William Watson Goodwin, Syntax of the Moods and Tenses of the Greek Verb

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[*] 146. An aorist participle with the present or imperfect of any of the above verbs (144) cannot coincide with the verb in time, and retains its own reference to past time. This combination seldom occurs.¹ E.g.

• “Ὅπερ λαβοῦσα τυγχάνει μήτηρ χεροῖν,” “which, as it happens, the mother has taken in her hands (happens to have taken).” EUR. Bacch. 1140.
• “Ἄριστα τυγχάνουσι πράξαντες,” “it happens that they fared the best.” ISOC. iv. 103.
• “Δικαίως ἂν τὴν αὐτὴν εὐεργεσίαν ἀπολάβοιμεν, ἥνπερ αὐτοὶ τυγχάνομεν εἰς ὑμᾶς ὑπάρξαντες,” “we should justly receive back the same kindness which it is our own fortune to have first shown to you (we happen to have begun.” Id. xiv. 57.
• “Πρὸς τί τοῦτ᾽ εἰπὼν κυρεῖς;” “wherefore did you chance to speak thus (does it chance that you spoke)?” SOPH. El. 1176.
• “Ποῦ κυρεῖ ἐκτόπιος συθείς;” Id. OC 119.
• “Ὅρα καθ᾽ ὕπνον μὴ καταυλισθεὶς κυρῇ,” “see lest it may chance that he has retired to sleep within.” Id. Ph. 30.

Compare “συνεκύρησε παραπεσοῦσα,” “happened to collide.” HDT. viii. 87 (889). “Μῖξις μία λύπης τε καὶ ἡδονῆς ξυμπίπτει γενομένη,” “i.e. happens to have occurred (Badham proposes γιγνομένη).” Phil. 47d

• “Οὐδ᾽ ἄρα Κίρκην ἐξ Ἀίδεω ἐλθόντες ἐλήθομεν,” “nor was it unknown to Circe that we had returned from Hades.” Od. xii. 16.
• “Ὅσοι ἐτύγχανον οὕτως ἀθρόοι ξυνεξελθόντες,” “all who happened to have thus come out together.” THUC. iii. 111.
• “Εἴ τί που αἰγῶν περιλειφθὲν ἐτύγχανε γένος,” “if any race of goats happened to have been left.” Leg. 677E.
• “Ἀρισταγόρῃ δὲ συνέπιπτε τοῦ αὐτοῦ χρόνου πάντα συνελθόντα,” “and it was the fortune of A. that all these came to him at the same time.” HDT. v. 36. (Here it is difficult to distinguish the doubly past time; but the analogy of the other examples, and the difficulty of conceiving an imperfect and aorist as coincident in time, seem decisive.)
• “Ὀρθῶς σφι ἡ φήμη συνέβαινε ἐλθοῦσα,” “rightly, as it happened, had the report come to them.” Id. ix. 101.

Just below: “τῆς αὐτῆς ἡμέρης συνέβαινε γίνεσθαι,” “i.e. they (the battles of Plataea and Mycale) happened to fall on the same day.” (9.101)

In LYS. xii. 27 we have the aorist and perfect participles together with ἐτύγχανε, each expressing its own time: ὅστις ἀντειπών γε ἐτύγχανε καὶ γνώμην ἀποδεδειγμένος, who charced to have spoken in opposition and to have shown his opinion.

It appears from these examples that the aorist participle can coincide in its time only with forms which have a similar aoristic or complexive meaning, while in other cases the verb and participle are distinct in time.