Henry George Liddell, Robert Scott, A Greek-English Lexicon

A.prayer or vow, once in Hom. (cf. εὖχος, εὐχωλή）“, ἐπὴν εὐχῇσι λίσῃ” Od.10.526, cf. Hes.Th.419, Thgn.341, Hdt.1.31, etc.; “θεὸς εὔφρων εἴη . . εὐχαῖς” Pi.O.4.15; “εὐχὰς ἀνασχεῖν τινι” S.El.636; εὐχὴν ἐπιτελέσαι, Lat. vota persolvere, Hdt.1.86; “εὐχὰς ἀποδιδόναι” X. Mem.2.2.10; “εὐχὴν ἀνέστησεν” SIG1142 (Phrygia, i/ii A.D.); εὐχῇ χρῆσθαι, Lat.votis potiri, Pl.Lg.688b; κατὰ χιλίων . . εὐχὴν ποιήσασθαι χιμάρων to make a vow of a thousand goats, Ar.Eq.661; “ἐν θεῶν εὐχαῖσι” S.OT239, etc.; “εὐχαὶ πρὸς θεούς” Pl.Lg.700b; “εὐχὰς εὔχεσθαι τοῖς θεοῖς” D.19.130; “εὐχὰς εὔξεται ὑπὲρ τῆς πόλεως” Inscr.Prien.174.18 (ii B.C.); “εὐχὰς ποιεῖσθαι” Th.6.32, Arist.Mu.400a17; “εὐχὴν ἀποθύειν” Diph.43.10; κατ᾽ εὐχήν, ἐξ εὐχῆς, Lat.ex voto, Call.Epigr.48, AP6.357 (Theaet.); ἔχειν εὐχήν to be under a vow, Act.Ap.18.18.

2. wish or aspiration, opp. reality, εὐχαῖς ὅμοια λέγειν to build 'castles in the air', Pl. R.499c, cf. 540d; μὴ εὐ. δοκῇ εἶναι ὁ λόγοςib.450d; κατὰ τὴν τῶν παίδων εὐ. like a boy's wish, Id.Sph.249d; εὐχῆς ἄξια things to be wished, but not expected, Isoc.4.182; πολιτεία ἡ κατ᾽ εὐχὴν γινομένη the ideal state, Arist.Pol.1295a29, cf. 1288b23; ζῆν κατ᾽ εὐχήν ib. 1260b29.

3. prayer for evil, i.e. curse, imprecation, “πατρὸς κατ᾽ εὐχάς” A.Th.820, cf.E.Ph.70.