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conic section
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conic section

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The four types of curve that may be obtained by cutting a single or double right-circular cone with a plane (two-dimensional surface).

Curve obtained when a conical surface is intersected by a plane. If the intersecting plane cuts both extensions of the cone, it yields a hyperbola; if it is parallel to the side of the cone, it produces a parabola. Other intersecting planes produce circles or ellipses.

The Greek mathematician Apollonius of Perga wrote eight books with the title Conic Sections, which superseded previous work on the subject by Aristarchus and Euclid.



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It could only do some partial unifications, such as the geometry of conics and the theory of equations.
In his Geometrie (1637) Descartes, although objecting to the "barbarous" notation of Arabic algebraists, followed Viete (who, surprisingly, is omitted from this History's biobibliographical index) and extended his analytic programme, drawing on Apollonius's Conics, as did Pierre de Fermat in his roughly contemporary work on plane and solid loci (726-30).
It is for this reason that I decided to write about the Arabic translation of the Conics of Apollonius, and its impact on the research, as well as on the mathematics of Descartes and Fermat.
 
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