"La Géométrie... is... divided into three parts. The first... contains an explanation of some of the principles of algebraic geometry and shows a real advance over the Greeks. To the Greeks... the product of two variables [corresponded] to the area of some rectangle, and the product of three variables to the volume of some rectangular parallelepiped. Beyond this the Greeks could not go. To Descartes... x2 [is] the fourth term in the proportion 1 : x = x : x2... representable by an appropriate line length which can easily be constructed when x is known. ... The second part... deals with... a now obsolete classification of curves and with an interesting method of constructing tangents to curves. ... The third part...concerns... the solution of equations of degree greater than two. Use is made of what we now call "Descartes' rule of signs,"... determining limits to the number of negative and positive roots [of] a polynomial."
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Original Language: English
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, An Introduction to the History of Mathematics (1953)
https://en.wikiquote.org/wiki/La_G%C3%A9om%C3%A9trie
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La Géométrie
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