The Project Gutenberg eBook ofEncyclopaedia Britannica, 11th Edition, "Apollodorus" to "Aral"

The Project Gutenberg eBook ofEncyclopaedia Britannica, 11th Edition, "Apollodorus" to "Aral"This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.Title: Encyclopaedia Britannica, 11th Edition, "Apollodorus" to "Aral"Author: VariousRelease date: October 8, 2010 [eBook #34047]Most recently updated: January 7, 2021Language: EnglishCredits: Produced by Marius Masi, Don Kretz and the OnlineDistributed Proofreading Team at https://www.pgdp.net*** START OF THE PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA, 11TH EDITION, "APOLLODORUS" TO "ARAL" ***

This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.

Title: Encyclopaedia Britannica, 11th Edition, "Apollodorus" to "Aral"Author: VariousRelease date: October 8, 2010 [eBook #34047]Most recently updated: January 7, 2021Language: EnglishCredits: Produced by Marius Masi, Don Kretz and the OnlineDistributed Proofreading Team at https://www.pgdp.net

Title: Encyclopaedia Britannica, 11th Edition, "Apollodorus" to "Aral"

Author: Various

Release date: October 8, 2010 [eBook #34047]Most recently updated: January 7, 2021

Language: English

Credits: Produced by Marius Masi, Don Kretz and the OnlineDistributed Proofreading Team at https://www.pgdp.net

*** START OF THE PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA, 11TH EDITION, "APOLLODORUS" TO "ARAL" ***

Articles in This Slice

APOLLODORUS,an Athenian painter, who flourished at the end of the 5th centuryB.C.He is said to have introduced great improvements in perspective and chiaroscuro. What these were it is impossible to say: perspective cannot have been in his day at an advanced stage. Among his works were an Odysseus, a priest in prayer, and an Ajax struck by lightning.

APOLLODORUS,an Athenian grammarian, pupil of Aristarchus and Panaetius the Stoic, who lived about 140B.C.He was a prolific and versatile writer. There is extant under his name a treatise on the gods and the heroic age, entitledΒιβλιοθἠκη, a valuable authority on ancient mythology. Modern critics are of opinion that, if genuine, it is an abridgment of a larger work by him (Περὶ θεῶν).

Edition, with commentary, by Heyne (1803); text by Wagner (1894) (Mythographi Graeci, vol. i. Teubner series). Amongst other works by him of which only fragments remain, collected in Müller,Fragmenta Historicorum Graecorum, may be mentioned:Χρονικά, a universal history from the fall of Troy to 144B.C.;Περιήγησις, a gazetteer written in iambics;Περὶ Νεῶν, a work on the Homeric catalogue of ships; and a work on etymology (Έτυμολογίαι).

APOLLODORUS,of Carystus in Euboea, one of the most important writers of the New Attic comedy, who flourished at Athens between 300 and 260B.C.He is to be distinguished from an older Apollodorus of Gela (342-290), also a writer of comedy, a contemporary of Menander. He wrote 47 comedies and obtained the prize five times. Terence borrowed hisHecyraandPhormiofrom theΈκυράandΈπιδικαζόμενοςof Apollodorus.

Fragments in Koch,Comicorum Atticorum Fragmenta, ii. (1884); see also Meineke,Historia Critica Comicorum Graecorum(1839).

APOLLODORUS,of Damascus, a famous Greek architect, who flourished during the 2nd centuryA.D.He was a favourite of Trajan, for whom he constructed the stone bridge over the Danube (A.D.104-105). He also planned a gymnasium, a college, public baths, the Odeum and the Forum Trajanum, within the city of Rome; and the triumphal arches at Beneventum and Ancona. The Trajan column in the centre of the Forum is celebrated as being the first triumphal monument of the kind. On the accession of Hadrian, whom he had offended by ridiculing his performances as architect and artist, Apollodorus was banished, and, shortly afterwards, being charged with imaginary crimes, put to death (Dio Cassius lxix. 4). He also wrote a treatise onSiege Engines(Πολιορκητικά), which was dedicated to Hadrian.

APOLLONIA,the name of more than thirty cities of antiquity. The most important are the following: (1) An Illyrian city (known as Apolloniaκατ᾽ Έπίδαμνονorπρὸς Έπιδάμνῳ) on the right bank of the Aous, founded by the Corinthians and Corcyraeans. It soon became a place of increasing commercial prosperity, as the most convenient link between Brundusium and northern Greece, and as one of the starting-points of the Via Egnatia. It was an important military post in the wars against Philip and during the civil wars of Pompey and Caesar, and towards the close of the Roman republic acquired fame as a seat of literature and philosophy. Here Augustus was being educated when the death of Caesar called him to Rome. It seems to have sunk with the rise of Aulon, and few remains of its ruins are to be found. The monastery of Pollina stands on a hill which probably is part of the site of the old city. (2) A Thracian city on the Black Sea (afterwards Sozopolis, and now Sizeboli), colonized by the Milesians, and famous for its colossal statue of Apollo by Calamis, which Lucullus removed to Rome.

APOLLONIUS,surnamedὁ δύσκολος(“the Surly or Crabbed”), a celebrated grammarian of Alexandria, who lived in the reigns of Hadrian and Antoninus Pius. He spent the greater part of his life in his native city, where he died; he is also said to have visited Rome and attracted the attention of Antoninus. He was the founder of scientific grammar and is styled by Prisciangrammaticorum princeps. Four of his works are extant:On Syntax, ed. Bekker, 1817; and three smaller treatises, onPronouns,ConjunctionsandAdverbs, ed. Schneider, 1878.

Grammatici Graeci, i. in Teubner series; Egger,Apollonius Dyscole(1854).

APOLLONIUS,surnamedὁ μαλακός(“the Effeminate”), a Greek rhetorician of Alabanda in Caria, who flourished about 120B.C.After studying under Menecles, chief of the Asiatic school of oratory, he settled in Rhodes, where he taught rhetoric, among his pupils being Mark Antony.

APOLLONIUS,surnamed “the Sophist,” of Alexandria, a famous grammarian, who probably lived towards the end of the 1st centuryA.D.He was the author of a Homeric lexicon (Λέξεις Όμηρικαί), the only work of the kind we possess. His chief authorities were Aristarchus and Apion’s Homeric glossary.

Edition by Villoison (1773), I. Bekker (1833); Leyde,De Apollonii Sophistae Lexico Homerico(1885); E.W.B. Nicholson on a newly discovered fragment inClassical Review(Nov. 1897).

APOLLONIUS MOLON(sometimes called simplyMolon), a Greek rhetorician, who flourished about 70B.C.He was a native of Alabanda, a pupil of Menecles, and settled at Rhodes. He twice visited Rome as an ambassador from Rhodes, and Cicero and Caesar took lessons from him. He endeavoured to moderate the florid Asiatic style and cultivated an “Atticizing” tendency. He wrote on Homer, and, according to Josephus, violently attacked the Jews.

See C. Müller,Fragmenta Historicorum Graecorum, iii.; E. Schürer,History of the Jewish People, iii. (Eng. tr. 1886).

APOLLONIUS OF PERGA[Pergaeus], Greek geometer of the Alexandrian school, was probably born some twenty-five years later than Archimedes,i.e.about 262B.C.He flourished in the reigns of Ptolemy Euergetes and Ptolemy Philopator (247-205B.C.). His treatise onConicsgained him the title of The Great Geometer, and is that by which his fame has been transmitted to modern times. All his numerous other treatises have perished, save one, and we have only their titles handed down, with general indications of their contents, by later writers, especially Pappus. After theConicsin 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. (241-197B.C.). Only four Books have survived in Greek; three more are extant in Arabic; the eighth has never been found. Although a fragment has been found of a Latin translation from the Arabic made in the 13th century, it was not until 1661 that a Latin translation of Books v.-vii. was available. This was made by Giovanni Alfonso Borelli and Abraham Ecchellensis from the free version in Arabic made in 983 by Abu ’l-Fath of Ispahan and preserved in a Florence MS. But the best Arabic translation is that made as regards Books i.-iv. by Hilal ibn Abi Hilal (d. about 883), and as regards Books v.-vii. by Tobit ben Korra (836-901). Halley used for his translation an Oxford MS. of this translation of Books v.-vii., but the best MS. (Bodl. 943) he only referred to in order to correct his translation, and it is still unpublished except for a fragment of Book v. published by L. Nix with German translation (Drugulin, Leipzig, 1889). 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 theConicscan best be judged from Apollonius’ own prefaces. Books i.-iv. form an “elementary introduction,”i.e.contain the essential principles; the rest are specialized investigations in particular directions. For Books i.-iv. he claims only that the generation of the curves and their fundamental properties in Book i. are worked out more fully and generally than they were in earlier treatises, and that a number of theorems in Book iii. and the greater part of Book iv. are new. That he made the fullest use of his predecessors’ works, such as Euclid’s four Books on Conics, is clear from his allusions to Euclid, Conon and Nicoteles. The generality of treatment is indeed remarkable; he gives as the fundamental property of all the conics the equivalent of the Cartesian equation referred toobliqueaxes (consisting of a diameter and the tangent at its extremity) obtained by cutting an oblique circular cone in any manner, and the axes appear only as a particular case after he has shown that the property of the conic can be expressed in the same form with reference to any new diameter and the tangent at its extremity. It is clearly the form of the fundamental property (expressed in the terminology of the “application of areas”) which led him to call the curves for the first time by the namesparabola,ellipse,hyperbola. Books v.-vii. are clearly original. 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,Λόγου ἀποτομή,Cutting off a Ratio; 2nd,Χωρίου ἀποτομή,Cutting of an Area; 3rd,Διωρισμένη τομή,Determinate Section; 4th,Έπαφαί,Tangencies; 5th,Νεύσεις,Inclinations; 6th,Τόποι ἐπίπεδοι,Plane Loci. Each of these was divided into two books, and, with theData, thePorismsandSurface-Lociof Euclid and theConicsof Apollonius were, according to Pappus, included in the body of the ancient analysis.

1st.De Rationis Sectionehad for its subject the resolution of the following problem: Given two straight lines and a point in each, to draw through a third given point a straight line cutting the two fixed lines, so that the parts intercepted between the given points in them and the points of intersection with this third line may have a given ratio.

2nd.De Spatii Sectionediscussed the similar problem which requires the rectangle contained by the two intercepts to be equal to a given rectangle.

An Arabic version of the first was found towards the end of the 17th century in the Bodleian library by Dr Edward Bernard, who began a translation of it; Halley finished it and published it along with a restoration of the second treatise in 1706.

3rd.De Sectione Determinataresolved the problem: Given two, three or four points on a straight line, to find another point on it such that its distances from the given points satisfy the condition that the square on one or the rectangle contained by two has to the square on the remaining one or the rectangle contained by the remaining two, or to the rectangle contained by the remaining one and another given straight line, a given ratio. Several restorations of the solution have been attempted, one by W. Snellius (Leiden, 1698), another by Alex. Anderson of Aberdeen, in the supplement to hisApollonius Redivivus(Paris, 1612), but by far the best is by Robert Simson,Opera quaedam reliqua(Glasgow, 1776).

4th.De Tactionibusembraced the following general problem: Given three things (points, straight lines or circles) in position, to describe a circle passing through the given points, and touching the given straight lines or circles. The most difficult case, and the most interesting from its historical associations, is when the three given things are circles. This problem, which is sometimes known as the Apollonian Problem, was proposed by Vieta in the 16th century to Adrianus Romanus, who gave a solution by means of a hyperbola. Vieta thereupon proposed a simpler construction, and restored the whole treatise of Apollonius in a small work, which he entitledApollonius Gallus(Paris, 1600). A very full and interesting historical account of the problem is given in the preface to a small work of J.W. Camerer, entitledApollonii Pergaei quae supersunt, ac maxime Lemmata Pappi in hos Libras, cum Observationibus, &c. (Gothae, 1795, 8vo).

5th.De Inclinationibushad for its object to insert a straight line of a given length, tending towards a given point, between two given (straight or circular) lines. Restorations have been given by Marino Ghetaldi, by Hugo d’Omerique (Geometrical Analysis, Cadiz, 1698), and (the best) by Samuel Horsley (1770).

6th.De Locis Planisis a collection of propositions relating to loci which are either straight lines or circles. Pappus gives somewhat full particulars of the propositions, and restorations were attempted by P. Fermat (Oeuvres, i., 1891, pp. 3-51), F. Schooten (Leiden, 1656) and, most successfully of all, by R. Simson (Glasgow, 1749).

Other works of Apollonius are referred to by ancient writers, viz. (1)Περὶ τοῦ πυρίου,On the Burning-Glass, where the focal properties of the parabola probably found a place; (2)Περὶ τοῦ κοχλίου,On the Cylindrical Helix(mentioned by Proclus); (3) a comparison of the dodecahedron and the icosahedron inscribed in the same sphere; (4)Ή καθόλου πραγματεία, perhaps a work on the general principles of mathematics in which were included Apollonius’ criticisms and suggestions for the improvement of Euclid’sElements; (5)Ώκυτόκιον(quick bringing-to-birth), in which, according to Eutocius, he showed how to find closer limits for the value of π than the 31⁄7and 310⁄71of Archimedes; (6) an arithmetical work (as to which seePappus) 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 fromorderedtounorderedirrationals (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 (ε).

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 theConicsby H. Balsam (Berlin, 1861); (6) the definitive Greek text of Heiberg (Apollonii Pergaei quae Graeceexstant 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 (222-181B.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 theArgonautica, Longinus’ (De Sublim. p. 54, 19) and Quintilian’s (Instit, x. 1, 54) verdict of mediocrity seems hardly deserved; although it lacks the naturalness of Homer, it possesses a certain simplicity and contains some beautiful passages. There is a valuable collection of scholia. The work, highly esteemed by the Romans, was imitated by Virgil (Aeneid, iv.), Varro Atacinus, and Valerius Flaccus. Marianus (aboutA.D.500) paraphrased it in iambic trimeters. Apollonius also wrote epigrams; grammatical and critical works; andΚτίσεις(the foundations of cities).

Editio Princeps(Florence, 1496); Merkel-Keil (with scholia, 1854); Seaton (1900). English translations: Verse, by Greene (1780); Fawkes (1780); Preston (1811); Way (1901); Prose by Coleridge (1889); see also Couat,La Poésie alexandrine; Susemihl,Geschichte der griech. Lit. in der alexandnnischen Zeit.

APOLLONIUS OF TRALLES(in Caria), a Greek sculptor, who flourished in the 2nd centuryB.C.With his brother Tauriscus, he executed the marble group known as the Farnese Bull, representing Zethus and Amphion tying the revengeful Dirce to the tail of a wild bull.

SeeGreek Art, pl. i. fig. 51.

APOLLONIUS OF TYANA,a Greek philosopher of the Neo-Pythagorean school, born a few years before the Christian era. He studied at Tarsus and in the temple of Asclepius at Aegae, where he devoted himself to the doctrines of Pythagoras and adopted the ascetic habit of life in its fullest sense. He travelled through Asia and visited Nineveh, Babylon and India, imbibing the oriental mysticism of magi, Brahmans and gymnosophists. The narrative of his travels given by his disciple Damis and reproduced by Philostratus is so full of the miraculous that many have regarded him as an imaginary character. On his return to Europe he was saluted as a magician, and received the greatest reverence from priests and people generally. He himself claimed only the power of foreseeing the future; yet in Rome it was said that he raised from death the body of a noble lady. In the halo of his mysterious power he passed through Greece, Italy and Spain. It was said that he was accused of treason both by Nero and by Domitian, but escaped by miraculous means. Finally he set up a school at Ephesus, where he died, apparently at the age of a hundred years. Philostratus keeps up the mystery of his hero’s life by saying, “Concerning the manner of his death,if he did die, the accounts are various.” The work of Philostratus composed at the instance of Julia, wife of Severus, is generally regarded as a religious work of fiction. It contains a number of obviously fictitious stories, through which, however, it is not impossible to discern the general character of the man. In the 3rd century, Hierocles (q.v.) endeavoured to prove that the doctrines and the life of Apollonius were more valuable than those of Christ, and, in modern times, Voltaire and Charles Blount (1654-1693), the English freethinker, have adopted a similar standpoint. Apart from this extravagant eulogy, it is absurd to regard Apollonius merely as a vulgar charlatan and miracle-monger. If we cut away the mass of mere fiction which Philostratus accumulated, we have left a highly imaginative, earnest reformer who laboured to infuse into the flaccid dialectic of paganism a saner spirit of practical morality.

See L. Dyer,Studies of the Gods in Greece(New York, 1891); A. Chassang,Le Merveilleux dans l’antiquité(1882); D.M. Tredwell,Sketch of the Life of Apollonius of Tyana(New York, 1886); F.C. Baur,Apollonius von Tyana und Christus, ed. Ed. Zeller (Leipzig, 1876,—an attempt to show that Philostratus’s story is merely a pagan counterblast to the New Testament history); J. Jessen,Apollonius v. Tyana und sein Biograph Philostratos(Hamburg, 1885); J. Göttsching,Apollonius von Tyana(Berlin, 1889); J.A. Froude,Short Studies, vol. iv.; G.R.S. Mead,Apollonius of Tyana(London, 1901); B.L. Gildersleeve,Essays and Studies(New York, 1890); Philostratus’sLife of Apollonius(Eng. trans. New York, 1905); O. de B. Priaulx,The Indian Travels of Apollonius(1873); F.W.G. Campbell,Apoll. of Tyana(1908); see alsoNeo-Pythagoreanism.

APOLLONIUS OF TYRE,a medieval tale supposed to be derived from a lost Greek original. The earliest mention of the story is in theCarmina(Bk. vi. 8, II. 5-6) of Venantius Fortunatus, in the second half of the 6th century, and the romance may well date from three centuries earlier. It bears a marked resemblance to theAntheia and Habrokomesof Xenophon of Ephesus. The story relates that King Antiochus, maintaining incestuous relations with his daughter, kept off her suitors by asking them a riddle, which they must solve on pain of losing their heads. Apollonius of Tyre solved the riddle, which had to do with Antiochus’s secret. He returned to Tyre, and, to escape the king’s vengeance, set sail in search of a place of refuge. In Cyrene he married the daughter of King Archistrates, and presently, on receiving news of the death of Antiochus, departed to take possession of the kingdom of Antioch, of which he was, for no clear reason, the heir. On the voyage his wife died, or rather seemed to die, in giving birth to a daughter, and the sailors demanded that she should be thrown overboard. Apollonius left his daughter, named Tarsia, at Tarsus in the care of guardians who proved false to their trust. Father, mother, and daughter were only reunited after fourteen years’ separation and many vicissitudes. The earliest Latin MS. of this tale, preserved at Florence, dates from the 9th or 10th century. The pagan features of the supposed original are by no means all destroyed. The ceremonies observed by Tarsia at her nurse’s grave, and the preparations for the burning of the body of Apollonius’s wife, are purely pagan. The riddles which Tarsia propounds to her father are obviously interpolated. They are taken from theEnigmataof Caelius Firmianus Symposius. The many inconsistencies of the story seem to be best explained by the supposition (E. Rohde,Der griechische Roman, 2nd ed., 1900, pp. 435et seq.) that the Antiochus story was originally entirely separate from the story of Apollonius’s wanderings, and was clumsily tacked on by the Latin author. The romance kept its form through a vast number of medieval rearrangements, and there is little change in its outlines as set forth in the Shakespearian play ofPericles.

Back to Index Next