Indirect statement with participles
In contrast to verbs expressing speaking or thinking, verbs expressing sense perception (such as seeing and hearing), knowing, or showing can express indirect statement using a supplementary participle. Verbs you already know that express these ideas include δείκνυμι, ὁράω, and ἀκούω. The tense of the participle has the same sense as the tense of the infinitive in indirect statement after verbs of speaking or thinking, with the present participle used for an original imperfect verb.
If the subject of the indirect speech is different from the subject of the introductory verb, it is usually expressed in the accusative case. Like any participle, the participle in the indirect statement will agree with its subject in gender, case, and number. If the subject of the indirect speech is the same as the subject of the introductory verb, the participle is in the nominative and the subject is not generally repeated.
Examples
ἐδείκνυ Ἐρατοσθένη ταῦτα πράττοντα.
‘He was showing that Eratosthenes was doing these things.’
ἐδείκνυ Ἐρατοσθένη ταῦτα πράξαντα.
‘He was showing that Eratosthenes had done these things.’
οἱ μάρτυρες ἔδειξαν ἀκούοντες.
‘The witnesses demonstrated that they were listening.’
The verb ἀκούω takes a genitive object for the person heard, and an accusative for things heard:
ὁ ἀνὴρ ἤκουσε τῆς γυναικός.
‘The husband heard his wife.”
ὁ ἀνὴρ ὕστερον πάντα ἤκουσε.
‘The husband heard everything later.’
So a participle can modify the genitive object to represent what was being heard directly:
ὁ ἀνὴρ ἤκουσε τῆς γυναικός τινι λεγούσης.
‘The husband heard his wife (as she was) speaking to someone.’
ὁ ἀνὴρ ἤκουσε τῆς γυναικός ἐκ τῆς οἰκίας ἐρχομένης.
‘The husband heard his wife (as she was) going out of the house.’
Or the participle can represent indirect speech, with an accusative + participle:
ὁ ἀνὴρ ἤκουσε τὴν γυναῖκά τινι λέγουσαν.
‘The husband heard that his wife was speaking to someone.’
ὁ ἀνὴρ ἤκουσε τὴν γυναῖκα ἐκ τῆς οἰκίας ἐλθοῦσαν.
‘The husband heard that his wife had gone out of the house.”