Apollonius of Perga

Uploaded by Encyclopediax on Feb 18, 2013

Apollonius was a great mathematician, known by his contempories as " The Great

Geometer, " whose treatise Conics is one of the greatest scientific works from the ancient world.
Most of his other treatise were lost, although their titles and a general indication of their contents
were passed on by later writers, especially Pappus of Alexandria.

As a youth Apollonius studied in Alexandria ( under the pupils of Euclid, according to

Pappus ) and subsequently taught at the university there. He visited Pergamum, capital of a

Hellenistic kingdom in western Anatolia, where a university and library similar to those in

Alexandria had recently been built. While at Pergamum he met Eudemus and Attaluus, and he

wrote the first edition of Conics. He addressed the prefaces of the first three books of the final

edition to Eudemus and the remaining volumes to Attalus, whom some scholars identify as King
Attalus I of Pergamum.

It is clear from Apollonius' allusion to Euclid, Conon of Samos, and Nicoteles of Cyrene

that he made the fullest use of his predecessors' works. Book 1-4 contain a systematic account

of the essential principles of conics, which for the most part had been previously set forth by

Euclid, Aristaeus and Menaechmus. A number of theorems in Book 3 and the greater part of

Book 4 are new, however, and he introduced the terms parabola, eelipse, and hyperbola. Books

5-7 are clearly original. His genius takes its highest flight in Book 5, in which he considers

normals as minimum and maximum straight lines drawn from given points to the curve

( independently of tangent properties ), discusses how many normals can be drawn from

particular points, finds their feet by construction, and gives propositions determining the center

of curvature at any points and leading at once to the Cartesian equation of the evolute of any

conic.

The first four books of the Conics survive in the original Grrek and the next three in

Arabic translation. Book 8 is lost. The only other extant work of Apollonius is Cutting Off of a

Ratio ( or On Proportional Section ), in an Arabic translation. Pappus mentions five additional

works, Cutting off an Area ( or On Spatial Section ) , On Determinate Section, Tangencies, and

Plane Loci.

Tangencies embraced the following general problem : given three...