- 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 Determinate Problems
Against Descartes on Determinate Problems
- Chapter:
- (p.61) 4 Against Descartes on Determinate Problems
- Source:
- Isaac Newton on Mathematical Certainty and Method
- Author(s):
Niccolò Guicciardini
- Publisher:
- The MIT Press
This chapter explores Newton’s critical approach to the Cartesian construction of equations, and briefly reviews the phases involved in the analytical and synthetic processes for the solution of determinate problems posited by the Cartesian school of thought. It explores the themes of demarcation and simplicity presented by Isaac Newton in the final section of his Lucasian Lectures on Algebra. The chapter then points out that, according to Newton, Cartesian analysis is more likely less elegant than geometry; does not show an easy way to achieve synthesis; and is not an easy way to achieve synthesis.
Keywords: Isaac Newton, construction of equations, Lectures on Algebra, 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
