- 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
The Method of Series
The Method of Series
- Chapter:
- (p.138) (p.139) 7 The Method of Series
- Source:
- Isaac Newton on Mathematical Certainty and Method
- Author(s):
Niccolò Guicciardini
- Publisher:
- The MIT Press
This chapter explores the method of series developed in Newton’s De Analysi per aequationes numero terminorum infinitas. Newton’s method in the use of infinite series was heavily derived from the work of a fellow mathematician, John Wallis, most notably in Arithmetica Infinitorum. Wallis was a Savilian professor of geometry in Oxford University. His Arithmetica Infinitorum deals with the “quadrature of curvilinear figures,” which was an important topic in mathematics during the seventeenth century. Using a Wallisian interpolation technique, Newton came up with a mathematical discovery—the binomial series of fractional powers—which gave him access to the realm of infinite series as found in his work De Analysi.
Keywords: Newton, John Wallis, De Analysi, Arithmetica Infinitorum, infinite series
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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
