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).
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