μηδα^μ-οῦ , Adv.
A.nowhere, Th.1.35, Pl.Lg.958d; “μ. ἄλλοθι” Id.Phd. 68a: c. gen., μ. τῶν ὄντων, Lat. nusquam gentium, Id.Prm.162c: metaph., ὅπου τὸ χαίρειν μ. νομίζεται is of no account, A.Eu.423, cf. 624, S.Aj.1007; “μηδαμοῦ παρά τισιν εἶναι” X.Mem.1.2.52: as two words, “μηδὲ ἁμοῦ” IG12.16.11 (v B.C.).
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''.
μηδαμοῦ does carry the special meaning you've mentioned, which seems a more apt translation
in this passage, but strictly speaking, it's genitive.
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