Passage 5.3.4
οὐ μὴν οὐδὲ Ἀμαρυγκεὺς οὔτε αὐτὸς διέμεινεν ἰδιωτεύων οὔτε Διώρης ὁ Ἀμαρυγκέως. ἃ δὴ καὶ Ὅμηρος παρεδήλωσεν ἐν καταλόγῳ τῶν Ἠλείων, τὸν μὲν σύμπαντα αὐτῶν στόλον ποιήσας τεσσαράκοντα εἶναι νεῶν, τούτων δὲ τὰς ἡμισείας ὑπὸ Ἀμφιμάχῳ τετάχθαι καὶ Θαλπίῳ, τῶν λοιπῶν δὲ εἴκοσι δέκα μὲν ναυσὶ Διώρην τὸν Ἀμαρυγκέως ἡγεῖσθαι, τοσαύταις δὲ ἑτέραις Πολύξενον τὸν Ἀγασθένους. Πολυξένῳ δὲ ἀνασωθέντι ἐκ Τροίας ἐγένετο υἱὸς Ἀμφίμαχος---τὸ δὲ ὄνομα τῷ παιδὶ ἔθετο ὁ Πολύξενος κατὰ φιλίαν ἐμοὶ δοκεῖν πρὸς Ἀμφίμαχον τὸν Κτεάτου τελευτήσαντα ἐν Ἰλίῳ---, Ἀμφιμάχου δὲ Ἠλεῖος·
Neither did Amarynceus himself remain in private life, nor did his son Diores, the son of Amarynceus. Homer indicates this clearly in the Catalogue of the Eleans, making their total fleet amount to forty ships, half of which he assigns to Amphimachus and Thalpius; of the remaining twenty, ten ships are commanded by Diores, son of Amarynceus, and the other ten by Polyxenus, son of Agasthenes. Polyxenus, upon returning safely from Troy, had a son named Amphimachus; and it seems to me that Polyxenus gave this name to the child because of the friendship he had for Amphimachus, son of Cteatus, who had died at Ilium. This Amphimachus became an Elean.