Sir Richard C. Jebb, Commentary on Sophocles: Trachiniae

(1) It is a gen. of connection, equiv. to the gen. with “περί”, and going with the whole phrase εἱμαρμένα ἐκτελευτᾶσθαι rather than with either word alone. ‘He said that such things were destined to be accomplished in regard to the toils of Heracles.’ This is only a rarer and bolder form of the gen. used in poetry after verbs of ‘speaking about’ ( El.317“τοῦ κασιγνήτου τί φής”;), ‘asking about’ ( Ph.439“φωτὸς ἐξερήσομαι”), ‘hearing about’ ( O. C.307“κλύων σοῦ”). And there is another passage of Sophocles which shows a similarly bold use of it, viz., O. C.355（“μαντεῖα”) “ἃ τοῦδ᾽ ἐχρήσθη σώματος”, ‘the oracles that had been given concerning me’: an example which (to my mind) strongly confirms this view.

(2) It is also possible, though less probable, that the gen. should be taken as partitive with ἐκτελευτᾶσθαι: destined to be accomplished as part of (in the number of) his toils. For this we might compare such uses of the partitive gen. as “πλεῖν τοῦ πρώτου στόλου” ( Ph.73), “ἐξετάζεσθαι τῶν συγχαιρόντων” ( Dem. or. 21 § 202), “ἀριθμεῖσθαι τῶν μακάρων”, etc.

(3) πόνων depends on πρὸς θεῶν εἱμαρμένα as if it were a subst. “εἱμαρμένην”:— ‘he said that such a doom for the toils of H. was to be fulfilled.’

(4) πόνων depends on ἐκτελευτᾶσθαι as equiv. to “τελευτὴν γίγνεσθαι”: ‘he said that such events were to be accomplished as the end of his toils.’ I do not think that the Greek words will bear either of the two latter versions.