Lexical Definition

‎ἀεί‎ aeí (ah-eye') always ^G:ADV
from an obsolete primary noun (apparently meaning continued duration)

always, ever.

• "ever," by qualification regularly
• by implication, earnestly

Abbott-Smith

ἀεί, adv., [in LXX: Is 42:14 (מֵעוֹלָם) 51:13 (תָּמִיד), Ps 94 (95):10*, al.;]
ever;
1. of continuous time, unceasingly, perpetually: Ac 7:51, 2 Co 4:11 6:10, Tit 1:12, He 3:10.
2. Of successive occurrences, on every occasion (MM, VGT, s.v.): I Pe 3:15, II Pe 1:12.†

Abbott-Smith References

Liddell-Scott-Jones

ἀεί,

adverb ever, always, [Refs 8th c.BC+]; with other specifications of time, ἐμμενὲς αἰεί[Refs 8th c.BC+]; ἀ. καθ᾽ ἡμέραν, καθ᾽ ἡμέραν ἀ., ἀ. καὶ καθ᾽ ἡμέραν, ἀ. κατ᾽ ἐνιαυτόν, ἀ. διὰ βίου, etc., [Refs 5th c.BC+]; δεῦρ᾽ ἀεί until now, [Refs 5th c.BC+]; αἰεί κοτε, ποτε from of old, [Refs 5th c.BC+]; compare εἰσαεί:—with the Article, ὁ ἀ. χρόνος eternity, [Refs 5th c.BC+]; οἱ ἀ. ὄντες the immortals, [Refs 5th c.BC+] —but ὁ αἰ. βασιλεύων the king for the time being, [Refs 5th c.BC+]; ὁ αἰ. ἐντὸς γιγνόμενος every one as he got inside, [Refs 5th c.BC+]; τοῖσι τούτων αἰ. ἐκγόνοισι to their descendants for ever, [ἀεί is postponed for the sake of meter—Dialectic forms (cf. Hdn.Gr. 1.497">Refs 5th c.BC+], Et.Gud.z):

__1 αἰεί, Epic dialect, Ionic dialect, poetical, and Early Attic dialect [ἀεί) in \_Attic dialect\_ Inscrr. to 4th c.BC ">Refs 4th c.BC+]
__2 ἀεί [ᾰ three times in [Refs 8th c.BC+], ᾱ?\~X Attic dialect] normal in Attic dialect Inscrr. from [Refs 4th c.BC+]
__3 αἰέν, [Refs 8th c.BC+]
__4 Doric dialect αἰές, [Refs 5th c.BC+]; also ἀές, [Refs]
__5 Aeolic dialect αἶι(ν), ἄιν, Hdn.Gr.[same place];[ἀείδασμος}. ">Refs]
__6 αἰέ, Hdn.Gr. [prev. cited]
__7 ἀέ, [Refs 5th c.BC+] (ᾰἐ); compare ἀέ-ναος.
__8 Boeotian dialect ἠί, [Refs 2nd c.AD+]
__9 Tarentum dialect αἰή, [Refs]
__II τὸ ἀ. eternity, τὸ ἀ. τοῦτο οὐκ αἰώνιόν ἐστιν ἀλλὰ χρονικόν[ἀεί">Refs 1st c.AD+] = ἕως in Attic dialect is based on misinterpretation of such phrases as ἐς τόνδε αἰ. τὸν πόλεμον[Refs 5th c.BC+], cf. Latin aevum.)