Etymology
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contrariwise (adv.)

"on the contrary, on the other hand," mid-15c.; see contrary + wise (n.).

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Definitions of contrariwise

contrariwise (adv.)
in a contrary disobedient manner;
Synonyms: perversely / contrarily
contrariwise (adv.)
with the order reversed;
Synonyms: vice versa / the other way around
contrariwise (adv.)
contrary to expectations; "he didn't stay home; on the contrary, he went out with his friends";
Synonyms: contrarily / to the contrary / on the contrary
From wordnet.princeton.edu