The Cambridge Grammar of Classical Greek says “More frequent alternative forms exist for the 2 sg. act. opt. (παιδεύσ-ειας next to παιδεύσ-αις), 3 sg. act. opt. (παιδεύσ-ειε(ν) next to παιδεύσ-αι) and 3 pl. act. opt. (παιδεύσ-ειαν next to παιδεύσ-αιεν).”
In what sense are these “more frequent”? Are they the more usual endings in Attic, I think Goodwin describes them as aeolic. I would be grateful for some help on this. Are both endings found in attic but “the alternative” forms more often found in (particular) authors.
I think of them as indifferent alternatives in attic. Smyth merely says the longer forms (-ειε etc.) are “more common” but I expect either of the big German grammars gives more detail. Verse will serve as some sort of control but not a very reliable one for prose. Inscriptions might give a better idea.
It’s the παιδεύσαι (or λύσαι) form that’s tricky, since it can be mistaken for the infinitive (παιδεῦσαι).
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These are definitely Attic forms. Smyth § 668 also states that they are more common than -σαις, -σαι, and -σαιεν. I would do some more digging but there’s a cat on my lap.
Chantraine (Morphologie § 313) provides some examples of non-Attic usage (Lesbian, Elean, possibly Aeolic). As far as frequency goes, he only says that this ‘other type’ exists and that Attic uses it “habituellement à la 2e et à la 3e pers. du singulier et à la 3e pers. du pl.“