Reciprocate
late 16th century: from Latin reciprocat- ‘moved backwards and forwards’, from the verb reciprocare, from reciprocus (see reciprocal).
wiktionary
From Latin recīprocō(“to move back and forth”), possibly from a phrase such as reque proque(“back and forth”), from re-(“back”), prō(“forwards”) and -que(“and”). Compare reciprocal.
etymonline
reciprocate (v.)
1610s, "to give and return mutually," a back-formation from reciprocation, or else from Latin reciprocatus, past participle of reciprocare "rise and fall, move back and forth; reverse the motion of," from reciprocus "returning the same way, alternating" (see reciprocal). Sense of "cause to move back and forth" is from 1650s; intransitive sense of "move backward and forward" is from 1670s. Meaning "to give or do in response, act in return or response" is from 1820. Related: Reciprocated; reciprocating.
