The particles νή or μά, followed by an accusative, signal the person or object by which one swears an oath.
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 on μὰ τὸν Ζῆνα ‘by Zeus’.
Where νή is always affirmative (and, furthermore, is related to ναί ‘yes’), μά is invariably negative, unless preceded by ναί. Consequently, we translate ‘[yes,] by Zeus!’ as νὴ Δία or ναὶ μὰ Δία.
These accusatives are often analysed as a direct object with a (sometimes implicit) verb of ‘swearing’.
μὰ τὸν Ἀπόλλω οὔκ, ἤν γε μὴ | ὀμόσῃς ἐμοί—
Bij Apollon, nee, tenzij je mij zweert...
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!
ἀλλ’ ἐξολεῖς με ναὶ μὰ τὴν ἀμυγδαλῆν
Yes, yes, you will perish, by the almond tree!