Webster's Revised Unabridged Dictionary · 1913

Me

Me (me) , pronoun

One. See Men, pron. [Obsolete] — Chaucer

Me (mē) , pers. pron.

[Anglo-Saxon , dat. & acc., mec, acc. only; akin to Dutch mij, German mich, Icelandic & Gothic mik, Latin me, Greek me`, 'eme`, Sanskrit , mām. r187. Compare 2d Mine.]

The person speaking, regarded as an object; myself; a pronoun of the first person used as the objective and dative case of the pronoun I; as, he struck me; he gave me the money, or he gave the money to me; he got me a hat, or he got a hat for me.
Me rather had my heart might frrl your love Than my unpleased eye see your courtesy. — Shakespeare

In methinks, me is properly in the dative case, and the verb is impersonal, the construction being, it appears to me. In early use me was often placed before forms of the verb to be with an adjective; as, me were lief.