ἐπεξέρχομαι

A. march out, make a sally, Hdt. 3.54, 6.101, Th. 3.26, etc.; ἐ. τινὶ ἐς μάχην Id. 5.9; of a message, ἐ. τινί reach him, Hdt. 8.99 codd. (ἐπες‐ Reiske).
2. proceed against, prosecute, τινί Antipho 1.1: generally, τῷ δράσαντι Th. 3.38; attack, Pl. Prt. 345d; ἐ. τινὶ φόνου proceed against one for murder, Id. Euthphr. 4d; also ἐ. τινὶ δίκην Id. Lg. 866b; [γραφήν] follow it up, Lex ap. D. 21.47; ἐ.φόνον Antipho 2.1.2: abs., ἐπεξέρχῃ λίαν thou visitest with severity, E. Ba. 1346: c. acc. pers., prosecute, Lys. 31.18; punish, Plu. Caes. 69; τὴν πόλιν E. Andr. 735: c. dat., take vengeance for, Nic.Dam. 130.18J.
3. proceed to an extremity, κἀπαπειλῶν ὧδ’ ἐπεξέρχῃ; S. Ant. 752; ἐ. πρὸς τέλος ἁπάσης πολιτείας Pl. Lg. 632c.
4. follow up, τῇ παρούσῃ τύχῃ Th. 4.14; pursue, develop, an argument, τῷ λόγῳ Pl. R. 361d, Grg. 492d.
II. c. acc., go through or over, πάντα τῆς χώρης Hdt. 4.9; τὸ πᾶν γὰρ ἐ. διζήμενον Id. 7.166.
2. carry out, accomplish, ἔργῳ τι (opp. ἐνθυμεῖσθαι) Th. 1.120; opp. ἐπινοεῖν, ib.70; πᾶν πρὸ τοῦ δουλεῦσαι ἐ. try every course, Id. 5.100: abs., opp. παραινέσαι, ib.9; νίκην App. BC 5.91; ἐ. τι εἰς τέλος Luc. JTr. 17.
3. discuss, relate or examine accurately or fully, οὐδ’ εἰ πάντ’ ἐ. σκοπῶν S. Fr. 919, cf. A. Pr. 870, Th. 3.67, Pl. Lg. 672a; ἀκριβείᾳ περὶ ἑκάστου ἐ. Th. 1.22; τι δῑ ὀλίγων Pl. Lg. 778c.
Liddell, Scott & Jones
A Greek-English Lexicon, 1940
An open-access project