extension of
the theory of irrationals expounded in Euclid, Book x., from binomial to
multinomial and from _ordered_ to _unordered_ irrationals (see extracts
from Pappus' comm. on Eucl. x., preserved in Arabic and published by
Woepcke, 1856). Lastly, in astronomy he is credited by Ptolemy with an
explanation of the motion of the planets by a system of epicycles; he
also made researches in the lunar theory, for which he is said to have
been called Epsilon ([epsilon]).

The best editions of the works of Apollonius are the following: (1)
_Apollonii Pergaei Conicorum libri quatuor, ex versione Frederici
Commandini_ (Bononiae, 1566), fol.; (2) _Apollonii Pergaei Conicorum
libri octo, et Sereni Antissensis de Sectione Cylindri et Coni libri
duo_ (Oxoniae, 1710), fol. (this is the monumental edition of Edmund
Halley); (3) the edition of the first four books of the Conics given
in 1675 by Barrow; (4) _Apollonii Pergaei de Sectione, Rationis libri
duo: Accedunt ejusdem de Sectione Spatii libri duo Restituti:
Praemittitur, &c., Opera et Studio Edmundi Halley_ (Oxoniae, 1706),
4to; (5) a German translation of the _Conics_ by H. Balsam (Berlin,
1861); (6) the definitive Greek text of Heiberg (_Apollonii Pergaei
quae Graece exstant Opera_, Leipzig, 1891-1893); (7) T.L. Heath,
_Apollonius, Treatise on Conic Sections_ (Cambridge, 1896); see also
H.G. Zeuthen, _Die Lehre van den Kegelschnitten im Altertum_
(Copenhagen, 1886 and 1902). (T. L. H.)

APOLLONIUS OF RHODES (RHODIUS), a Greek epic poet and grammarian, of
Alexandria, who flourished under the Ptolemies Philopator and Epiphanes
(222-181 B.C.). He was the pupil of Callimachus, with whom he
subsequently quarrelled. In his youth he composed the work for which he
is known--_Argonautica_, an epic in four books on the legend of the
Argonauts. When he read it at Alexandria, it was rejected through the
influence of Callimachus and his party. Disgusted with his failure,
Apollonius withdrew to Rhodes, where he was very successful as a
rhetorician, and a revised edition of his epic was well received. In
recognition of his talents the Rhodians bestowed the freedom of their
city upon him--the origin of his surname. Returning to Alexandria, he
again recited his poem, this time with general applause. In 196, Ptolemy
Epiphanes appointed him librarian of the Museum, which office he
probably held until his death. As to the _Argonautica_, Longinus' (_De
S