ἐφευρὼν ὀνομαζόμενον σκαιόν τινα ἔρωτα ἐλοιδόρησεν μάλ᾽ ἐν δίκῃ
in such cases, does the object belongs to the participle or verb or both?
i guess, usually, as here to the part.
Both. First it registers as the object of ἐφευρὼν and then of ἐλοιδόρησεν in turn.
Similarly on the right-hand side, with parallel phrasing: … θεῖον δ᾽ αὖ τινα ἔρωτα ἐφευρὼν καὶ προτεινάμενος ἐπῄνεσεν …