c. 1200, "nun's head covering," from Anglo-French and Old North French veil (12c., Modern French voile) "a head-covering," also "a sail, a curtain," from Latin vela, plural of velum "sail, curtain, covering," from PIE root *weg- (1) "to weave a web." Vela was mistaken in Vulgar Latin for a feminine singular noun. To take the veil "become a nun" is attested from early 14c.
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Harper, D. (n.d.). Etymology of voile. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/voile