Etymology
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misquote (v.)

1590s, "misconstrue, misinterpret;" see mis- (1) "badly, wrongly" + quote (v.). First recorded in Shakespeare.

Looke how we can, or sad or merrily, Interpretation will misquote our lookes. ["I Hen. IV," v.ii.13]

The more usual modern sense of "cite incorrectly" is by 1690s. Related: Misquoted; misquoting. As a noun, "an incorrect quotation," from 1855.

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mislay (v.)

c. 1400, misleien, "to misinterpret or misquote an authority," from mis- (1) "badly, wrongly" + lay (v.) in the now-obsolete Middle English sense of "cite, allege, say." Main modern meaning of "lay in a wrong or unaccustomed place, put in a place afterward forgotten" is from 1610s. Related: Mislaid; mislaying.

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