amphitheater (n.)

late 14c., "open air place in ancient times for viewing spectacles and plays," from Old French theatre (12c., Modern French théâtre, improperly accented) and directly from Latin theatrum "play-house, theater; stage; spectators in a theater" (source also of Spanish, Italian teatro), from Greek theatron "theater; the people in the theater; a show, a spectacle," literally "place for viewing," from theasthai "to behold" (related to thea "a view, a seeing; a seat in the theater," theates "spectator") + -tron, suffix denoting place. (In Old English glosses, theatrum is rendered by wafungstede "a place for sights").

Meaning "building where plays are shown" is from 1570s in English. Transferred sense of "plays, writing, production, the stage" is from 1660s. Generic sense of "place of action" is from 1580s; especially "region where war is being fought" (1914). Spelling with -re arose late 17c. and prevailed in Britain after c. 1700 by French influence, but American English retained or revived the older spelling in -er.