Etymology
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back up (v.)
1767, "stand behind and support," from back (v.) + up (adv.). Meaning "move or force backward" is by 1834. Of water prevented from flowing, by 1837.
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mutatis mutandis 
"with the necessary changes," Latin, literally "things being changed that have to be changed," from the ablative plurals of, respectively, the past participle and gerundive of mutare "to change" (from PIE root *mei- (1) "to change, go, move").
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Brownian movement (n.)
"rapid oscillatory motion observed in very small particles," 1850, for Scottish scientist Dr. Robert Brown (1773-1858), who first described it.
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