### Topic Page: Apollonius, of Perga

**Apollonius of Perga**from

*Philip's Encyclopedia*

Greek mathematician and astronomer. He built on the foundations laid by Euclid. In Conics, he showed that an ellipse, a parabola, and a hyperbola can be obtained by taking plane sections at different angles through a cone. In astronomy, he described the motion of the planets in terms of epicycles, which remained the basis of the system used until the time of Copernicus.

**Apollonius of Perga (c. 245-c.190 BC)**from

*The Hutchinson Dictionary of Scientific Biography*

Place: Greece

Subject: biography, maths and statistics

Greek mathematician whose treatise on conic sections represents the final flowering of Greek mathematics.

Apollonius was born early in the reign of Ptolemy Euergetes, king of Egypt, in the Greek town of Perga in southern Asia Minor (now part of Turkey). Little is known of his life. It is thought that he may have studied at the school established by Euclid at Alexandria, especially since much of his work was built on Euclidean foundations.

Apollonius' fame rests on his eight-volume treatise, The Conics, seven volumes of which are extant. The first four books consisted of an introduction and a statement of the state of mathematics provided by his predecessors. In the last four volumes Apollonius put forth his own important work on conic sections, the foundation of much of the geometry still used today in astronomy and ballistic science.

Apollonius described how a cone could be cut so as to produce circles, ellipses, parabolas, and hyperbolas; the last three terms were coined by him. He investigated the properties of each and showed that they were all interrelated because, as he stated, ‘any conic section is the locus of a point that moves so that the ratio of its distance, f, from a fixed point (the focus) to its distance, d, from a straight line (the directrix) is a constant’. Whether this constant, e, is greater than, equal to, or less than one determines which of the three types of curve the function represents. For a hyperbola e > 1; for a parabola e = 1; and for an ellipse e < 1. At the time, Apollonius' discoveries lay in the realm of pure mathematics; it was only later that their immensely valuable application became apparent, when it was discovered that conic sections form the paths, or loci, followed by planets and projectiles in space.

Other than The Conics, only one treatise of Apollonius survives; it is entitled Cutting off a Ratio. It was found written in Arabic and was translated into Latin in 1706, but is of little mathematical significance.

Apollonius' brilliant concept of geometry was a milestone in the understanding of mechanics, navigation, and astronomy. Above all, his work on epicircles and ellipses played a major part in Ptolemy's working out of the cosmology that would dominate western astronomy from the 2nd century AD to the 16th century.

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