Both
Middle English: from Old Norse báthir .
wiktionary
From Middle English bothe, boþe, from Old English bā þā(“both the; both those”) and Old Norse báðir, from Proto-Germanic *bai. Cognate with Saterland Frisian bee(“both”), West Frisian beide(“both”), Dutch beide(“both”), German beide(“both”), Swedish både, båda, Danish både, Norwegian både, Icelandic báðir. Replaced Middle English bō from a form of Old English bēġen.
etymonline
both (adj., pron.)
"the two, the one and the other," 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 *bai, 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.
