Apollonius of Perga

Apollonius of Perga was an ancient Greek mathematician whose treatise Conics developed the systematic study of ellipses, parabolas, and hyperbolas.

Conic section: A curve formed by intersecting a plane with a cone, including ellipses, parabolas, and hyperbolas. Conic sections are the subject that Conics classified and analyzed.
Apollonius's Conics: An ancient Greek mathematical treatise that systematically studies conic sections in eight books. This is the work through which Apollonius's conic geometry survives.
Euclid: An ancient Greek mathematician traditionally credited with Elements, a foundational treatise on geometry and number theory. His geometric tradition preceded and shaped the setting for Apollonius's work.
Ptolemy: A second-century Greco-Egyptian astronomer and mathematician whose Almagest presented a geocentric model of the cosmos. His astronomy developed within the mathematical culture shaped by Hellenistic geometry.
Cartesian coordinate system: A system that locates points using numerical coordinates measured from perpendicular axes. Coordinate equations offer an algebraic approach unlike Apollonius's synthetic geometric proofs.
Ellipse: A closed plane curve whose points have a constant sum of distances from two fixed foci. Apollonius established the name and geometric treatment of this conic.
Cone: A three-dimensional solid with a circular base tapering to an apex, or the surface generated by its sides. Plane intersections with cones provide the geometric origin of conic curves.
Menaechmus: An ancient Greek mathematician associated with early studies of conic sections and the duplication of the cube. His earlier conic investigations form part of the history preceding Apollonius.
Kepler's laws of planetary motion: Three laws describing planetary orbits, areas swept by planets, and the relation between orbital periods and sizes. Kepler identified planetary orbits as ellipses, a major later use of conic geometry.
Analytic geometry: A method that studies geometric objects using algebraic equations and coordinate systems. It recasts conics through equations rather than the classical constructions of Conics.

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