Participle (not in indirect discourse).—The participle, as a verbal adjective, is timeless. The tenses of the participle express only continuance, simple occurrence, and completion with permanent result. Whether the action expressed by the participle is antecedent, coincident, or subsequent to that of the leading verb (in any tense) depends on the context. The future participle has a temporal force only because its voluntative force points to the future.
a. Present (continuative). The action set forth by the present participle is generally coincident (rarely antecedent or subsequent) to that of the leading verb:
ἐργαζόμεναι μὲν ἠρίστων, ἐργασάμεναι δὲ ἐδείπνουν
1. Antecedent action ( = imperf.):
οἱ Κύ_ρειοι πρόσθεν σὺν ἡμῖν ταττόμενοι νῦν ἀφεστήκα_σιν
τοὺς τότε παρόντας αἰτιά_σονται συμβούλους
2. Subsequent action (especially when the leading verb denotes motion): ἔπεμψαν πρέσβεις ἀγγέλλοντας τὴν τοῦ Πλημυρίου λῆψιν
τὴν νῦν Βοιωτία_ν καλουμένην ᾤκησαν
3. The present participle denotes that an action is in process, is attempted, or is repeated.
b. Future (chiefly voluntative):
οὐ συνήλθομεν ὡς βασιλεῖ πολεμήσοντες
c. Aorist (simple occurrence). The action set forth by the aorist participle is generally antecedent to that of the leading verb; but it is sometimes coincident or nearly so, when it defines, or is identical with, that of the leading verb, and the subordinate action is only a modification of the main action.
ἤδη δ' ἐπὶ ταῦτα πορεύσομαι τοσοῦτον αὐτὸν ἐρωτήσα_ς
νῦν μὲν δειπνεῖτε· δειπνήσαντες δὲ ἀπελαύνετε
μή τι ἐξαμάρτητε ἐμοῦ καταψηφισάμενοι
εὖ γ' ἐποίησας ἀναμνήσα_ς με
ἀπαλλαχθήσομαι βίου θανοῦσα
3. The action of an attributive aorist participle is rarely subsequent to that of the leading verb. When this is the case, the action of the participle is marked as past from the point of view of the present (like the aor. indic.):
οἱ Ἕλληνες ὕστερον κληθέντες οὐδὲν πρὸ τῶν Τρωϊκῶν ἁθρόοι ἔπρα_ξαν
d. Perfect (completion with permanent result): καταλαμβάνουσι Βρα_σίδα_ν ἐπεληλυθότα
ὁ πρόσθε κεκτημένος
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].