Chapter

Descartes’s Geometry and Pappus’ Problem

Emily R. Grosholz

in Cartesian Method and the Problem of Reduction

Published in print January 1991 | ISBN: 9780198242505
Published online October 2011 | e-ISBN: 9780191680502 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198242505.003.0002
Descartes’s                         Geometry and Pappus’ Problem

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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

Chapter.  8697 words.  Illustrated.

Subjects: History of Western Philosophy

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