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* THEOLOGY. 202 THEOPHILTJS. Methodist work. The Systematic Theology of A. H. Strong (Rochester, 1880) is by a Baptist. Percival, Digest of Theology (PhiUidelpliia, 1892), and Mortimer, Catholic Faith and Prac- tice (London. 1901), are scholarly presentations of the Higli Church Anglican view of the teach- ing of the undivided Church. Treatises from the point of view of the different religious denomina- tions will be found mentioned in many of the articles upon the various religious bodies. The standard encyclopa-dic works are the Herzog Realencyklopiidie (2d ed., 18 vols., Leipzig, 1877-88; 3d ed., by Hauck, 1896 et seq.), and (Roman Catholic) Wetzer and Welte, Kirchen- lexikon (12 vols., Freiburg, 1882-1901). THE'ON (Lat., from Gk. eiav) OF ALEX- ANDRIA (c.370 A.D.). One of the last of the Greek mathematicians and astronomers. He was a teacher at Alexandria and the father of the celebrated Hypatia ( q.v. ), whose name is also connected with the history of mathematical sci- ence. Theon's chief works are an edition of Euclid's Elements and a commentary on Ptol- emy's Almagest. The former was prepared for his students at Alexandria and the various man- uscripts have played an important role in all subsequent attempts to reproduce the Elements. The latter is especially valuable for its notes showing the use of sexagesimal fractions, and the operations of division and square root. THEON OF SMYRNA, smer'na (c.lOO a.d). A Greek matliematician and astronomer. He was the author of a work, commonly known as the Expositio, treating of mathematical rules neces- sary for the study of Plato. Two books of this work, probably the whole of it, are extant, one on arithmetic and the other on astronomy. The work contains two propositions on the theory of numbers of peculiar interest: (1) If n be any number, ?s- or n" — 1 is divisible by 3 or 4 or both. If «■ is divisible by 3 and not by 4, »" — 1 is divisi- ble by 4. (2) If two groups of numbers be ar- ranged as follows : «i ^ 1 + rf, = 1 + = 1 «, = 1-|-1 rf.,= 2+1= 3 n, = 2 + 3 ^3 = 4 -f 3 = 7 n, = .5 + 7 f/^=10 + 7=n nr=:»lr-l + rfr.l d, = 211,-1 + (l,.i, then (/- is of the form 2n^± ; e.g. rfj2 = i =2.n,2 l,d„- = 9 = 2.n„^+l. Thoon called these numbers diameters. It is interesting to observe that the ratios rfi _ rfz _ 3 rfs_ 7 111 ' "2 2 ' jij 5 " are the convergents of the continued fraction ^ 2' -I- 2 -I- 2 and hence approximate the value of /2, also that these diameters are solutions of a pair of indeterminate quadratic equations, relations un- known to Theon. THEOPH'ANO (c.955-91). The wife of Otho II. of the Holy Roman Empire. She was the daughter of the Byzantine Emperor Romanus II., and was married to Otho II. at Rome in 972. She was a woman of great beauty and noble character and soon won great influence over the Emperor, in whose Court she introduced much of the learning and refinement of Constantinople. After the death of her husband (983) she ruh'd as Regent for her son Otho 111. till her death. THEOPHANY (ML. theophania, theofania, from Gk. dio(pdi'ia, theophania, 0(o<pdveia. tlieo- phaneia. manifestation of a divinity, from tftis, theos, god + (palveffSai, phainesthai, to appear). An appearance of gods, or of God, to men. In the heathen religions theophanies under various fofms were regarded as of frequent occurrence. In Christianity the terra has sometimes been ap- plied to the appearance of God in Christ, in distinction from the epiphany, which was the appearance in the form of a dove, and the audible communication of God, at the baptism of Jesus (Mark i. 9-11 and parallels). It is now generally restricted to the appearances of Ciod as related in the Old Testament. They are I)iesented in many ways as simple historical occurrences, often without suggestion as to the manner, sometimes as in the form of man, some- times as the 'angel of .Jehovah.' THEOPHILANTHROPISTS (from Gk. $e6!, .theos, god + ipiXavepairla, philnnthropia, love to man, from tplXot, pliilos, dear -{- ifSpunros, anthrOpos, man). A sect which arose in France under the Directory, held its first meeting on January 15, 1797, and was dissolved by Na- poleon in 1802. They reduced all religion to the doctrines of God and immortality and the prin- ciples of morality resulting from these. They established regular divine service, which had its liturgy, its prayer and hymn book, and its jireachers. They received from the Directory ten churches in Paris for their assemblies, and s])read somewhat throughout the country. Their spirit and' purpose may be seen from their creed: "We believe in the existence of God and the im- mortality of the soul. Pray to God, love your brother, make yourself useful to your country. Tlie good is everything that serves to support and perfect man, the evil what has a tendency to corrupt and debase him. Children, honor your fatiiers and mothers, obey with loyaltj-. sup- port their age; fathers and mothers, instruct your children. Wives. be.hold in your husbands the heads of your houses, and make one an- other happy." Thomas Paine was a member of the sect. Their literarv productions were print- ed at Basel (2 vols., ]7'97-99). Consult Gregoire, Histoire des sectes religieuses, vol. i. (Paris, 1828). THEOPH'ILUS (Lat., from Gk. ee6<piot). The person to whom tlie author of the third Gospel and the Acts addressed these works. He is spoken of in terms of highest respect, as 'most excellent.' The notices (Luke i. 1-4, Acts i. 1) imply that be was a man of some standing, the friend, if not the patron, of the evangelist, and a convert to Christianity, who would be interested in a full and accurate account of its begin- nings. Beyond these notices nothing is known of him. Early Christian tradition is silent con- cerning him. Later conjectures, ancient and modern, are more interesting than convincing. Some, following a hint by Origen, have conjec- tured that the term is used by Luke in a fictitious sense, since all Christians are theophiloi (lov- ers or friends of God). Ramsay {Saint Paul the Traveller and the Roman Citizen, p. 388) thinks that the term 'most excellent' implies that Theophilus was an officer of equestrian