Infinitesimal Differences : Controversies between Leibniz and his Contemporaries.
Title:
Infinitesimal Differences : Controversies between Leibniz and his Contemporaries.
Author:
Goldenbaum, Ursula.
ISBN:
9783110211863
Personal Author:
Physical Description:
1 online resource (336 pages)
Contents:
Frontmatter -- Table of Contents -- Introduction -- Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals -- Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics -- Indivisibilia Vera - How Leibniz Came to Love Mathematics -- Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz -- Archimedes, Infinitesimals and the Law of Continuity: On Leibniz's Fictionalism -- An Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus -- Productive Ambiguity in Leibniz's Representation of Infinitesimals -- Generality and Infinitely Small Quantities in Leibniz's Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves -- Leibniz's Calculation with Compendia -- Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals -- Truth in Fiction: Origins and Consequences of Leibniz's Doctrine of Infinitesimal Magnitudes -- Rule of Continuity and Infinitesimals in Leibniz's Physics -- Leibniz on Infinitesimals and the Reality of Force -- Dead Force, Infinitesimals, and the Mathematicization of Nature -- Backmatter.
Abstract:
The development of the calculus during the 17th century was successful in mathematical practice, but raised questions about the nature of infinitesimals: were they real or rather fictitious? This collection of essays, by scholars from Canada, the US, Germany, Japan and Switzerland, gives a comprehensive study of the controversies over the nature and status of the infinitesimal. Aside from Leibniz, the scholars considered are Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. The collection also contains newly discovered marginalia of Leibniz to the writings of Hobbes.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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