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αὐξάνω Pi.Fr.153, Hdt.7.16.ά, A.Pers.756, E.Supp.233, Fr.362.28, Pl.Ti.41d:—
also αὔξω (poet. ἀέξω, q.v.) Thgn.823, Pi.O.5.4, Emp.37, S.Tr.117 (lyr.), Ar.Ach.227, X.Smp.7.4, Pl.R.573a, D. 3.26, etc. (so Att. Inscrr. and Ptolemaic Pap.; both forms in NT): impf. ηὔξανον only Ps.-E.Fr.1132.25; ηὖξον Hdt.9.31, etc.: fut. αὐξήσω Th.6.40, etc. (αὐξανῶ only in LXX Ge.17.6, al.): aor. I ηὔξησα Sol. 11, X.HG7.1.24: pf. ηὔξηκα Pl.Ti.90b, X.Hier.2.15:—
Pass., αὐξάνομαι Hdt.2.14, E.Med.918, Ar.Av.1065, Isoc.4.104, Pl.Phd.96c, D. 18.161; αὔξομαι Emp.26.2, Ar.Ach.227, Pl.R.328d, etc., impf. ηὔξετο Hes.Th.493, Hdt.3.39 (v.l. αὔξετο): pf. ηὔξημαι E.IA1248, Pl.R. 371e, Ion. αὔξ- Hdt.1.58: plpf. ηὔξητο Id.5.78: aor. ηὐξήθην Th.1.89, Pl.Prt.327c: fut.αὐξηθήσομαι D.56.48; αὐξήσομαι X.Cyr.6.1.12, Pl.R. 497a:—
increase, not in Hom. (only ἀέξω), Pi.Fr.153, etc.; ὕβριν αὐ. Hdt.7.16.ά; ὄλβον A.Pers.756; opp. ἰσχναίνειν, Pl.Plt.293b; εἰς ἄπειρον αὐ. τι Id.Lg.910b; ἐπὶ τὸ ἔσχατον Id.R.573a; ἐπὶ πλεῖον ηὖξον τὴν μαγειρικὴν τέχνην Athenio1.16, etc.

2. increase in power, strengthen, αὐ. τὰ Ἑλλήνων increase their power, Hdt.8.30; νόμοισιν αὐ. πόλιν S.Ant.191, cf. X.Mem.3.7.2; exalt by one's deeds, glorify, πόλιν, πάτραν, Pi.O.5.4, P.8.38, cf. IG22.834, etc.; exalt by praise, extol, ἐπαινεῖν καὶ αὔξειν τινά Pl.Ly.206a; σέ γε ..καὶ τροφὸν καὶ ματέρ' αὔξειν honour thee as .., S.OT1092 (lyr.); of an orator, amplify, exaggerate, αὔξειν καὶ μειοῦν Arist.Rh.1403a17.

3. with an Adj., τρέφειν καὶ αὐ. τινὰ μέγαν bring up to manhood, Pl.R.565c; μείζω πόλιν αὐ. E.IA572 (lyr.); τὸν ὄγκον ..ἄπειρον αὐξήσει Pl.R.591d.

4. αὔξειν ἔμπυρα to sacrifice, Pi.I.4(3).62; cf. ἀέξω.

5. in Logic, = καταπυκνόω (q. v.), Arist.APo.79a30, al.; but ὁ αὐξόμενος λόγος, name of a fallacy, Plu.Thes.23, 2.559b.

II. Pass., grow, increase, in size, number, strength, power, etc., Hes.Th.493, Pi.P.8.93, D.61.5, etc.; αὐ. ἐς πλῆθος, ἐς ὕψος, Hdt.1.58, 2.14; of a child, grow up, Id.5.92.έ; ἐν γὰρ τοῖς πόνοισιν αὔξεται, of Theseus, E.Supp.323; ηὐξανόμην ἀκούων I grew taller as I heard, Ar.V.638; of the wind, rise, Hdt.7.188; ηὔξηται ἡ πόλις ὥστ' εἶναι τελέα Pl.R.371e.

2. with an Adj., αὔξεσθαι μέγας wax great, grow up, E.Ba.183; αὐ. μείζων A.Supp. 338, Pl.Lg.681a; αὐ. ἐλλόγιμος Id.Prt.327c; μέγας ἐκ μικροῦ ..ηὔξηται D.9.21.

III. later, Act. intr., like Pass., ἡ σελήνη αὐξάνει Arist. APo.78b6, cf. HA620a21, Aristeas 208, D.S.4.64, Ep.Col.2.19, D. Chr.4.128, D.C.48.52, etc.

IV. of Verbs, take the augment, both Act. and Pass., Hdn.Epim.280; αὔξουσα (sc. συλλαβή), ἡ, augment, ibid. (Cf. ἀέξω.)