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Euclid,Archmedes, and Apollonius are the three mathematical giants of the
third centry B.C. Apollonius, who was younger than Archimedes by about
twenty-five years, was born about 262 B.C. in Perga, in southern Asia Minor.
The little that is known about the life of Apollonius is briefly told. As a young
man he went to Alexandria, studied under the successors if Euclid, and remained
there for a long
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time. Later, he visited Pergamum, in western Asia
Minor, where there was a recently founded university and library patterned
after that at Alexandria. he returned to Alexandria and died there sometime
around
190 B.C.
Although Apollonius was an astonomer of note and although he wrote on
a variety of mathenatical subjects, his chief bid to fame rests on his extraordinary
Conic Sections, a work that earned him the name, among his contemporaries,
of "The Great Geometer." Apollonius' Conic Sections, in eight books
and containing about 400 propositions, is a thorough investigation of these
curves, and completely srperseded the earlier works on the subject by menaechmus,
Aristaeus, and Euclid. Only the first seven of the eight books have
come down to us, the first four in Greek and the following three from a ninth-century
Arabian translation. The first four books, of which I,II,and III are
presunably founded on Euclid's previous work, deal with the general elementary
theory of conics, whereas the later books are devoted to more specialized
inverstigarions.
Prior to Apollonius, the Greeks derived the conic sections from three types
of cones of revolution, according as the vertex angle of the cone is less than,
equal to, or greater than a right angle. By cutting each of three such cines with
a plane perpendicuar to an element of the cone, an ellipse, parabola, and
hyperbola, respecticely, result. Only one branch of a hyperbola eas considered.
Apllonius, however, in Book I of his treatise, obtains all the conic
sections in the now-familiar way from one right or oblipue circular double cone.
The names ellipse, parabola, and Hyperbola were supploed by Apollonius
and were borrowed from the early Pythagpream terminology of application of
areas. When the Pythagoreans applied a rectangle to a line segment (that is,
placed the base of the rectangle along the line segment with ine end if the base
coinciding with one end of the segment), they said thet had a case of "ellipsis,"
"parabole," or "hyperbole" according as the base if the applied rectangle fell
short fo the line segment, exactly coincided with it, or exceeded it.
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