(Refer to history where it's appropriate!. For example you may refer to the Gregory and Newton's works when you're dealing with the reflective propert of parabola)

The parabola was studied by Menaechmus who was a pupil of Plato and Eudoxus. He attempted to duplicate the cube, namely to find side of a cube that has area double that of a given cube. Hence he attempted to solve x^3 = 2 by geometrical methods.

In fact the geometrical methods of ruler and compass constructions cannot solve this (but Menaechmus did not know this). Menaechmus solved it by finding the intersection of the two parabolas x2 = y and y2 = 2x.

Euclid wrote about the parabola and it was given its present name by Apollonius. The focus and directrix of a parabola were considered by Pappus.

Pascal considered the parabola as a projection of a circle and Galileo showed that projectiles follow parabolic paths.

Gregory and Newton considered the properties of a parabola which bring parallel rays of light to a focus.