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Article ID: CBB521943513

Leibniz and the infinite (2018)

Quaderns d'Història de l'Enginyeria
Volume: XVI
Pages: 11-31

URI: https://upcommons.upc.edu/handle/2117/118710

Publication Date: 2018
Edition Details: Special issue: 300 Aniversari: Gottfried Wilhelm Leibniz (Leipzig, 1646-Hannover, 1716)
Language: English

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How did Leibniz handle the infinite in mathematics? Above all one has to study his Arithmetical quadrature of the circle etc. in order to answer to this question. Its last, still available version was written between June and September 1676. A new, bilingual, annotated Latin-German edition has just appeared. The paper mainly deals with theorems, thoughts, and explanations of this treatise putting them into the historical context (Kepler, Galileo, Grégoire de St. Vincent, Mengoli, Pardies, Johann Bernoulli, Euler). Four issues will be especially discussed: 1. Leibniz’s notions of infinitely small and infinite emphasizing his crucial distinction between the unbounded and bounded infinite. It sheds new light on the meaning of the fictionality of these fictitious quantities. 2. How did Leibniz demonstrate that a certain quantity is infinitely small or infinite? Three possibilities will be explained (definition, third proportional, trichotomy law). 3. Asymptotic spaces: What happens in the neighbourhood of the asymptote? Finite spaces are equated with infinitely long spaces. Infinitely long spaces might be finite. Hyperboloids and the logarithmic curve serve as examples. Is there any connection with the spirituality of the human soul? 4. The divergence of the harmonic series: Leibniz’s own demonstration is compared with Mengoli’s solution that Leibniz came to know only during his second sojourn in London (October 1676).

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Article Maria Rosa Massa Esteve; Antoni Maria Claret Roca Rosell (2018) Gottfried Wilhelm Leibniz, 300 anys després (Gottfried Wilhelm Leibniz, Three Hundred Years Later). Quaderns d'Història de l'Enginyeria (pp. 1-10). unapi

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