question:let’s focus on these two aorist participles, “νομίσαντες…ἐπιθυμήσαντες”, which seem to have the meaning of imperatives,especially the second one; but I can’t check it in Smy.
Yes, it’s very common for participles to take on the mood of the main verb, so in this case ψηφίσασθε is imperative and thus the participles that agree with its subject also have an imperative force. I know this happens a lot in the New Testament, where it’s easier for me to find examples, like ἐγερθεὶς ἆρόν σου τὴν κλίνην from Matthew which can be translated as “rise and take…”, and in fact Mark in the equivalent passage has ἔγειρε καὶ ἆρον τὸν κράββατόν σου (I suspect the participle construction was considered more elegant – at least it seems that way to me.)
A quick search of Smyth or Goodwin didn’t find anything, but I’ll take another look later on.
A textbook example of a Greek aorist participle with acquired imperative force is the famous Spartan challenge Μολὼν λαβέ “having come, take [them]” i.e. “come and get them!”, referring to the weapons the Persians had demanded they surrender.