μισθ-όω · misth-oō — LSJ
let out for hire, farm out, in pres. and impf., offer to let, τινί τι Ar. Lys. 958, Lys. 7.10, D. 50.52; μισθοῖ αὑτὸν Ὀλυνθίοις offers his services for pay to them, Id. 23.150, cf. 149; ἑαυτὸν ἐπί τι for a purpose, Id. 18.21; μ. τὸ τέμενος IG 1(2).94.5; οἶκον Lys. 32.23, D. 27.15, 28.15; τοὺς οἴκους τῶν ὀρφανῶν Arist. Ath. 56.7: c. inf., μ. τὸν νηὸν τριηκοσίων ταλάντων ἐξεργάσασθαι farm out the building of it for 300 talents, Hdt. 2.180; ὅσου τὴν τριηραρχίαν ἦσαν μεμισθωκότες D. 21.80.
Med., fut. μισθώσομαι Ar. V. 52: aor. ἐμισθωσάμην: pf. μεμίσθωμαι (v. infr.):—have let to one, hire, c. acc. pers. vel rei, πλοῖον, μισθωτούς, ἐπικουρικόν, Hdt. 1.24, Ar. Av. 1152, Th. 4.52; οἰκίαν ἣν ᾤκει μεμισθωμένος Is. 6.39; τίνα τῶν πολιτῶν ἑταιρεῖν μεμίσθωμαι; D. 45.79; τῆς οἰκίας ἧς ἐμεμίσθωτο Lys. 3.11; μισθωσάμενός τινος τὴν οἰκίαν D. 27.58; μ. τι παρά τινος Hdt. 1.68; τοὺς μεμισθωμένους παρʼ ἐμοῦ τὸ χωρίον Lys. 17.8; μ. τινὰ ταλάντου engage his services at a talent, Hdt. 3.131; ὀλίγου
Pass., aor. ἐμισθώθην: pf. μεμίσθωμαι (v. infr.):—to be hired for pay, Μαρδονίῳ μεμισθωμένος οὐκ ὀλίγου hired by him at no small price, Hdt. 9.38; ἐπί τινι for a thing, X. An. 1.3.1; ἐκ τοῦ μισθωθῆναι from the hire, D. 27.58; of a house, to be let on contract, Id. 28.1; of a mercenary, μισθωθεὶς ὑπό τινος Id. 23.149.