Passage 2.4.2
Βελλεροφόντην δὲ οὐκ αὐτοκράτορα ὄντα βασιλεύειν, εἶναι δὲ ἐπὶ Προίτῳ καὶ Ἀργείοις ἐγώ τε πείθομαι καὶ ὅστις τὰ Ὁμήρου μὴ πάρεργον ἐπελέξατο. φαίνονται δὲ καὶ Βελλεροφόντου μετοικήσαντος ἐς Λυκίαν οὐδὲν ἧσσον οἱ Κορίνθιοι τῶν ἐν Ἄργει δυναστῶν ἢ Μυκήναις ὑπακούοντες· ἰδίᾳ τε οὐδένα παρέσχοντο ἄρχοντα τῆς ἐπὶ Τροίαν στρατιᾶς, συντεταγμένοι δὲ Μυκηναίοις καὶ ὅσων ἄλλων Ἀγαμέμνων ἡγεῖτο μετέσχον τοῦ στόλου.
I am persuaded, as is anyone who has examined Homer's works not merely superficially, that Bellerophon did not rule as an independent sovereign but was subject to Proetus and the Argives. Moreover, it appears that, even after Bellerophon's migration to Lycia, the Corinthians remained no less subordinate to the rulers in Argos or Mycenae. They themselves did not provide an individual leader for the expedition against Troy; rather, they joined the force under Mycenae and participated in the campaign along with all others whom Agamemnon commanded.