Perseus analyses of νεῦσε:

νέω 1 (swim): aor ind act 3rd sg (homeric ionic)
νεύω (incline in any direction): aor ind act 3rd sg (homeric ionic)

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νέω 1

νέω (A), νεῖ Pl. R. 453d, νέομεν Pi. Fr. 218 codd. Ath.; inf. νεῖν Epich. 53, Th. 7.30; part. νέων Od. 5.344, Pl. R. 529c: impf. ἔνεον Ar. Eq. 321; Ep. ἔννεον Il. 21.11; poet. νέον Alc. 143: fut. νεύσομαι Hsch., νευσοῦμαι v.l. in X. An. 4.3.12: aor. ἔνευσα (δι-) Pl. Prm. 137a, (ἐξ-) E. Hipp. 470, Th. 2.90: pf. νένευκα (δια-) Pl. R. 441c:—

2. metaph., of shoes that are too large, ἔνεον ἐν ταῖς ἐμβάσιν was floating in my shoes, as if they were boats, Ar. Eq. 321; νεῖν ἐξ ὑπτίας, v. ὕπτιος II. fin. (Prob. cogn. with νάω, Lat. nare.)

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νεύω

νεύω, Il. 13.133, etc.: fut. νεύσω Od. 16.283, etc.: aor. ἔνευσα, Ep. νεῦσα (v. infr.): pf. νένευκα E. IA 1581, etc. (fut. Med. νεύσομαι only in compds.):—

A. incline in any direction:

4. incline, slope, ν. ἀπό τινος εἴς τι incline to wards, Th. 4.100; εἰς τὸ αὐτὸ ν. tend to the same point, Pl. Lg. 945d; πρὸς τὸ λυπῆσαν, πρὸς τοῖς ῥήμασιν, Alex.Aphr. Pr. 1.48,78; of countries, etc., slope, ν. εἰς δύσεις, πρὸς τὸ πέλαγος, Plb. 1.42.6, 1.73.5, etc.; of buildings, etc., look, face, εἰς νότον, etc., PLond. 3.978 (iv A.D.), etc.; μηδαμοῦ ν. to be in equilibrium, Plb. 6.10.7; ταῖς πρῴραις ἔξω νεύοντα τὰ σκάφη Id. 1.26.12: Geom., of straight lines, verge, tend to a point (i. e. to pass through it when produced), Arist. AP 0.76b9, Apollon.Perg. 1.2, etc.: metaph., to be inclined, ἄλλως ν. Theoc. 7.109; ν. εἰς ὀργάν, εἰς ἔλεον, APl. 16.136 (Antiphil.); ἐπὶ χάριν Phalar. Ep. 78; πρὸς γαστέρα Ath. 14.659a; πρὸς θῆλυ Trag.Adesp. 355.

II. metaph., decline, fall away, ἐκ . . τῶν ποτε λαμπρῶν νεύει βίοτος, νεύει δὲ τύχα E. Fr. 153: in Neo-Platonic philosophy, decline, sink in the scale of Being, Plot. 2.9.4, etc.

III. νεύει· ἐπανέρχεται ἢ μᾶλλον φεύγει, Hsch.

IV. Pass., only pf. part. νενευμένος inclined, Teucer in Cat.Cod.Astr. 7.202. (Cf. Skt. návate ‘turn round’, Lat. nuo.)