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date: 17 July 2019

Abstract and Keywords

This article examines the ‘dispute over tangents’ between René Descartes and Pierre de Fermat, which began in 1638, by comparing their methods of constructing tangents. Descartes’s method aims at a universality, whereas Fermat’s method aims at a generality. The article begins with a discussion of Descartes’s method of tangents, which he proposed in 1637 as a way of constructing ‘all the problems of geometry’. It then considers Fermat’s method, in which he introduces a rule for finding a maximum or minimum. It also looks at Descartes’s critiques of Fermat’s method as applied to the ellipse and the hyperbola, and how Fermat arrived at the question of the ‘specific property’ of a curve by constructing the tangents to non-geometric curves.

Keywords: tangents, René Descartes, Pierre de Fermat, universality, generality, geometry, ellipse, hyperbola, curves

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