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THE ENCYCLOPÆDIA BRITANNICA
A DICTIONARY OF ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION
ELEVENTH EDITION
VOLUME II SLICE III
Apollodorus to Aral
Articles in This Slice
APOLLODORUS (Athenian painter) APPREHENSION APOLLODORUS (Athenian grammarian) APPRENTICESHIP APOLLODORUS (of Carystus) APPROPRIATION APOLLODORUS (Greek architect) APPURTENANCES APOLLONIA APRAKSIN, THEDOR MATVYEEVICH APOLLONIUS (the Surly) APRICOT APOLLONIUS (Greek rhetorician) APRIES APOLLONIUS (the Sophist) APRIL APOLLONIUS MOLON APRIL-FOOLS’ DAY APOLLONIUS OF PERGA A PRIORI APOLLONIUS OF RHODES APRON APOLLONIUS OF TRALLES APSARAS APOLLONIUS OF TYANA APSE APOLLONIUS OF TYRE APSE and APSIDES APOLLOS APSINES APOLLYON APT APOLOGETICS APTERA APOLOGUE APTERALAPOLLODORUS, an Athenian painter, who flourished at the end of the 5th century B.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 140 B.C. He was a prolific and versatile writer. There is extant under his name a treatise on the gods and the heroic age, entitled Βιβλιοθἠκη, 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 144 B.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 260 B.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 his Hecyra and Phormio from the Έκυρά and Έπιδικαζόμενος of 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 century A.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 on Siege 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 Apollonia κατ᾽ Έπίδαμνον or πρὸς 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
APOLLONIUS, surnamed ὁ 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 Priscian grammaticorum princeps. Four of his works are extant: On Syntax, ed. Bekker, 1817; and three smaller treatises, on Pronouns, Conjunctions and Adverbs, ed. Schneider, 1878.
Grammatici Graeci, i. in Teubner series; Egger, Apollonius Dyscole (1854).
APOLLONIUS, surnamed ὁ μαλακός (“the Effeminate”), a Greek rhetorician of Alabanda in Caria, who flourished about 120 B.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 century A.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 in Classical Review (Nov. 1897).
APOLLONIUS MOLON (sometimes called simply Molon), a Greek rhetorician, who flourished about 70 B.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 262 B.C. He flourished in the reigns of Ptolemy Euergetes and Ptolemy Philopator (247-205 B.C.). His treatise on Conics gained 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 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. (241-197 B.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 the Conics can 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 to oblique axes (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 names parabola, 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 the Data, the Porisms and Surface-Loci of Euclid and the Conics of Apollonius were, according to Pappus, included in the body of the
1st. De Rationis Sectione had 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 Sectione discussed 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 Determinata resolved 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 his Apollonius Redivivus (Paris, 1612), but by far the best is by Robert Simson, Opera quaedam reliqua (Glasgow, 1776).
4th. De Tactionibus embraced 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 entitled Apollonius 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, entitled Apollonii Pergaei quae supersunt, ac maxime Lemmata Pappi in hos Libras, cum Observationibus, &c. (Gothae, 1795, 8vo).
5th. De Inclinationibus had 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 Planis is 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’s Elements; (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 31⁄7 and 310⁄71 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. 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 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).