the successors of Euclid; though he did spend a few years in Pergamum in western Asia Minor at a new university and library modelled

on that at Alexandria. Not much else is known about the life of Apollonius.

Apollonius is best remembered as one of the great mathematicians of antiquity. He was named ‘The Great Geometer’, mainly because

of his work on conic sections. His greatest work, named

eighth book is lost, but the other seven have been preserved. The first four are in Greek and expand on the work on conic sections of

Euclid and other mathematicians; the other three have come down to us as ninth century Arabic translations and are more specialised.

Apollonius was also an astronomer. In contrast to the model Eudoxus proposed to represent the motion of the planets using concentric

spheres, Apollonius proposed two alternative models called epicyclic motion and eccentric motion. In the epicyclic scheme, a planet was

assumed to move uniformly about a small circle whose centre also moved uniformly around the circumference of a larger circle whose

centre was the centre of the Earth. In the eccentric scheme, a planet was assumed to move uniformly about a large circle whose centre

also moved uniformly around the circumference of a smaller circle whose centre was the centre of the Earth. These ideas led directly to

the scheme for the motion of the planets later devised by Ptolemy.

Apollonius died in Alexandria around 200 BC.

from one circular double cone. If the double cone is cut by a plane, the curve formed by the intersection of the cone and the plane is

called a

A

Generally an

cone.

If the angle is increased so that the section goes through the base of the cone but with the vertex on the curved face of the cone and

on the opposite side of the centre of the base of the cone, then we get a

If the angle is increased still further so that the section goes through the base of the cone and with the vertex on the curved face of the

cone but on the same side of the centre of the base of the cone, then we get one branch of an

on the other half of the double cone.

Apollonius investigated the geometry of these conic sections and recorded them in his

the celestial mechanics of Kepler and Newton in the seventeenth century.