word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."
A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
mid-15c., "to act upon or adjudicate" a legal case, from Latin actus, past participle of agere "to set in motion, drive, drive forward," hence "to do, perform," also "act on stage, play the part of; plead a cause at law" (from PIE root *ag- "to drive, draw out or forth, move").
Most of the modern senses in English probably are from the noun. General sense of "to do, perform, transact" is from c. 1600. Of things, "do something, exert energy or force," by 1751. In the theater from 1590s as "perform as an actor" (intransitive), 1610s as "represent by performance on the stage" (transitive). Meaning "perform specific duties or functions," often on a temporary basis, is by 1804.
To act on "exert influence on" is from 1810. To act up "be unruly" is by 1900 (in reference to a horse). Earlier it meant "acting in accordance with" a duty, expectation, or belief (1645). To act out "behave anti-socially" (1974) is from psychiatric sense of "expressing one's unconscious impulses or desires" (acting out is from 1945). Related: Acted; acting.