ὑπερδέξιος · hyperdexios — LSJ
lying above one on the right hand, εἶχον ὑ. χωρίον . . χαλεπώτατον, καὶ ἐξ ἀριστερᾶς . . ποταμόν, v.l. for ὑπὲρ δεξιῶν in X. An. 4.8.2.
simply, lying above or over, ὑ. χωρίον higher ground, ib. 3.4.37, etc.; τὰ ὑ. ib. 5.7.31, cf. Aen. Tact. 1.2; ἐξ ὑπερδεξίου from above, X. HG 7.4.13, Plb. 2.3.6, etc.; ἡ ἐξ ὑ. τάξις up-stream, Id. 3.43.3; ἐκ τῶν ὑ. X. HG 4.2.14; ἐξ ὑπερδεξίων Luc. Tim. 45, Paus. 4.29.4: c. gen., commanding from above, or simply above, λόφος ὑ. τῷν πολεμίων Plb. 1.30.7, cf. 10.30.7; τοῦ τείχους Id. 8.4.9: also of streams, ἔστιν ἡ Σηστὸς ὑ. τοῦ ῥοῦ up-stream with regard to the current, Str. 13.1.22.
metaph., superior, having the advantage in a thing, τῷ πολέμῳ Plb. 5.102.3, etc.; victorious over, ὑ. τῆς κακίας τὴν ἀρετήν Plu. Num. 20; ὑ. ἐγένετο τοῦ λοιμοῦ, i. e. he recovered, Ruf. Fr. 114.
c. gen., convenient for, ὑ. χωρίον τοῦ ἀποκρούεσθαι τὴν ἔφοδον Arr. Tact. 9.2.