Chapter

Treatment of Curves: Notion of Genre

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/9780198242505.003.0003
Treatment of Curves: Notion of                         Genre

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This chapter investigates Descartes's treatment of curves and his notion of genre. The exposition shows in detail how his method acts as a powerful problem-solving device which nonetheless weakens its own results and diverts Descartes from important mathematical questions which some of his contemporaries were already exploring. It argues that even if he discovered new higher curves, his discoveries were surprisingly restricted, and that he did not fully exploit the possibilities opened up by his own new analytic geometry for investigating them. The first section argues that Descartes's commitment to his homogenous starting points and line segments, and to the reductive claims of his method, prevents him from being able to focus on his mathematical curves as such.

Keywords: curves; genre; analytic geometry; starting points; line segments

Chapter.  8165 words.  Illustrated.

Subjects: History of Western Philosophy

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