This is the only english translation of The Conics of Apollonius (3rd Century BCE), the culmination of the brilliant geometrical tradition of ancient Greece. With astonishing virtuosity, and with a storyteller’s flair for thematic development, Apollonius leads the reader through the mysteries of these intriguing curved lines, treated as objects of pure mathematics. His work in turn provided a basis for the very differently conceived investigations of modern mathematicians and scientists such as Viète, Descartes, Kepler, Pascal, and Newton.