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 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. l.c.) 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.
Apollonius' 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unpublished discoveries of that great mathematician; however this may have been, there is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.
Apollonius was the author of several other works. The following are described by Pappus in the 7th book of his Mathematical Collections:--
Of the first of these an Arabic version is still extant, of which a translation was
edited by
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, l. c.) A solution of this problem was published by Robt. Simson.
Plane Loci. Restored by Robt. Simson," Glasg. 1749.
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 Op. vol. iii. p. 559,) which is supposed to be referred to in a fragment
of the 2nd book of Pappus, edited by Wallis.
Op. vol. iii. p. 597.) (Montucla, Hist. des
Mathém. vol. i.; Halley, Praef ad Ap. Conic.; Wenrich, de auct. Graec. versionibus et comment. Syriacis, Arab. Armen. Persicisque,
Lips. 1842; Pope Blount, Censur. Celeb. Auth.