We can trace obligations to Meleager, Theocritus, Apollonius Rhodius and other Alexandrines, and amongst earlier writers to Homer, Pindar, Aeschylus and others.
In the days of its greatest power Rhodes became famous as a centre of pictorial and plastic art; it gave rise to a school of eclectic oratory whose chief representative was Apollonius Molon, the teacher of Cicero; it was the birthplace of the Stoic philosopher Panaetius; the home of the poet Apollonius Rhodius and the historian Posidonius.
5-65; Apollonius Rhodius, schol.
Apollonius, the commander of the Syrian garrison in Jerusalem, and Seron the commander of the army in Syria, came in turn against Judas and his bands and were defeated.
243-415; Apollonius Rhodius iii.
Apollonius of Tyana and the so-called Neopythagoreans drew similar ethical consequences from their eclectic study of Plato.
Ever afterwards, in memory of the threat of Heracles to ravage the land if Hylas were not found, the inhabitants of Kios every year on a stated day roamed the mountains, shouting aloud for Hylas (Apollonius Rhodius i.
In the course of constructions for surfaces to reflect to one and the same point (1) all rays in whatever direction passing through another point, (2) a set of parallel rays, Anthemius assumes a property of an ellipse not found in Apollonius (the equality of the angles subtended at a.
Apollonius of Rhodes who succeeded Eratosthenes as chief librarian at Alexandria (196 B.C.) reports in his Argonautica (iv.
Again, others (Apollonius Rhodius) laid down the course as up the Danube (Ister), from it into the Adriatic by a supposed mouth of that river, and on to Corcyra, where a storm overtook them.
In Greek, there are also extant the Argonautica of Apollonius Rhodius and the pseudo-Orpheus (4th century A.D.), and the account in Apollodorus (i.
9), based on the best extant authorities; in Latin, the imitation of Apollonius (a free translation or adaptation of whose Argonautica was made by Terentius Varro Atacinus in the time of Cicero) by Valerius Flaccus.
Her punishment is the subject of the famous group called "The Farnese Bull," by Apollonius and Tauriscus of Tralles, in the Naples museum (see Greek Art, Plate I.
Ptolemy's Almagest, the works of Apollonius, Archimedes, Diophantus and portions of the Brahmasiddhanta, were also translated.
It is given at some length in the fourth Pythian ode of Pindar, and forms the subject of the Argonautica of Apollonius Rhodius.
APOLLOS ('AiroXXd s; contracted from Apollonius), an Alexandrine Jew who after Paul's first visit to Corinth worked there in a similar way (1 Cor.
838) that he took the name from Apollonius, his master.
But there seems no reason for doubt; the great grammarians of imperial times (Apollonius Dyscolus and Herodian) were acquainted with the work in its present form, although, as was natural considering its popularity, additions and alterations may have been made later.
In recollection of its former services, the emperor Claudius remitted the heavy tribute which had been imposed on it; but the last remnant of its independence was taken away by Vespasian, who, in answer to a remonstrance from Apollonius of Tyana, taunted the inhabitants with having "forgotten to be free."
The other was written by a certain Apollonius forty years after the appearance of Montanus, consequently about 196.
Apollonius (Eusebius, Hist.
Apollonius Rhodius, i.
Vieta, however, did not accept it, as there existed a solution by means of the rule and the compass only, which he published himself in his Apollonius Gallus (1600).
26), and quoted by the anti-Montanist Apollonius (H.E.
The best extant specimen is the Argonautica of Apollonius Rhodius; the most characteristic is the Alexandra or Cassandra of Lycophron, the obscurity of which is almost proverbial.
The founder of the mathematical school was the celebrated Euclid (Eucleides); among its scholars were Archimedes; Apollonius of Perga, author of a treatise on Conic Sections; Eratosthenes, to whom we owe the first measurement of the earth; and Hipparchus, the founder of the epicyclical theory of the heavens, afterwards called the Ptolemaic system, from its most famous expositor, Claudius Ptolemaeus.
13; Apollonius Rhodius iv.
His chief poem of the later period was the Argonautae, closely modelled on the epic of Apollonius Rhodius.
It is a free imitation and in parts a translation of the work of Apollonius of Rhodes, already familiar to the Romans in the popular version of Varro Atacinus.
Priscian informs us in his preface that he has translated into Latin such precepts of the Greeks Herodian and Apollonius as seemed suitable, and added to them from Latin grammarians.
The latest name in the above list is that of Polybius, who died about 123 B.C. Apollonius Rhodius, Aratus and Theocritus were subsequently added to the " epic " poets.
The 2nd century is the age of the two great grammarians, Apollonius Dyscolus (the founder of scientific grammar and the creator of the study of Greek syntax) and his son Herodian, the larger part of whose principal work dealt with the subject of Greek accentuation.
Were brought from the East by Aurispa, who in 1423 returned with no less than two hundred and thirty-eight, including the celebrated Laurentian MS. of Aeschylus, Sophocles and Apollonius Rhodius.
At Florence the earliest editions of Homer (1488) and Isocrates (1493) had been produced by Demetrius Chalcondyles, while Janus Lascaris was the first to edit the Greek anthology, Apollonius Rhodius, and parts of Euripides, Callimachus and Lucian (1494-1496).
Suidas attributes numerous works to him, amongst others a number of letters to Apollonius of Tyana.
P. 520), who places them near the Caspian, also speaks of their ponies, and attributes to them Persian customs. In Apollonius Rhodius (iv.
This problem, also termed the " Apollonian problem," was demonstrated with the aid of conic sections by Apollonius in his book on Contacts or Tangencies; geometrical solutions involving the conic sections were also given by Adrianus Romanus, Vieta, Newton and others.
APOLLONIUS OF PERGA [PERGAEUS], Greek geometer of the Alexandrian school, was probably born some twenty-five years later than Archimedes, i.e.
After the Conics in eight Books had been written in a first edition, Apollonius brought out a second edition, considerably revised as regards Books i.-ii., at the instance of one Eudemus of Pergamum; the first three books were sent to Eudemus at intervals, as revised, and the later books were dedicated (after Eudemus' death) to King Attalus I.
Halley added in his edition (1710) a restoration of Book viii., in which he was guided by the fact that Pappus gives lemmas "to the seventh and eighth books" under that one heading, as well as by the statement of Apollonius himself that the use of the seventh book was illustrated by the problems solved in the eighth.
The degree of originality of the Conics can best be judged from Apollonius' own prefaces.
Apollonius' genius takes its highest flight in Book v., where he treats of 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 centre of curvature at any point and leading at once to the Cartesian equation of the evolute of any conic.
The other treatises of Apollonius mentioned by Pappus are - 1st, Aayov alroropii, Cutting off a Ratio; 2nd, Xcopiov a7rorop, Cutting off an Area; 3rd, Ocwpui j Av i Tog, Determinate Section; 4th, 'Eiraci)aL, Tangencies; 5th, 11-8364;1,o-as, Inclinations; 6th, Tinrot bri ret50t, Plane Loci.
Each of these was divided into two books, and, with the Data, the Porisms and Surface-Loci of Euclid and the Conics of Apollonius were, according to Pappus, included in the body of the ancient analysis.
Anderson of Aberdeen, in the supplement to his Apollonius Redivivus (Paris, 1612), but by far the best is by Robert Simson, Opera quaedam reliqua (Glasgow, 1776).
Vieta thereupon proposed a simpler construction, and restored the whole treatise of Apollonius in a small work, which he entitled Apollonius Gallus (Paris, 1600).
Other works of Apollonius are referred to by ancient writers, viz.
(1) Ile /3 c Tou irvpiov, On the Burning-Glass, where the focal properties of the parabola probably found a place; (2) Hepi On the Cylindrical Helix (mentioned by Proclus); (3) a comparison of the dodecahedron and the icosahedron inscribed in the same sphere; (4) `H Ka06Xov lrpa-yµareta, perhaps a work on the general principles of mathematics in which were included Apollonius' criticisms and suggestions for the improvement of Euclid's Elements; (5) ' (quick bringing-to-birth), in which, according to Eutocius, he showed how to find closer limits for the value of 7r than the 37 and 3,4-A of Archimedes; (6) an arithmetical work (as to which see Pappus) on a system of expressing large numbers in language closer to that of common life than that of Archimedes' Sand-reckoner, and showing how to multiply such large numbers; (7) a great 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.
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.
Heath, Apollonius, Treatise on Conic Sections (Cambridge, 1896); see also H.