242 APOLLONIUS. (Bologna, 15G6). The 5th, 6th, and 7th were translated from an Arabic manuscript in the Medicean library by Abraham EchelJensis and Borelli, and edited in Latin (Florence, 1661); and by Rav-ius (Kilonii, 1669). Apollonius was the author of several other works. The following are described by Pappus in the 7th book of his Mathematical Collections : — Tlepi A6yov 'AiroTOfMrjs and Tlepl Xwpiov 'Airo- ro(jLT)s^ 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. contain- ing a given rectangle. Of the first of these an Arabic version is still extant, of which a translation was edited by Hal- ley, with a conjectural restoration of the second. (Oxon. 1706.) Ilepl Ai(api(T(i(vis Tofiris. 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, /. c.) A solution of this problem was published by Robt. Simson. TltpX T6iruv ^EirnriSuv^ " A Treatise in two books on Plane Loci. Restored by Robt. Simson," Glasg. 1749. Tlfpl 'Evcupuv, 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, 8vo.) U€p 'Nevaecav. To draw through a given point a right line so that a given portion of it should be intercepted between two given right lines. (Re- stored by S. Horsley, Oxon. 1770.) Proclus, in his commentary on Euclid, mentions two treatises, De CocJilea and De Perturbatis Jiationi/jus. Ptolemy {Magn. Const, lib. xii. init.) refers to Apollonius for the demonstration of certain pro- positions relative to the stations and retrogradations of the planets. Eutocius, in his commentary on the Dimensio Circuli of Archimedes, mentions an arithmetical work called ' CIkvtoSoov^ (see Wallis, 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 Mathem. vol. i. ; Halley, JPraef. ad Ap. Conic. ; Wenrich, de auct. Grraec. versionibus et comment. Si/riacis^ Arab. Armen. Persicisque, Lips. 1842; Pope Blount, Censur. Celeb. Auth.) [W. F. D.] APOLLONIUS TYANAEUS {'AiroWMos Tvavcuos), a Pythagorean philosopher, bom at Tyana in Cappadocia about four years before the Christian era. Much of his reputation is to be attributed to the belief in his magical or super- natural powers, and the parallel which modem and ancient writers have attempted to draw between his character and supposed miracles, and those of the Author of our religion. His life by Philostratus is a mass of incongruities and fables : whether it have any groundwork of historical truth, and whe- ther it were written wholly or partly with a con- troversial aim, are questions we shall be better prepared to discuss after giving an account of the ooatents of the work itself. APOLLONIUS. Apollonius, according to the narrative of his biographer, was of noble ancestrj', and claimed kindred with the founders of the city of Tyana. We need not stop to dispute the other story of the incarnation of the god Proteus, or refer it, with Tillemont, to demoniacal agency. At the age of fourteen he was placed xmder the care of Euthyde- mus, a rhetorician of Tarsus ; but, being disgusted at the luxury of the inhabitants, he obtained leave of his father and instructor to retire to the neigh- bouring town of Aegae. Here he is said to have studied the whole circle of the Platonic, Sceptic, Epicurean, and Peripatetic philosophy, and ended by giving his preference to the Pythagorean, in which he had been trained by Euxenus of Hera- clea. (Phil. L 7.) Immediately, as if the idea of treading in the footsteps of Pythagoras had seized him in his earliest youth, he began to exercise himself in the severe asceticism of the sect; ab- stained from animal food and woollen clothing, foreswore wine and the company of women, suf- fered his hair to grow, and betook himself to the temple of Aesculapius at Aegae, who was supposed to regard him with peculiar favour. He was re- called to Tyana, in the twentieth year of his age, by liis father's death : after dividing his inherifr- ance with a brother whom he is said to have re- claimed from dissolute living, and giving the greater part of what remained to his poorer rekitives (Phil, i. 13), he returned to the discipline of Pythagoras, and for five years preserved the mystic silence, during which alone the secret troths of philosophy were disclosed. At the end of the five years, he travelled in Asia Minor, going from city to city, and everywhere disputing, like Pythagoras, upon divine rites. There is a blank in his biography, at this period of his life, of about twenty years, during which we must suppose the same employ- ment to have continued, unless indeed we have reason to suspect that the received date of his birth has been anticipated twenty years. He was be- tween forty and fifty years old when he set out on his travels to the east ; and here Philostratus sends forth his hero on a voyage of discovery, in which we must be content rapidly to foUow him. From Aegae he went to Nineveh, where he met Damis, the future chronicler of his actions, and, proceeding on his route to India, he discoursed at Babylon with Bardanes, the Parthian king, and consulted the magi and Brahmins, who were sup- posed to have imparted to him some theurgic se- crets. He next visited Taxila, the capital of Phraortes, an Indian prince, where he met larchas, the chief of the Brahmins, and disputed with In- dian Gymnosophists already versed in Alexandrian philosophy. (Phil. iii. 51.) This eastern journey lasted five years : at its conclusion, he returned to the Ionian cities, where we first hear of his pre- tensions to miraculous power, founded, as it would seem, on the possession of some dixnne knowledge derived from the east. If it be true that the honours of a god were decreed to him at this period of his life, we are of course led to suspect some collusion with the priests (iv. 1), who are said to have referred the sick to him for relief. From Ionia he crossed over into Greece (iv. 11), visited the temples and oracles which lay in his way, everywhere disputing about religion, and assuming the authority of a divine legislator. At the Eleusinian mysteries he was rejected as a ma- gician, and did not obtain admission to them until
