καταιν-έω · katain-eō — LSJ
agree to, approve of, agree
agree to a thing, approve of it, opp. ἀναίνομαι, c. acc. rei, Hdt. 4.80, 6.62; κ. [τι] ἐπί τινι to agree to it on conditions, Id. 3.53: c. dat. rei, Th. 4.122: abs., οὐ καταινέσαμεν ἀλλὰ ἀπειπάμεθα Hdt. 9.7.αʹ.
2 agree, promise to, agree that
agree, promise to do, c. aor. inf., γάμον μεῖξαι Pi. P. 4.222: c. fut. inf., καταίνεσον μή ποτε προδώσειν S. OC 1633, cf. 1637; also τοῦτον κ. βασιλέα σφίσι εἶναι agree that he should be king, Hdt. 1.98; κ. τινὰ ταγόν (sc. εἶναι) AP 9.98 (Stat. Flacc.).
3 grant, promise, promise in marriage, betroth
grant, promise, τοῦτʼ ἐμοὶ πόλις τὸ δῶρον . . κατῄνεσεν S. OC 432, cf. Ichn. 158; esp. promise in marriage, betroth, παῖδά τινι E. IA 695, cf. Plu. Pomp. 47; κ. πρὸς γάμον Nic.Dam. 10 J.