both (adj., pron.) Look up both at Dictionary.com
there are several theories, all similar, and deriving the word from the tendency to say "both the." One is that it is Old English begen (masc.) "both" (from Proto-Germanic *ba, from PIE *bho "both") + -þ extended base. Another traces it to the Proto-Germanic formula represented in Old English by ba þa "both these," from ba (feminine nominative and accusative of begen) + þa, nominative and accusative plural of se "that." A third traces it to Old Norse baðir "both," from *bai thaiz "both the," from Proto-Germanic *thaiz, third person plural pronoun. Compare similar formation in Old Frisian bethe, Dutch beide, Old High German beide, German beide, Gothic bajoþs.