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PERGI (Ancient city) TURKEY
Apollonius of Perga, in Pamphylia. A Greek mathematician called
"the Geometer," who lived at Pergamus and Alexandria in the first century
B.C., and wrote a work on Conic Sections in eight books, of which we have only
the first four in the original--the fifth, sixth, and seventh in an Arabic translation,
and the eighth in extracts.
This text is from: Harry Thurston Peck, Harpers Dictionary of Classical Antiquities. Cited Oct 2002 from The Perseus Project URL below, which contains interesting hyperlinks
Apollonius, surnamed Pergaeus, from Perga in Pamphylia, his native city, a mathematician
educated at Alexandria under the successors of Euclid. He was born in the reign
of Ptolemy Euergetes (Eutoc. Comm. in Ap. Con. lib. i.), and died under Philopator,
who reigned B. C. 222- 205 (Hephaest. ap. Phot. cod. cxc.). He was, therefore,
probably about 40 years younger than Archimedes. His geometrical works were held
in such esteem, that they procured for him the appellation of the Great Geometer
(Eutoc.). He is also mentioned by Ptolemy as an astronomer, and is said to have
been called by the sobriquet of e, from his fondness for observing the moon, the
shape of which was supposed to resemble that letter. His most important work,
the only considerable one which has come down to our time, was a treatise on Conic
Sections in eight books. Of these the first four, with the commentary of Eutocius,
are extant in Greek; and all but the eighth in Arabic. The eighth book seems to
have been lost before the date of the Arabic versions. We have also introductory
lemmata to all the eight, by Pappus. The first four books probably contain little
more than the substance of what former geometers had done; they treat of the definitions
and elementary properties of the conic sections, of their diameters, tangents,
asymptotes, mutual intersections, &c. But Apollonius seems to lay claim to originality
in most of what follows (See the introductory epistle to the first book). The
fifth treats of the longest and shortest right lines (in other words the normals)
which can be drawn from a given point to the curve. The sixth of the equality
and similarity of conic sections; and the seventh relates chiefly to their diameters,
and rectilinear figures described upon them.
We learn from Eutocius (Comm. in lib. i.), that Heraclius in his life
of Archimedes accused Apollonius of having appropriated to himself in this work
the unpublished discoveries of that great mathematician; however this may have
been, there is truth in the reply quoted by the same author from Geminus: that
neither Archimedes nor Apollonius pretended to have invented this branch of Geometry,
but that Apollonius had introduced a real improvement into it. For whereas Archimedes,
according to the ancient method, considered only the section of a right cone by
a plane perpendicular to its side, so that the species of the curve depended upon
the angle of the cone; Apollonius took a more general view, conceiving the curve
to be produced by the intersection of any plane with a cone generated by a right
line passing always through the circumference of a fixed circle and any fixed
point. The principal edition of the Conics is that of Halley, "Apoll. Perg. Conic,
lib. viii., &c.," Oxon. 1710. The eighth book is a conjectural restoration founded
on the introductory lemmata of Pappus. The first four books were translated into
Latin, and published by J. Bapt. Memus (Venice, 1537), and by Commandine (Bologna,
1566). The 5th, 6th, and 7th were translated from an Arabic manuscript in the
Medicean library by Abraham Echellensis and Borelli, and edited in Latin (Florence,
1661); and by Ravius (Kilonii, 1669).
Apollonius was the author of several other works. The following are described
by Pappus in the 7th book of his Mathematical Collections:
Peri Logou Apotomes and Peri Choriou Apotomes, in which it was shewn
how to draw a line through a given point so as to cut segments from two given
lines, 1st. in a given ratio, 2nd. containing a given rectangle. Of the first
of these an Arabic version is still extant, of which a translation was edited
by Halley, with a conjectural restoration of the second. (Oxon. 1706.)
Peri Diorimenes Tomes. To find a point in a given straight line such,
that the rectangle of its distances from two given points in the same should fulfil
certain conditions (See Pappus). A solution of this problem was published by Robt.
Simson. Peri Topon Epipedon, " A Treatise in two books on Plane Loci. Restored
by Robt. Simson" Glasg. 1749.
Peri Epaphon, in which it was proposed to draw a circle fulfilling any
three of the conditions of passing through one or more of three given points,
and touching one or more of three given circles and three given straight lines.
Or, which is the same thing, to draw a circle touching three given circles whose
radii may have any magnitude, including zero and infinity. (Ap. de Tactionibus
quae supers., ed. J. G. Camerer. Goth. et Amst. 1795)
Peri Neuseon, To draw through a given point a right line so that a given
portion of it should be intercepted between two given right lines. (Restored by
S. Horsley, Oxon. 1770.)
Proclus, in his commentary on Euclid, mentions two treatises. De Cochlea and De Perturbatis Rationibus.
Ptolemy (Magn. Const. lib. xii. init.) refers to Apollonius for the
demonstration of certain propositions relative to the stations and retrogradations
of the planets.
Eutocius, in his commentary on the Dimensio Circuli of Archimedes,
mentions an arithmetical work called Okutoboon, which is supposed to be referred
to in a fragment of the 2nd book of Pappus, edited by Wallis. (Op. vol. iii. p.
597.)
This text is from: A dictionary of Greek and Roman biography and mythology, 1873 (ed. William Smith). Cited Oct 2005 from The Perseus Project URL below, which contains interesting hyperlinks
Damophyle Damophule), a lyric poetess of Pamphylia, was the pupil and companion of Sappho (about 611 B. C.). Like Sappho, she instructed other damsels. She composed erotic poems and hymns. The hymns which were sung to Artemis at Perga were said to have been composed by her after the manner of the Aeolians and Pamphylians. (Philost. Vit. Apollon. i. 30.)
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