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Accusative: cause as satellite
ταῦτα δὴ λιποῦσ᾽ ἱκάνω χρυσεοστόλμους δόμους
‘For these reasons I have left the gold-decorated palace.’ (Aesch. Pers. 159)
The accusative signals a cause as a satellite. The difference with the accusative of goal is very small.
The word in the accusative, always neuter and usually a pronoun, denotes a situation. As a consequence the words in question are analysed as adverbs by many grammars. A few examples: τί; ‘why?’, ταῦτα (rarely τοῦτο) ‘for that reason’.
… καὶ προσέτι τῶν νεκρῶν ὁμοῦ ἐπ᾽ ἀλλήλοις ξυννενημένων, οἳ ἔκ τε τῶν τραυμάτων καὶ διὰ τὴν μεταβολὴν καὶ τὸ τοιοῦτον ἀπέθνῃσκον…
...and moreover, because the corpses were stacked on top of each other, of those who had died of wounds, of differences in temperature, or of the like... [provisional translation]
ταῦτ᾽ οὖν περί μου δέδοικε μὴ διαφθαρῶ.
πατὴρ γὰρ οὐδείς ἐστιν αὐτῷ πλὴν ἐμοῦ
So that is why he feared that I would perish: because he has no other father than me.
τί δῆτ’ οὐκ ἔρριψ’ ἐμαυτὴν τῆσδ’ ἀπὸ πέτρας, ὅπως τῶν πάντων πόνων ἀπηλλάγην;