
Issue: 2
Pages: 256-266
Publication date: 2023
Language: French

DOI: 10.1484/J.ALMA.5.136771

URI: https://www.brepolsonline.net/doi/abs/10.1484/J.ALMA.5.136771

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Metaphors; analogies Mathematics 17th century Germany Leibniz, Gottfried Wilhelm von

This paper revisits a famous episode in the history of mathematics: the 1695 discovery by Leibniz, in correspondence with Johann Bernoulli, of an “analogy” between the powers of a sum and the differentials of a product. It is often suggested that this discovery essentially depended on specific notational choices previously made by Leibniz: his use of a separate ‘d’ symbol, which, unlike Newton's notation, separated the differentiation operation from the variables it operates on; and his introduction of an “exponential” notation for differentials (e.g., d3x for dddx, d⁻1x for ∫x, etc.). Can we really make sense of the idea that the notations themselves—independently of the conceptual motivations Leibniz may have had to introduce them in the first place—played an essential role in this discovery? I argue that the notation did indeed play a part in this discovery and subsequent ones, but a rather subtle one, which cannot be understood (as is often suggested in the literature) in terms of an increase in “expressive power”; I also argue that Newton's notation could have served just as well. [English translation of title by DeepL.com: The role of notations in the discovery of Leibniz's analogy of powers and differences]

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Article Vincent Jullien; Carmen Martínez-Adame (2023) Foreward. Almagest (pp. 6-14). unapi

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