Infinitesimal Differences: Controversies between Leibniz and his Contemporaries

כריכה קדמית
Ursula Goldenbaum, Douglas Jesseph
Walter de Gruyter, 3 בנוב 2008 - 627 עמודים
0 ביקורות
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.
  

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תוכן

Introduction
1
Newton and Leibniz on the Status of Infinitesimals
7
John Wallis and his Critics
31
Indivisibilia Vera How Leibniz Came to Love Mathematics
53
Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz
95
On Leibnizs Fictionalism
107
Infinitesimals Differentials and the Leibnizian Calculus
135
Productive Ambiguity in Leibnizs Representation of Infinitesimals
153
Leibnizs Calculation with Compendia
185
Nieuwentijt Leibniz and Jacob Hermann on Infinitesimals
199
Origins and Consequences of Leibnizs Doctrine of Infinitesimal Magnitudes
215
Rule of Continuity and Infinitesimals in Leibnizs Physics
235
Leibniz on Infinitesimals and the Reality of Force
255
Dead Force Infinitesimals and the Mathematicization of Nature
281
Backmatter
307
זכויות יוצרים

Generality and Infinitely Small Quantities in Leibnizs Mathematics The Case of his Arithmetical Quadrature of Conic Sections and Related Curves
171

מהדורות אחרות - הצג הכל

מונחים וביטויים נפוצים

אודות המחבר (2008)

Ursula Goldenbaum, Emory University, Atlanta, GA, USA and Institute for Advanced Study at Princeton; Douglas Jesseph, North Carolina State University, Raleigh, USA.

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