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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 Determinate Problems

Against Descartes on Determinate Problems

(p.61) 4 Against Descartes on Determinate Problems
Isaac Newton on Mathematical Certainty and Method

Niccolò Guicciardini

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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