The ancient Greeks loved geometry and made great advances in this subject. Euclid's Elements was for 2000 years the main text in mathematics, giving a careful systematic treatment of both planar and three dimensional geometry, culminating in the five Platonic solids. Apollonius made a thorough study of conics: ellipse, parabola and hyperbola. Constructions played a key role, using straightedge and compass.This is one of a series of lectures on the History of Mathematics by Assoc. Prof. N J Wildberger at UNSW.