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 approach—treating a curve as the locus of an equation in the rectangular coordinates—was 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 Euclid’s Conics , is lost, and little information about its contents can be gleaned from Pappus....
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 Fall '08
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 Calculus, Conic Sections, Conic section, Pappus, Apollonius of Perga

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