Herbert Weir Smyth, A Greek Grammar for Colleges

a. With these verbs the participle contains the main idea, and is often represented in translation by the finite verb with an adverbial phrase; thus, παρὼν ἐτύγχανε he happened to be there, or he was there by chance X. A. 1.1.2.

b. The action of φθάνω and λανθάνω usually coincides with that of the supplementary participle (present with present, aorist with aorist). But the aorist of a finite verb is occasionally followed by the present participle when it is necessary to mark an action or a state as continuing. οὐκ ἔλαθον is like an imperfect and may take the present participle. The aorist of τυγχάνω very often takes the present participle. With a present or imperfect of τυγχάνω, λανθάνω, φθάνω, the (rare) aorist participle refers to an action or state anterior to that of the present or imperfect. Many of the cases of the present of τυγχάνω with the aorist participle are historical presents; and in some cases the aorist participle is used for the perfect. With other tenses than present or imperfect, an aorist participle with these verbs refers to an action or state coincident in time (cp. 1873).

c. τυγχάνω often loses the idea of chance, and denotes mere coincidence in time (I am just now, I was just then) or simply I am (was).

d. Examples. τυγχάνω: ““προξενῶν τυγχάνω” I happen to be proxenus” D. 52.5, ““ἄριστα τυγχάνουσι πρά_ξαντες” they happen to have fared the best” I. 4.103, ““ἐτύγχανον λέγων” I was just saying” X. A. 3.2.10, ““ὅστις ἀντειπών γε ἐτύγχανε καὶ γνώμην ἀποδεδειγμένος” who happened to have spoken in opposition and to have declared his opinion” L. 12.27, ἔτυχον καθήμενος ἐνταῦθα I was, by chance, sitting there P. Eu. 272e. λανθάνω: φονέα τοῦ παιδὸς ἐλάνθανε βόσκων he entertained the murderer of his son without knowing it (it escaped his notice that he was, etc.) Hdt. 1.44, ““ἔλαθον ἐσελθόντες” they got in secretly” T. 2.2, οὐκ ἔλαθες ἀποδιδρά_σκων you did not escape notice in attempting to escape (your attempt at escape did not escape notice) P. R. 457e, ““ἔλαθεν ἀποδρά_ς” he escaped without being noticed” X. H. 1.3.22, ““λήσετε πάνθ᾽ ὑπομείναντες” you will submit to every possible calamity ere you are aware” D. 6.27. φθάνω: οὐ φθάνει ἐξαγόμενος ὁ ἵππος κτλ. the horse is no sooner led out, etc. X. Eq. 5.10, φθάνουσιν (hist. pres.) ἐπὶ τῷ ἄκρῳ γενόμενοι τοὺς πολεμίους they anticipated the enemy in getting upon the summit (they got to the summit before the enemy) X. A. 3.4.49, ““οὐκ ἔφθασαν πυθόμενοι τὸν πόλεμον καὶ ἧκον” scarcely had they heard of the war when they came” I. 4.86, ὁπότεροι φθήσονται τὴν πόλιν ἀγαθόν τι ποιήσαντες which party shall anticipate the other in doing some service to the State I. 4.79. Without regard to its mood, the present and imperfect of φθάνω are followed by the present participle (rarely by the perfect); the future, aorist, and historical present are followed by the aorist participle.

e. οὐκ ἂν φθάνοις (φθάνοιτε) with the participle is used in urgent, but polite, exhortations, as οὐκ ἂν φθάνοις λέγων the sooner you speak the better (i.e. speak at once) X. M. 2.3.11. Strictly this is equivalent to you would not be anticipating (my wish or your duty), if you should speak. λέγε φθάσα_ς might be said according to 2061.

f. λανθάνω and φθάνω (rarely τυγχάνω) may appear in the participle, thus reversing the ordinary construction, as ““διαλαθὼν ἐσέρχεται ἐς τὴν Μι_τυλήνην” he entered Mitylene secretly” T. 3.25, ““φθάνοντες ἤδη δῃοῦμεν τὴν ἐκείνων γῆν” we got the start of them by ravaging their territory” X. C. 3.3.18. Cp. also 2062 a. The present participle is rare.