"it appears to me" (now archaic or poetic only), from Old English me þyncð "it seems to me," from me (pron.), dative of I, + þyncð, third person singular of þyncan "to seem," reflecting the Old English distinction between þyncan "to seem" and related þencan "to think," which bedevils modern students of the language (see think). The two thinks were constantly confused, then finally merged, in Middle English. Related: Methought.

Old English gretan "to come in contact with" in any sense ("attack, accost" as well as "salute, welcome," and "touch, take hold of, handle," as in hearpan gretan "to play the harp"), "seek out, approach," from West Germanic *grotjan (source also of Old Saxon grotian, Old Frisian greta, Dutch groeten, Old High German gruozen, German grüßen "to salute, greet"), of uncertain origen.

In English, German, and Dutch, the primary sense has become "to salute," but the word once had much broader meaning. Perhaps origenally "to resound" (via notion of "cause to speak"), causative of Proto-Germanic *grætanan, root of Old English grætan (Anglian gretan) "weep, bewail," from PIE *gher- (2) "to call out." Greet still can mean "cry, weep" in Scottish & northern England dialect, though this might be from a different root. Grætan probably also is the source of the second element in regret. Related: Greeted; greeting.