Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/201

APOLLONIUS 187 APOLLONIUS, surnamed MOLD, a distinguished Greek rhetorician, the instructor of Csesar and of Cicero. Born at Alabanda, he settled at Rhodes, and in the dictatorship of Sulla, was sent as ambassador from the Rhodians to Rome. He was the first Greek who addressed the senate without the aid of an interpreter. Cicero renewed his studies under him when he afterwards visited Rhodes on his return from Asia. The works of Apollonius have perished. Another rhetorician of the same name, likewise a native of Alabanda, and an inhabitant of Rhodes, was surnamed The Effem inate (6 MaXaKos). Both are mentioned by Cicero with high respect, Cicero, Brutus, 89, 90, 91 ; De Inv. i. 56; De Oral. i. 17, 28 ; Quintal, iii. 1, 16 ; xii. 6, 7, &c. APOLLOXIUS, surnamed DYSCOLTJS (ArcncoA.os), or The Crabbed, was a native of Alexandria, and lived in the reigns of Hadrian and Antoninus Pius. He was the first systematic writer on grammar, and is styled by Priscian " Grammaticorum Frinceps." Of his extant grammatical works the principal one is the treatise On Syntax, the best edition of which is that of Bekker, Berlin, 1817. APOLLONIUS, a Greek epic poet, surnamed RHODITJS, from his long residence in Rhodes, though he is supposed to have been a native of Alexandria, He is known to us as the author of the Argonautica, a poem which he began while in youth, studying under the poet Callimachus. His master is supposed to have slighted the production of the youthful Apollonius, and their connection ended in the most violent enmity, though we are ignorant of the parti culars of their quarrel. The disappointed youth retired to Rhodes, where he is conjectured to have polished and completed his svork, supporting himself by the profession of rhetoric, and receiving from the Rhodians the freedom of their city. He was at length recalled to Alexandria to succeed Eratosthenes in the care of the great library about 194 B.C., in the reign of Ptolemy Euergetes, who had been educated by Aristarchus, and rivalled his predecessors in the munificent encouragement he gave to learning. The only extant work of Apollonius is his poem above mentioned, in four books, on the Argonautic expedition. Both Longinus and Quintilian have assigned to this work the mortifying character of mediocrity. It was first printed at Florence in 1496, with the ancient Greek Scholia, in a 4to volume, now exceedingly rare. An excellent edition was published by Brunck in 1780, and another by Beck, in 1797 ; but the best is that of Professor Schafer (Leipsic, 2 vols. 8vo, 1810-13). The poem was translated into English verse by Fawkes and Green in 1780; another translation in English verse, with critical notes, was pub lished by W. Preston in 1803. APOLLONIUS of TKALLES and his brother TAUKISCUS were the sculptors of the famous Farnese Bull, a group representing Zethus and Amphion tying the revengeful Dirce to the tail of a wild bull. This work is now at Naples. There were several other sculptors named Apol lonius. APOLLONIUS, a grammarian of Alexandria, author of a Homeric Lexicon, Aea? O/r^piKcu, which was first pub lished by Villoison, in two vols. fol., at Paris, in 1773. APOLLONIUS of PERGA (PEEGJEUS), next to Archi medes the most illustrious of the ancient Greek geome tricians, was born probably about 250 B.C., and died during the reign of Ptolemy Philopator (222-205 B.C.), flourishing thus about forty years later than Archimedes. He studied at Alexandria under the successors of Euclid, and is one of the brightest ornaments of that famous mathematical school. But few of the mathematical works of Apollonius have escaped the ravages of time. Of the greater part we have merely the names and general description given by Pappus in his preface to book vii. of the Matliematical Collections. His treatise on the Conic /Sections gained him the title of The Great Geometer, and is that by which his fame has been transmitted to modern times. It is not, indeed, to be for a moment supposed that Apollonius discovered all, or even the greater part, of the demonstrations which he gives, any more than that Euclid devised the propositions that go by his name. Pappus mentions several treatises on conies known to have existed previously in particular the five books of Aristseus " The Ancient " (350 B.C.) on Solid Loci ; and there can be little doubt that Apollonius availed himself of these, as well as of the discoveries of Conon, Euclid, Eudoxus, Menechmus, Nicoteles, Thrasidseus, and others, who had explored the way before him. At this distance of time we cannot distinguish the original from the borrowed propositions ; but, though it is certain that he both added to and improved upon the existing theory of conies, the mere embodying in a complete and logical treatise of a number of miscellaneous theorems was in itself a work of great mathematical genius. Eutocius informs us that Apollonius was the first to show that all the three sections may be cut from the same cone, by varying the position of the intersecting plane ; for previous authors had supposed the plane of section always perpendicular to the slant side of the cone, an hypothesis which requires that the three sections be cut from cones of dif ferent species, namely, the parabola from a right-angled cone, the ellipse from one with an obtuse, and the hyperbola from one with an acute vertical angle. But Archimedes, as Ubaldus shows in his commentary on the jEquipon- derantes, had been acquainted with this fact. Pappus ascribes to Apollonius the names by which the three sections are now distinguished ; the term Parabola, however, occurs in the writings of Archimedes. Of the Conicorum Libri Octo of Apollonius, unfortunately only four have reached us directly through the original Greek. Three more have been preserved in an Arabic version, but the eighth has never been found. Though many attempts had been made to discover the last four books, they continued to be regarded as lost till 1658, when Borelli, the celebrated author of the treatise De motu Animalium, discovered in the Medici library at Florence an Arabic manuscript, entitled Apollonii Pergaei Conicorum Libri Octo. With the assistance of Abraham Ecchellensis he translated and published in 1661 the fifth, sixth, and seventh books; but the eighth, notwithstanding the title, was wanting. Some years previously Golius, Oriental professor at Leyden, had returned from the East with an Arabic version of the whole seven books, and had projected the publication of a transla tion ; but it never appeared. A note appended to the MS. of Golius stated that the eighth book had never been translated into Arabic. It was long a favourite problem with geometers to attempt to restore the lost books of Apollonius, that is, to infer from the general nature of their contents, as described by Pappus, the propositions they had contained. Maurolycus, a Sicilian geometer of the 16th century, Viviani, the last favourite pupil of Galileo, Fermat, Halley, Simson, and a number of others, all attempted this with more or less success. Halley, guided by the descriptions of Pappus, and the assertion that hi? preliminary lemmas to the seventh book really belonged tc the eighth, as well as by the statement of Apollonius him self that the eighth was a continuation of the seventh book, restored this book for the edition issued by the Oxford Press in 1710, the only edition of the Greek text that has as yet appeared. The last four books of the conies of Apollonius formed the chief part of the higher geometiy of the ancients ; and they present some elegant geometrical solutions of problems, which offer considerable difficulty even to the modern analytical method. For example, the

fifth book treats of the greatest and least lines that can be