355. οὐκί, οὐκ, οὐ. The full form οὐκί occurs in the formula ἠὲ καὶ οὐκί or else not (Il. 2.238, etc.), and one or two similar phrases.
Il. 15.137 ὅς τʼ αἴτιος ὅς τε καὶ οὐκί
Il. 20.255 πόλλʼ ἐτεά τε καὶ οὐκί
The general use of οὐ is to deny the predication to which it is attached (while μή forbids or deprecates). In some instances, however, οὐ does not merely negative the verb, but expresses the opposite meaning: οὔ φημι is not I do not say, but I deny, refuse; οὐκ ἐῶ I forbid, etc. (Kruger, § 67, 1, 1).
According to Delbrück (Synt. Forsch. iv. p. 147) the negative particle was treated originally like the prepositions, is. it was placed immediately before the verb, and closely connected with it, as in the Latin ne-scio, ne-queo, nolo, and in some parallel Slavic forms. The same relation appears in the accent of οὔ φημι, and in the use of οὐ in the combinations οὐκ ἐθέλω, οὐκ ἐάω, etc., in which οὐ is retained where general rules would require μή (§ 359).