Page:The New International Encyclopædia 1st ed. v. 18.djvu/888

* SYMMACHUS. 774 SYMMETRY. place, and the Ostrogothic Kinj; Theodoric, al- though an Arian, was apjiealed to, and gave his voice for Symniachus. Theodoric. lieing again ap- pealed to, caused the Bishop of Altimim to admin- ister the affairs of the Church for a time, and left the decision to a synod. In its fourth session the synod (502) finally decided in favor of Symma- clius. In vindication of the action of the synod the deacon Ennodius, afterwards Bishop of Ticini- um (Pavia), gave clear expression to the prin- ciple that the Pope (Ennodius is among the first to limit this title to the Bishop of Rome) is above every Iiuman tribunal and is responsible only to God himself. Later councils during Symmachus's pontificate condemned all interference of laj'men in the election of popes and regulated the disposi- tion of goods belonging to the Church. SYMMACHUS, Greek Version of. See Bible, section on Versions. SYMMACHUS, Quintus ArRELius. A dis- tinguislied Pioman orator, scholar, and statesman, who was born probablj' not long after a.d. 340, was educated in Gaul, and after holding several lesser offices, became prefect of Rome ( a.d. 384 ). Seven j'ears later he was raised to the consulship. The date of his death is unknown, but we know that he was alive in a.d. 404. A sincere pagan in an age when classic paganism was almost ex- tinct, he proved in his own person a pattern of its choicest virtues, and manfully, if in vain, strove to regain for it a place of honor in the State. Symmacluis's extant writings consist of ten books of letters {Epistolaniiit Lihri X.) and the fragments of nine orations. The best editions of Svmmachus's entire worlcs are bv Seeck (Ber- lin, 'l883) and KroU (Leipzig, 1893). Consult: Morin, Elude siur la vie et les ccrits de Sym- maque, prffet de Rome (Paris, 1847) ; Dill, Roman Society in the Last Century of the West- ern Empire (London, 1899). SYMMES, simz, John Cleves (c.1780-1829) . An American soldier and author, born in Sussex County, N. J. He entered the United States Army as ensign in 1802, became captain Janu- ary 20, 1813, and served through the War of 1812, distinguishing himself particularly at Niagara and in the sortie from Fort Erie. He subsequently lived in Newport, Ky., and gave his entire time to developing and advocating his thoorj' that the earth and all the other planetary bodies are composed of a number of hollow con- centric spheres, open at their poles. He believed the inside of the earth to be habitable, and in 1822 and again in 1823 petitioned Congress to fit out an expedition to test the theory. In support of his contention he published many pamphlets and a volume entitled Theory of Concentric Spheres (1826). Consult an article on "Symmes's Theory of the Earth," in the Atlantic 'Monthly for April, 1873. SYMMETRY (Lat. symmetria. from Gk. avufit-pia, from avyijeTpoc, symmetros, having a common measure, from avv, syn, together + fifrpm'. metroyi, measure, from fterpeh', metrein, to measure). A term used in geometry to ex- press a characteristic property of two congruent or quasi-coneruent figures which have a certain relation with respect to a point, line, or plane. Two systems of points. A,. B,. C,, A,, B., Cj. ..... are said tn be symmetric with respect to an axis when all lines Ai Aj, Bi Bj, .... are bisected at right angles by that axis. Two figures are said to be symmetric with respect to an axis when their systems of points are svm- metric with respect to that axis. A figure is A M B FIGURE SYMMETRIC WITH RESPECT TO AN AXIS. said to be symmetric with respect to an axis when the axis divides it into two symmetric tlg- P01.T9 SYMMETRIC WITH RESPECT TO A CENTRE. ures. Two systems of points A,, B„ C„ ..... and Aj, B;, Cj, are said to be symmetric nith respect to a centre when all lines A^ A^, B^ B,, Ci Cj,. . . ., are bisected by 0. SYMMETRICAL TRIANGLES. Two figures are said to be symmetric with re- spect to a centre when their systems of points are symmetric with respect to that centre. E.g. in the figure triangles A, B^ C,, A, Bj Cj are sym- metric with respect to 0. Figures of three dimensions besides being sym- metric with respect to an axis or a centre may be symmetric with respect to a plane. E.g. the sphere is symmetric with respect to its centre, with re- spect to any diameter as axis, and with respect to any diametrical plane as a plane of sym- metry. Symmetric pol^vhedral angles may be con- sidered as quasi-congruent, and are such as have their dihedral angles equal, and the plane angles of their faces also equal, but arranged in reverse order. Tlius. in the following figure. V and V are sym- metric trihedral angles, the letters showing ♦he reverse arrangement. Opposite polyhedral angles are such that each is formed by producing the edges and faces of the other through the vertex.