κάτειμι · kateimi — LSJ
go, come down, ποταμόνδε Od. l.c.; Ἴδηθεν Il. 4.475: in Trag., as fut. to κατέρχομαι, E. Alc. 73, etc.; esp. go down to the grave, κατίμεν δόμον Ἄϊδος εἴσω Il. 4.457; Ἄϊδόσδε 20.294; εἰς Ἅιδου δόμους E. l.c.; so κάτειμι alone, S. Ant. 896; of a ship, sail down to land, νῆα . . κατιοῦσαν ἐς λιμένʼ ἡμέτερον Od. 16.472; of a person, travel down the Nile, κ. ἐπὶ or εἰς Ἀλεξάνδρειαν, PLips. 45.12, 14 (iv A.D.); of a river, ποταμὸς πεδίονδε κάτεισι χειμάρρους Il. 11.492; of a wind, come sweeping down,
come back, return, ἀγρόθεν Od. 13.267; ἐς ἄστυ 15.505; of exiles, return home, Hdt. 1.62, 3.45, 5.62, A. Ag. 1283, And. 1.80, etc.; ἐκ τῶν Μήδων Hdt. 4.3:—as Pass. of κατάγω, E. Med. 1015; ὑπὸ τῶν ἑταίρων παρακληθεὶς κάτεισι Th. 8.48.
come in, of revenue, PFay. 20.7 (iii/iv A.D.).