Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics

Kapitel in diesem Buch

1. Frontmatter I
2. Table of Contents V
3. Introduction 1
4. Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals 7
5. Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics 31
6. Indivisibilia Vera – How Leibniz Came to Love Mathematics 53
7. Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz 95
8. Archimedes, Infinitesimals and the Law of Continuity: On Leibniz’s Fictionalism 107
9. An Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus 135
10. Productive Ambiguity in Leibniz’s Representation of Infinitesimals 153
11. Generality and Infinitely Small Quantities in Leibniz’s Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves 171
12. Leibniz’s Calculation with Compendia 185
13. Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals 199
14. Truth in Fiction: Origins and Consequences of Leibniz’s Doctrine of Infinitesimal Magnitudes 215
15. Rule of Continuity and Infinitesimals in Leibniz’s Physics 235
16. Leibniz on Infinitesimals and the Reality of Force 255
17. Dead Force, Infinitesimals, and the Mathematicization of Nature 281
18. Backmatter 307