καθήκω · kathēkō — LSJ
come or go down, esp. to fight, A. Ch. 455 (lyr.).
come down to, reach to, ἐς θάλασσαν Hdt. 7.22, 130; ἐπὶ θάλ. Id. 2.32, 5.49, Th. 2.27; πρὸς τὸν Μηλιακὸν κόλπον Id. 3.96; κέρκος . . εἰς λεπτὸν καθήκουσα tapering away, Arist. HA 503a20: metaph., of descent, ὃ [γένος] εἰς αὐτὸν κ. Arr. An. 1.11.8.
come in due course to any one, καθῆκεν ἐς ἡμᾶς ὁ λόγος the turn of speaking came to us, Aeschin. 2.25; παρὰ τετάρτην ἡμέραν ἑκάστῃ σημαίᾳ καθήκειν τὴν λειτουργίαν Plb. 6.33.9, cf. PCair.Zen. 218.24 (iii B.C.); τῆς βολῆς καθηκούσης ἐς αὐτόν Plu. Alc. 2; ἐν τῷ ξυμποσίῳ . . ἐπὶ τὸν Θεσμόπολιν καθῆκε τὸ σκῶμμα Luc. Merc.Cond. 34.
of Time, ὁπότε καθήκοι ὁ χρόνος X. HG 4.7.2; ὅταν οἱ χρόνοι καθήκωσι Arist. HA 591a8; πρότερον ἢ τὴν ὥραν καθήκειν PRev.Laws 41.14 (iii B.C.); in part., τοῦ καθήκοντος χρόνου the normal time, S. OT 75, D. 4.35, cf. Aeschin. 3.126; αἱ κ. ἡμέραι the regular, proper days, D. 59.80; ἐν τῇ κ. ὥρᾳ Arist. HA 568a17; ἐν τοῖς κ. καιροῖς ib. 573a30; of events, ἑορτῆς εἰς τὰς ἡμέρας ἐκείνας καθηκούσης as the festival fell on those days, Plu. Fab. 18, cf. Plb. 4.7.1; ἐκκλησίαν ποιῆσαι, ὅταν ἐκ τῶν νόμων καθ
to be meet, fit, proper, τοῖς κ. [νομίμοις] Arist. Pol. 1325a13; τὰς ἐσθῆτας τὰς κ. ἀεὶ ταῖς περιθεταῖς suiting them, Plb. 3.78.3; ὁ καθήκων ἐκ τῶν νομίμων ἀριθμός a quorum, D.C. 39.30; also καθῆκόν ἐστιν αὐτὸν ἐπαινεῖσθαι Inscr.Prien. 114.32 (i B.C.).
impers., καθήκει μοι it belongs to me, is my duty, c. inf., οἷς καθήκει ἁθροίζεσθαι X. An. 1.9.7, cf. Cyr. 8.1.4, etc.: in later writers, impf. καθῆκε in pres. sense, it is meet, proper, οὐδʼ ἅψασθαι καθῆκέ τινων Aristeas 149; οὐ κ. αὐτὸν ζῆν Act.Ap. 22.22: freq. in part., τὰ καθήκοντα oneʼs due or duty, X. Cyr. 1.2.5; τὰ κατήκοντα Σπαρτιήτῃσι Hdt. 7.104; ποιεῖν τὸ κ. Men. 575: esp. in Stoic philos. (from signf. I.3 acc. to D.L. 7.108, cf. κατά B. I.3), περὶ τοῦ κ., title of work by Zeno, cf. S
τὰ κατήκοντα the present crisis, Hdt. 1.97, 5.49; τὰ κ. πρήγματα Id. 8.19, 40, 102.
τὰ καθήκοντα the payments due, UPZ 42.15 (ii B.C.); τὴν -ουσαν ἡμῖν δίδοσθαι σύνταξιν τῶν δεόντων ib. 6.
Adv. pres. part. καθηκόντως fittingly, properly, Epicur. Ep. 2p.53U., OGI 90.28 (Rosetta, ii B.C.), Plb. 5.9.6, v.l. in D.S. 1.93; πρός τι Porph. Abst. 1.43; consistently with duty, Stoic. 3.188, Plu. Virt.mor. 2.448e; appropriately, c. dat., τῷ τόπῳ Aristeas 81; κ. ἔχειν πρός τι Id. 87.
τὸ καθῆκον the precise proportion, Thphr. Lap. 46.