reciprocity (n.)

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 The sense of "moving backward and forward, having an alternating back and forth motion" (c. 1600) is obsolete.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.