reciprocate (v.)

1520s, "a reflexive mode of expression;" 1560s, "act of making a return (especially if mutual), mutual giving and returning, interchange of acts," from Latin reciprocationem (nominative reciprocatio) "retrogression, alternation, ebb," noun of action from past-participle stem of reciprocare "move back, turn back," also "come and go, move back and forth;" from reciprocus "returning the same way; alternating" (see reciprocal).

1570s, "existing on both sides, exclusive or interchangeable" (of duties, etc.), with -al (1) + stem of Latin reciprocus "returning the same way, alternating," from pre-Latin *reco-proco-, from *recus (from re- "back;" see re-, + -cus, adjective formation) + *procus (from pro- "forward," see pro-, + -cus). Related: Reciprocally.

From 1590s as "given, felt, or shown in return;" c. 1600 as "corresponding or answering to each other, mutually equivalent." The sense of "moving backward and forward, having an alternating back and forth motion" (c. 1600) is obsolete. The noun meaning "that which is reciprocal" (to another) is from 1560s. In scientific and mechanical uses, reciprocating, reciprocative (1804), and reciprocatory (1826) have been tried.

"moving backwards and forwards," 1690s, present-participle adjective from reciprocate (v.). Specifically of machines, "having reciprocating parts," by 1822.

Reciprocating engine. A form of engine in which the piston and piston-rod move back and forth in a straight line, absolutely relative to the cylinder, as in oscillating-cylinder engines: in contradistinction to rotary engine. [Century Dictionary, 1895]