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Cartesian Method and the Problem of
                        Reduction$
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Emily R. Grosholz

Print publication date: 1991

Print ISBN-13: 9780198242505

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780198242505.001.0001

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Descartes’s Geometry and Pappus’ Problem

Descartes’s Geometry and Pappus’ Problem

Chapter:
(p.15) 1 Descartes’s Geometry and Pappus’ Problem
Source:
Cartesian Method and the Problem of Reduction
Author(s):

Emily R. Grosholz

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198242505.003.0002

The discussion of the Cartesian method begins with the Geometry. This chapter deals with the opening pages of Book I of the Geometry and Descartes's solution to Pappus's problem. The basics for Cartesian mathematics were straight line segments and their proportions. The complexes were problems and higher algebraic curves, both represented by algebraic equations. The assumption that a subject matter can be elaborated out of self-evident and simple starting points often involves Descartes in problems of circularity. The opening pages of the Geometry resemble that of Euclid's Elements; the centerpiece is Descartes's solution to Pappus's problem. By rewriting the conditions of the problem as an equation, he has converted it from a proportionality involving lines, areas, or volumes to an equation about line segments.

Keywords:   Geometry, Pappus's problem, Elements, line segments, Cartesian method, equations

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