This essay *Apollonius of Perga* has a total of 604 words and 4 pages.
Apollonius of Perga

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 things,

each of which may be a point, straight line, or circle, construct a circle

tangent to the three. Sometimes known as the problem of Apollonius, the most

difficult case arises when the three given things are circles.

Of the other works of Apollonius referred to by ancient writers, one, On

the Burning Mirror, concerned optics. Apollonius demonstrated that parallel

light rays striking a spherical mirror would not be reflected to the center of

sphericity, as was previously believed. The focal properties of the parabolic

mirror were also discussed. A work on entitled On the Cylindrical Helix is

mentioned by Proclus. Apollonius also wrote Comparison of the Dodecahedron and

the Icosahedron, considering the case in which they are inscribed in the same

sphere. According to Eutocius, in Apollonius\' work Quick Delivery, closer

limits for the value of Pi than the 3 1/7 and 3 10/71 of Archimedes were

calculated. In a work of unknown title Apollonius developed his system of

tetrads, a method for expressing and multiplying large numbers. His On

Unordered Irrationals extended the theory of irrationals originally advanced by

Eudoxus of Cnidus and found in Book 10 of Euclid\'s Elements.

Lastly, from references in Ptolemy\'s Almagest, it is known that

Apollonius introduced the systems of eccentric and epicyclic motion to explain

planetary motion. Of particular interest was his determination of the points

where a planet appears stationary.

Bibliography

1. Boyer, Carl B. , The History of Analytic Geometry (1956) McGraw - Hill

2. Heath, Thomas L. , Manual of Greek Mathematics (1921; repr. 1981)

3. Van der Waerden, Bartel L., Science Awakening (1961).

Category: Science
## Topics Related to Apollonius of Perga

Ancient Greek mathematicians, Apollonius of Perga, Euclid, Eutocius of Ascalon, Conic section, Nicoteles of Cyrene, Problem of Apollonius, Pappus of Alexandria, Conon of Samos, Apollonius, Archimedes, Analytic geometry

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