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Genitive absolute: condition as a satellite
ὡς ἡδὺ τὸ ζῆν μὴ φθονούσης τῆς τύχης
‘How pleasant it is to be alive when fate bears no malice.’ (Men. Mon. 563)
The genitive absolute, often preceded by the negation μή, signals a condition as a satellite. The subject of the genitive absolute is never the same as that of the main clause (so coreferential situations are impossible).
οἴνου δὲ μηκέτ’ ὄντος οὐκ ἔστι Κύπρις
οὐδ’ ἄλλο τερπνὸν οὐδὲν ἀνθρώποις ἔτι
γυναικὶ μὴ μάχεσθαι μηδὲ ἄγαν φρονεῖν ἀλλοτρίων παρόντων· τὸ μὲν γὰρ ἄνοιαν, τὸ δὲ μανίαν δύναται παρέχειν
Do not argue with your spouse, nor show her too much affection in the presence of others. The former can give rise to folly, the latter to madness.
ἐμοῦ μὴ γενομένης, ποῦ ἂν σὺ ἦσθα;
If I had not existed, where would you be?