αἰνέω · aineō — LSJ
properly, tell, speak of, A. Ag. 98, 1482 (both lyr.), Ch. 192; σε κρηγύην αἰνεῖ reports of you as honest, Herod. 4.47.
usu. praise, approve, opp. νεικέω, ψέγω, Il. 10.249, Thgn. 612, etc.; ἀνδρὸς ὃν οὐδʼ αἰνεῖν τοῖσι κακοῖσι θέμις Arist. Fr. 673:— Pass., ὑπὸ Σιμωνίδεω αἰνεθείς Hdt. 5.102; ἐπʼ ἔργμασιν ἐσθλοῖς Theoc. 16.15.
esp. in religious sense, glorify God, LXX 1 Ch. 16.4, Ev.Luc. 2.13, PMag.Par. 1.1146, al.:—also c. dat., τῷ κυρίῳ, τῷ θεῷ, LXX 1 Ch. 16.36, Apoc. 19.5.
approve, advise, recommend Od. 16.380, 403: c. inf., recommend to do a thing, euphem. for κελεύω, A. Ch. 555, 715 : c. part., αἰνεῖν ἰόντα to commend oneʼs going, Id. Pers. 643:—ὦ δεινὸν αἶνον αἰνέσας giver of dire counsel, S. Ph. 1380:— c. acc. rei, to be content with, acquiesce in, γάμον Pi. P. 3.13, cf. N. 1.72, A. Eu. 469, Supp. 902, 1070 (lyr.), E. Med. 1157; θῆσσαν τράπεζαν αἰνέσαι Id. Alc. 2.
praise, with collateral sense, decline courteously, νῇ ὀλίγην αἰνεῖν, μεγάλῃ δʼ ἐνὶ φορτία θέσθαι Hes. Op. 643 (cf. Plu. Aud.poet. 2.22f), cf. S. Fr. 109; but, thank, cj. in E. Supp. 388.
abs., approve, ὁ δᾶμος αἰνεῖ IG 9(1).119 (Locr.).
to promise or vow, τινί τι or τινὶ ποιεῖν τι, S. Ph. 1398, E. Alc. 12.