356. These forms are generally used as negative connecting particles (but not, and not). Sometimes however they have a strengthening or emphatic force, corresponding to the similar use of καί in affirmative sentences.
Il. 5.485 τύνη δʼ ἕστηκας, ἀτὰρ οὐδʼ ἄλλοισι κελεύεις
you stand still (yourself), and (what is more)
do not call on the others to fight
and in combination with περ
Il. 4.387 ἔνθʼ οὐδὲ ξεῖνός περ ἐὼν κτλ.
So καὶ ὅς even he, οὐδʼ ὅς not even he, etc.
οὐδείς is originally an emphatic form (like the later οὐδὲ εἷς). In Homer the neuter οὐδέν is occasionally found, sometimes as an emphatic adverb = not at all.
Il. 1.244 ὅ τʼ ἄριστον Ἀχαιῶν οὐδὲν ἔτισας
So Il. 1.412, 16.224, 22.332 & 513, 24.370; Od. 4.195, 9.287): sometimes as a substantive, nothing at all (nominative and accusative).
Od. 9.34 ὡς οὐδὲν γλύκιον
no single thing is sweeter
Cp. 18.130, 22.318. The adjectival use is found with ἔπος (Od. 4.350, 17.141), also in
Il. 10.216 τῇ μὲν κτέρας οὐδὲν ὁμοῖον
Il. 22.513 οὐδὲν σοί γʼ ὄφελος
where οὐδέν may be adverbial. The genitive neuter appears in the compound οὐδενόσ-ωρος worth nothing (Il. 8.178). The masculine occurs only in the phrase τὸ ὃν μένος οὐδενὶ εἴκων (Il. 22.459; Od. 11. 515).
The form μηδείς is post-Homeric, except the form μηδέν, which occurs only in Il. 18.500 ὁ δʼ ἀναίνετο μηδὲν ἑλέσθαι.
357. Double Negation. This characteristic feature of Greek is caused by the tendency to repeat the negative particle with any word or phrase to which the negation especially applies.
Il. 1.114 ἐπεὶ οὔ ἑθέν ἐστι χερείων, οὐ δέμας κτλ.
since she is not inferior—not in fοrm, etc.
The emphatic οὐδέ and μηδέ are chiefly used in this way
οὐ μὰν οὐδʼ Ἀχιλεὺς κτλ.
no, not even Achilles, etc.
Il. 2.703 οὐδὲ μὲν οὐδʼ οἳ ἄναρχοι ἔσαν
Od. 8.280 τά γʼ οὔ κέ τις οὐδὲ ἴδοιτο,
οὐδὲ θεῶν μακάρων
Il. 6.58 μηδʼ ὅν τινα γαστέρι μήτηρ
κοῦρον ἐόντα φέροι μηδʼ ὃς φύγοι.