vice versa

"the order being changed," c. 1600, Latin, from vice, ablative of vicis "a change, alternation, alternate order" (from PIE root *weik- (2) "to bend, to wind") + versa, feminine ablative singular of versus, past participle of vertere "to turn, turn about" (from PIE root *wer- (2) "to turn, bend"). "The phrase has the complete force of a proposition, being as much as to say that upon a transposition of antecedents the consequents are also transposed" [Century Dictionary].