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Unformatted text preview: , the line is the directrix , and the ratio is called the eccentricity of the conic section. This focusdirectrix property of conics is not mentioned by Apollonius, but Heath deduces from the way it is treated by Pappus that this lemma must have been stated without proof, and regarded as wellknown, by Euclid. We outline a proof in Appendix B . The focusdirectrix characterization of conic sections can be turned into an equation. This approachtreating a curve as the locus of an equation in the rectangular coordinateswas introduced in the early seventeenth century by Ren e Descartes (15961650) and Pierre de ermat (16011665). Here, we sketch how this characterization leads to equations for the conic sections. 9 This work, like Euclids Conics , is lost, and little information about its contents can be gleaned from Pappus....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Conic Sections

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