- Title Pages
- Epigraph
- Preface
- Abbreviations and Conventions
-
I Preliminaries -
1 Newton on Mathematical Method: A Survey -
2 Newton on Certainty in Optical Lectures -
3 Descartes on Method and Certainty in the Géométrie -
II Against Cartesian Analysis and Synthesis -
4 Against Descartes on Determinate Problems -
5 Against Descartes on Indeterminate Problems -
6 Beyond the Cartesian Canon: The Enumeration of Cubics -
III New Analysis and the Synthetic Method -
7 The Method of Series -
8 The Analytical Method of Fluxions -
9 The Synthetic Method of Fluxions -
IV Natural Philosophy -
10 The Principia -
11 Hidden Common Analysis -
12 Hidden New Analysis -
V Ancients and Moderns -
13 Geometry and Mechanics -
14 Analysis and Synthesis -
VI Against Leibniz -
15 The Quarrel with Leibniz: A Brief Overview -
16 Scribal Publication, 1672−1699 -
17 Fluxions in Print, 1700−1715 - Conclusion
- A Brief Chronology of Newton’s Mathematical Work
- References
- Index
Against Descartes on Indeterminate Problems
Against Descartes on Indeterminate Problems
- Chapter:
- (p.79) 5 Against Descartes on Indeterminate Problems
- Source:
- Isaac Newton on Mathematical Certainty and Method
- Author(s):
Niccolò Guicciardini
- Publisher:
- The MIT Press
This chapter explores Newton’s criticisms of the Cartesian method to indeterminate problems, and states that Newton has formed a strong conviction in rejecting Descartes’ canon for indeterminate problems. Newton believes that the synthesis of indeterminate problems proposed by Descartes in Géométrie proved to be unsatisfactory, and also that the Cartesian analysis was also inferior to the method of analysis used by the ancient scholars of geometry. The chapter goes on to explain that Newton claimed that the ancient methods of geometry are more concise and elegant, and that their analytic method always leads to the synthesis, the construction of a curve, in a straightforward manner.
Keywords: Newton, Géométrie, Cartesian analysis, geometry
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- Title Pages
- Epigraph
- Preface
- Abbreviations and Conventions
-
I Preliminaries -
1 Newton on Mathematical Method: A Survey -
2 Newton on Certainty in Optical Lectures -
3 Descartes on Method and Certainty in the Géométrie -
II Against Cartesian Analysis and Synthesis -
4 Against Descartes on Determinate Problems -
5 Against Descartes on Indeterminate Problems -
6 Beyond the Cartesian Canon: The Enumeration of Cubics -
III New Analysis and the Synthetic Method -
7 The Method of Series -
8 The Analytical Method of Fluxions -
9 The Synthetic Method of Fluxions -
IV Natural Philosophy -
10 The Principia -
11 Hidden Common Analysis -
12 Hidden New Analysis -
V Ancients and Moderns -
13 Geometry and Mechanics -
14 Analysis and Synthesis -
VI Against Leibniz -
15 The Quarrel with Leibniz: A Brief Overview -
16 Scribal Publication, 1672−1699 -
17 Fluxions in Print, 1700−1715 - Conclusion
- A Brief Chronology of Newton’s Mathematical Work
- References
- Index
