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Old English wadan "to go forward, proceed," in poetic use only, except as oferwaden "wade across," from Proto-Germanic *wadan (cf. Old Norse vaða, Danish vade, Old Frisian wada, Dutch waden, Old High German watan, German waten "to wade"), from PIE root *wadh- "to go," found only in Germanic and Latin (cf. Latin vadere "to go," vadum "shoal, ford," vadare "to wade"). Italian guado, French gué "ford" are Germanic loan-words.
Specifically of walking into water from c.1200. Originally a strong verb (past tense wod, past participle wad); weak since 16c. Figurative sense of "to go into" (action, battle, etc.) is recorded from late 14c. Related: Waded; wading.