The three conic sections are the parabola, hyperbola, and ellipse (the circle is considered a special case of an ellipse). They first arose in the fourth century b.c. in the work of the Greek mathematician Menaechmus who was trying to solve the problem of doubling the cube. Menaechmus constructed the conic sections through the intersection of a plane with three different types of a right circular cone.

Euclid (c.300 b.c.) is known to have written a four-volume work, now lost, on conic sections. The conics had been known for almost a century when Archimedes (287 b.c.-212 b.c.) computed the area of an ellipse, the area of sectors of a parabola, and the volumes of segments of the solids of revolution of conic sections using a method similar to that of integral calculus. The third great mathematician of the golden age of Greek...