Hi Enosh, με is the accusative in an accusative + infinitive construction here.
I understand from your intro that you’re using the JACT books: check out the reference grammar in the back of the grammar and exercises volume, section 397(ii) (Accusative + infinitive or participle).
There’s a useful note in that section on why the accusative is used:
N.B. all the above examples have put the subject of the ‘that’ clause into the > accusative > because > the subject of the indirect speech is different from that of the speaker> . Where the subject of the ‘that’ clause is the same as that of the main verb, no subject in the ‘that’ clause will be stated; or if it is, it will be in the nominative, …
There are some other grammatical points here (e.g. the use of the infinitive rather than the participle), but the grammar of tragedy can show variations from textbook rules (although even the textbook rule here is expressed to be a general one rather than universal) (section 397(iv) in the same reference grammar in your JACT book):
The following > generally > take the participle in indirect speech: … οἶδα ‘know that …’
The negative used as well also requires a little explanation. All these points perhaps for another day!
Thank you, Chad! Your clear explanations and JACT references are very helpful. I’ll remember this acc. + inf./part. construction for indirect speeches.