late 14c., adewe, from Old French a Dieu, a Deu, shortened from phrases such as a dieu (vous) commant "I commend (you) to God," from a "to" (see ad-) + dieu "God," from Latin deum, accusative of deus "god," from PIE *deiwos "god" (from root *dyeu- "to shine," in derivatives "sky, heaven, god"). Originally said to the party left (farewell was to the party setting forth), but in English used as a general parting salutation. As a noun, "expression of kind wishes upon departure," late 14c. Compare native parting salutation good-bye, a contraction of God be with ye.
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