ANTHEMIUS, son of Stephanus of Tralles, Greek mathema tician and architect. He produced, under the patronage of Justin ian, the original and daring plans for the church of St. Sophia in Constantinople. The building was finished in 537, but in 558, after the death of Anthemius, it had to be restored, owing to the collapse of the dome. Anthemius wrote a treatise on burning glasses, where in the course of constructions for surfaces to re flect to one and the same point, (I) all rays in whatever direction passing through another point, (2) a set of parallel rays, he assumes a property of an ellipse not found in Apollonius (the equality of the angles subtended at a focus by two tangents drawn from a point), and (having given the focus and a double ordinate) he uses the focus and directrix to obtain any number of points on a parabola—the first instance on record of the practical use of the directrix.
A fragment of the treatise, entitled IIEpi irapa&5 wv ,unxavpµarwv, was published by L. Dupuy (1777) and in Hist. de l'Acad. des Inscr., vol. xlii. (1786) ; revised ed. by A. Westerman, Scriptores rerum mirabilium Graeci (5839). On Anthemius generally see Procopius, De Aedific. i. I ; Agathias Hist. v. 6-9. Gibbon's Decline and Fall chap. xl.; Bury, Later Roman Empire p. f.