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Isaac Newton on Mathematical Certainty and Method$
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Niccolo Guicciardini

Print publication date: 2009

Print ISBN-13: 9780262013178

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262013178.001.0001

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Hidden New Analysis

Hidden New Analysis

(p.267) 12 Hidden New Analysis
Isaac Newton on Mathematical Certainty and Method

Niccolò Guicciardini

The MIT Press

This chapter presents proof that Newton developed advanced quadrature techniques, and also examines Corollary 3, Proposition 41, Book 1; and Corollary 2, Proposition 91, Book 1, of his Principia. In the two propositions, Newton simplified the problem into the calculation of the area bounded by a curve, and in the next series of corollaries and scholia, he employed the general solution to particular cases: That one must calculate the quadrature for specific cases. The solutions to corollaries and scholia heavily rely upon such calculations, but Newton did not provide details on how to do them. The chapter then explores some of the examples for using new analysis in the Principia.

Keywords:   Newton, new analysis, Principia, quadrature

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