Perseus analyses of αἴσῃ:

αἰ̄σῃ,Αἶσα (who dispenses to every one his lot): fem dat sg (attic epic ionic)
αἴσηι,αἶσις: fem dat sg (epic)

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Αἶσα

Αἶσα, ἡ,

II. as Appellat.,

3. generally, share in a thing, ληΐδος, ἐλπίδος, αἶ., Od. 5.40, 19.84; χθονός Pi. P. 9.56; at a common meal (Argive), Hegesand. 31 ; τῶ Διὸς τῶ ϝοίνω αἶ. Inscr.Cypr. 148; λαχεῖν αἶ. IG 5 (2).40 (Tegea ); for the prov. ἐν καρὸς αἴσῃ v.s. κάρ. —Ep., Lyr., and Trag., but only in lyr. in S. and E.

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αἶσις

αἶσις, ἡ,

A. = κεῦσις, Hdn. Epim. 37. ἀϊσόμενος· φραξάμενος, Hsch. ἀΐσονες· φραγμοί, Id.