GJCaesar wrote:ὑπ᾽ ἀλλήλων goes with ἀντισπωμένης δὲ τῆς ἑκάστου δυνάμεως. μηδαμοῦ is not a genitive, but a proverb, meaning ''nowhere''. In this sense, I believe it means that ''in no case/on no place''.
It's not entirely accurate to say μηδαμοῦ is not a genitive. It bears the sign of the genitive, οῦ,
which is also common in adverbs of places. (Smyth 342
μηδαμοῦ does carry the special meaning you've mentioned, which seems a more apt translation
in this passage, but strictly speaking, it's genitive. (Smyth 346c