History
The earliest known work on conic sections was by Menaechmus in the fourth century BC. He discovered a way to solve the problem of doubling the cube using parabolae. (The solution, however, does not meet the requirements imposed by compass and straightedge construction.) The area enclosed by a parabola and a line segment, the so-called "parabola segment", was computed by Archimedes via the method of exhaustion in the third century BC, in his The Quadrature of the Parabola. The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve, as Apollonius had proved. The focus–directrix property of the parabola and other conics is due to Pappus.
Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity.
The idea that a parabolic reflector could produce an image was already well known before the invention of the reflecting telescope. Designs were proposed in the early to mid seventeenth century by many mathematicians including René Descartes, Marin Mersenne, and James Gregory. When Isaac Newton built the first reflecting telescope in 1668 he skipped using a parabolic mirror because of the difficulty of fabrication, opting for a spherical mirror. Parabolic mirrors are used in most modern reflecting telescopes and in satellite dishes and radar receivers.
Read more about this topic: Parabola
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