συγχράομαι
ἐπ' αὐτὸν ἥκεις τὸν βατῆρα τῆς θύρας → you've come to the crux of the matter, come to the point, hit the nail on the head, you've come to the very threshold of the door, you are come to the very threshold of the door, you've arrived at the truth of the matter
English (LSJ)
A make use of, avail oneself of, τῇ συμμαχίᾳ τοῖς καιροῖς, etc., Plb.1.8.1, 18.51.6, etc.; πρὸς τὴν ἀδικίαν ταῖς ναυσί Id.4.6.2; συναγωνιστῇ τῷ ποταμῷ as a coadjutor, Id.3.14.5; τῇ ἀπὸ τῶν φίλων εὐνοίᾳ SIG685.45 (Crete, ii B.C.); πόρῳ OGI544.23 (Ancyra, ii A.D.); of commercial dealings, σ. τῇ νήσῳ Peripl.M.Rubr.31: generally, have dealings, associate with, Σαμαρείταις Ev.Jo.4.9, cf. Diog.Oen.Fr.64. II borrow jointly, τινῶν τριήρεις Plb.1.20.14:— Pass., σιτικὰ τὰ συγχρησθέντα PPetr.2p.64 (iii B.C., cf. Arch.Pap.3.518).
