Conics
Konika
The ellipse, parabola, and hyperbola are not three unrelated curves but a single family of conic sections, generated by cutting a single double cone at different angles, and their properties can be derived systematically from this unified construction.
- unification of ellipse, parabola, hyperbola as conic sections
- naming the conic sections
- systematic derivation from a single double cone
- survival partly only through Arabic translation
- later indispensability for Kepler's planetary orbits
Apollonius of Perga's Conics, composed in eight books of which seven survive, unified and vastly extended earlier Greek work on the curves produced by slicing a cone, giving the ellipse, parabola, and hyperbola the names by which they are still known and deriving their properties with a rigor comparable to Euclid's Elements. Apollonius shows that all three curves, along with the circle, can be generated from a single double cone by varying the angle of the cutting plane. Though written with no immediate application in view, the Conics became indispensable roughly eighteen centuries later when Kepler needed the mathematics of the ellipse to describe planetary orbits.
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