The words used here in telling about the ordeals of Hēraklēs match closely the words used at the very beginning of the Odyssey to tell about the ordeals of Odysseus:
|1 That man, tell me O Muse the song of that man, that versatile [polu-tropos] man, who in very many ways |2 veered from his path and wandered off far and wide, after he had destroyed the sacred citadel of Troy. |3 Many different cities of many different people did he see, getting to know different ways of thinking [noos]. |4 Many were the pains [algea] he suffered in his heart [thūmos] while crossing the sea |5 struggling to merit [arnusthai] the saving of his own life [psūkhē] and his own homecoming [nostos] as well as the homecoming of his comrades [hetairoi].
Odyssey 1.1-5
|1 ἄνδρα μοι ἔννεπε, Μοῦσα, πολύτροπον, ὃς μάλα πολλὰ |2 πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσε· |3 πολλῶν δ’ ἀνθρώπων ἴδεν ἄστεα καὶ νόον ἔγνω, |4 πολλὰ δ’ ὅ γ’ ἐν πόντῳ πάθεν ἄλγεα ὃν κατὰ θυμόν, |5 ἀρνύμενος ἥν τε ψυχὴν καὶ νόστον ἑταίρων.