ἀργυρόω
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 to cover with silver, ὀστέον Dialex.2.13; βωμόν IG3.899.4: —Pass., to be silvered, silver-plated, ῥύπος ἠργυρωμένος Men.Mon.469; ἀργυρούμενα ἢ ἐνηργυρωμένα σκεύη Timae.Astr. in Cat.Cod.Astr.1.97.4. II metaph. of persons, ἀργυρωθέντες σὺν οἰνηραῖς φιάλαις rewarded with silver wine-cups, Pi.N.10.43; also ἀοιδαὶ ἀργυρωθεῖσαι πρόσωπα songs with silvered brow, i.e. mercenary, Id.I.2.8.
Greek (Liddell-Scott)
ἀργῠρόω: καλύπτω δι’ ἀργύρου, «ἀσημώνω» Συλλ. Ἐπιγρ. 435: ― ἀλλαχοῦ ἀείποτε ἐν τῷ παθητ. ἐπαργυροῦμαι, «ἀσημώνομαι», ῥύπος ἠργυρωμένος Μενάνδρ. Μονόστ. 469: παρὰ Πινδ. ἐπὶ προσώπων, ἀργυρωθέντες σὺν οἰνηραῖς φιάλαις, ἀνταμειφθέντες δι’ ἀργυρῶν ποτηρίων οἴνου, Ν. 10. 80· οὕτως, ἀοιδαὶ ἀργυρωθεῖσαι πρόσωπα, ᾠδαὶ ἔχουσαι ἄργυρον ἐπὶ τῶν προσώπων, δηλ. μισθωταί, ὤνιοι, εὐτελεῖς, Ι. 2, 13.