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Genitive: object with compound verbs
ἀκριβῶς οἶδ’ ὅτι κατέγνωτ’ ἂν αὐτοῦ.
‘I know very well that you would have condemned him.’ (Aeschin. 1.79)
The genitive signals an object with a number of compound verbs (in particular with ἀπο-, ἐκ-, κατα-, προ- etc.).
The semantic role of the object depends on the meaning which the prefix has in the compound in question. Common prefixes include ἀπο- and ἐκ- (source), κατα- (malefactive) and προ- (place or standard of comparison). Less frequent are ἐπι- and περι-.
Verbs of accusing and condemning are often compounded with κατα-: καταδικάζω, καταγιγνώσκω, καταψηφίζομαι 'to condemn'; καταγελάω 'to ridicule', καταφρονέω 'to despise', κατηγορέω 'to accuse'
The genitive cannot be converted into the subject of a passive predicate, although a different object can: θάνατος αὐτῶν κατεγνώσθη (the sentence of death was passed on them).
ἡ γλῶσσά σου μὴ προτρεχέτω τοῦ νοῦ
Take care that your tongue is not too quick for your mind.