of or belonging to a δαίμων: properly miraculous, marvellous, but:
in Hom. only in voc., δαιμόνιε, -ίη, good sir, or lady, addressed to chiefs or commoners, Il. 2.190, 200, al., Hes. Th. 655: pl., Od. 4.774: esp. in addressing strangers, 23.166, 174; used by husbands and wives, Il. 6.407, 486 (Hector and Andromache), 24.194 (Priam to Hecuba): later c. gen., δαιμόνιε ἀνδρῶν Hdt. 4.126, 7.48, 8.84: freq. in Com., in an iron. sense, ὦ δαιμόνιʼ ἀνδρῶν Ar. Ec. 564, 784, etc.; ὦ δαιμόνιʼ Id. Ra. 44, 175; ὦ δαιμόνιʼ ἀνθρώπων Id. Av. 1638, cf. Pl. R. 344d, 522b, Grg. 4
from Hdt. and Pi. downwds. (Trag. in lyr.), heaven-sent, miraculous, marvellous, βῶλαξ Pi. P. 4.37; τέρας B. 15.35, S. Ant. 376; ὁρμή Hdt. 7.18; ἀραί, ἄχη, A. Th. 892, Pers. 581; ἡ φύσις δ. ἀλλʼ οὐ θεία Arist. Div. Somn. 463b14; εὐεργεσία D. 2.1; εἰ μή τι δ. εἴη were it not a divine intervention, X. Mem. 1.3.5, cf. S. El. 1270; τὰ δαιμόνια visitations of heaven, ways of God, Th. 2.64, X. Mem. 1.1.12; πολλαὶ μορφαὶ τῶν δ. E. Alc. 1159, al.; δ. ἀνάγκη Lys. l.c.; δ. τύχη of ill fortune, Pl. Hp. Ma.
of persons, τῷ δ. ὡς ἀληθῶς καὶ θαυμαστῷ Id. Smp. 219b; ὁ περὶ τοιαῦτα σοφὸς δ. ἀνήρ ib. 203a; δαιμόνιος τὴν σοφίαν Luc. Philops. 32: Comp. -ώτερος D.C. 53.8.
Adv. -ίως by Divine power, opp. ἀνθρωπίνως, Aeschin. 3.133, cf. Pl. Ti. 25e; marvellously, Ar. Nu. 76; δ. περί τι ἐσπουδακώς Aeschin. 1.41; δ. ποιεῖ, of remedies, Aët. 15.14, al.; [οἶνος] δ. γέρων Alex. 167.5; δ. καὶ μεγαλοπρεπῶς prob. in Epicur. Fr. 183 (cf. δάϊος): neut. pl. as Adv., δαιμόνια Ar. Pax 585; δαιμονιώτατα ἀποθνῄσκει most clearly by the hand of the gods, X. HG 7.4.3: also in fem. dat., δαιμονίᾳ, formed like κοινῇ, θεσπεσίῃ, etc., Pi. O. 9.110.