ἐδόκουν δ᾽ αὐτῷ οἱ γιγνώσκεσθαι δοκοῦντες ὑπὸ τοῦ ἄρχοντος
can we use the participle γιγνώμενοι instead of the inf. here?
No, because the inf γιγνώσκεσθαι is governed by the ptcp δοκοῦντες
so, constructions with a participle governing another participle are avoided, right?
Rather that δοκεῖν regularly governs an infinitive. οἱ…δοκοῦντες is a substantivized participle. It serves as the subject of the sentence. If you were to rewrite it as an independent clause it would be eg ἐκεῖνοι γιγνώσκεσθαι δοκοῦσιν ὑπὸ τοῦ ἄρχοντος. Make sense?
Strings of participles are sometimes avoided for stylistic reasons, but the construction here is more basic.
yes, thankx