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νή or μά with the accusative: that by which one swears
δύο τρόπω νὴ τὸν Δία
‘There are two types [of memory], by Zeus.’ (Aristoph. Cl. 480)
The particles νή or μά, followed by an accusative, signal the person or object by which one swears an oath.
Lexical usage
The name of the deity is sometimes omitted out of respect (νὴ/μὰ τόν ‘by …’) or replaced by a different word, such as an animal (νὴ or μὰ τὸν κύνα ‘by the dog’ – as often as 14 times in Plato), a vegetable (ναὶ μὰ τὴν ἀμυγδαλῆν ‘yes, by the cabbage’ – Eupolis, Fragmenten (ed. Kock) 70) or a different object (ναὶ μὰ τόδε σκῆπτρον ‘yes, by this sceptre’ – Homeros, Ilias 1.234). Many of these 'oaths' are not meant seriously, such as μὰ τὸν χῆνα ‘by the goose’, a parody of μὰ τὸν Ζῆνα ‘by Zeus’.
Translation tips
While νή is always affirmative (and, incidentally, cognate to ναί ‘yes’), μά is invariably negative, unless preceded by ναί. Consequently, we translate ‘[yes,] by Zeus!’ as νὴ Δία or ναὶ μὰ Δία.
Varia
These accusatives are sometimes analysed as a direct object with a (sometimes implicit) verb of ‘swearing’.
μὰ τὸν Ἀπόλλω οὔκ, ἤν γε μὴ
ὀμόσῃς ἐμοί—
For Apollon, no, unless you swear to me... [provisional translation]
ἀλλ’ ἔγωγε μὰ τοὺς θεοὺς τοὺς Ὀλυμπίους οὐδ’ ἐν ταῖς αὐταῖς ἡμέραις ἄξιον ἡγοῦμαι μεμνῆσθαι τοῦ θηρίου τούτου κἀκείνων τῶν ἀνδρῶν
No, by the Olympian gods, I do not consider it right to remember this monster and those men on the same day! ֍