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Philosophy of mathematics and mathematical practice in the seventeenth century /
This book provides the first comprehensive account of the relationship between philosophy of mathematics and the mathematical practice of the seventeenth century - the most eventful period of mathematical development in history. Starting with the Renaissance debates on the certainty of mathematics,...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Oxford University Press,
1996.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover
- Contents
- 1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century
- 1.1 The Quaestio de Certitudine Mathematicarum
- 1.2 The Quaestio in the Seventeenth Century
- 1.3 The Quaestio and Mathematical Practice
- 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity
- 2.1 Magnitudes, Ratios, and the Method of Exhaustion
- 2.2 Cavalieri's Two Methods of Indivisibles
- 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles
- 2.4 Guldin's Centrobaryca and Cavalieri's Objections
- 3. Descartes' Géométrie
- 3.1 Descartes' Géométrie
- 3.2 The Algebraization of Mathematics
- 4. The Problem of Continuity
- 4.1 Motion and Genetic Definitions
- 4.2 The "Causal" Theories in Arnauld and Bolzano
- 4.3 Proofs by Contradiction from Kant to the Present
- 5. Paradoxes of the Infinite
- 5.1 Indivisibles and Infinitely Small Quantities
- 5.2 The Infinitely Large
- 6. Leibniz's Differential Calculus and Its Opponents
- 6.1 Leibniz's Nova Methodus and L'Hôpital's Analyse des Infiniment Petits
- 6.2 Early Debates with Clüver and Nieuwentijt
- 6.3 The Foundational Debate in the Paris Academy of Sciences
- Appendix: Giuseppe Biancani's De Mathematicarum Natura
- Notes
- References
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Y.