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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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Against Descartes on Indeterminate Problems

Against Descartes on Indeterminate Problems

(p.79) 5 Against Descartes on Indeterminate Problems
Isaac Newton on Mathematical Certainty and Method

Niccolò Guicciardini

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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