Origins
The Greeks built theatres as hillsides. A semicircle of stone seats was carved into a natural slope, all eyes aimed at a single stage, and the open sky served as ceiling. The word theatron came from theasthai, "to gaze, to behold" — a theatre was literally "a beholding place," and the sacred act was watching. The oldest surviving Greek theatre, the Theatre of Dionysus on the south slope of the Athenian Acropolis, was where the tragedies of Aeschylus, Sophocles, and Euripides were first performed in the fifth century BCE.
Rome reshaped the geometry. Where Greek drama asked an audience to contemplate a distant stage, Roman spectacle asked it to surround the action. Two Greek semicircles pressed together form an oval, so the Romans took theatron and prefixed it with amphi- ("on both sides, around") — amphitheatron, theatre on both sides. The earliest Roman amphitheatres were wooden, built in the late Republic for magistrates staging gladiatorial games. The first permanent stone amphitheatre was constructed at Pompeii around 70 BCE, survived the eruption of Vesuvius, and can still be visited. The Flavian Amphitheatre in Rome, commissioned by Vespasian and dedicated by Titus in 80 CE, became the archetype. Known today as the Colosseum — a nickname that derives from the hundred-foot bronze Colossus of Nero that once stood beside it — it held around 50,000 spectators and hosted games for nearly four centuries.
The root theasthai runs deeper than architecture. The Greeks' word for a beholding of ideas became theory; a theorem is something seen to be true; a theatre is still the place of looking. Theology is the study of what can be beheld of god; theoria in Hellenistic philosophy named contemplation itself, the highest activity of the mind. All of these share the Greeks' conviction that to understand something was to watch it carefully, and the amphitheatre simply changed who was watching whom — spectator and spectacle now encircled each other in a way no Greek hillside could manage.
Proto-Indo-European Roots
The prefix amphi- descends from Proto-Indo-European *h₂m̥bʰi ("around, on both sides"), one of the most widely attested prepositions in the family. It appears in Latin ambi- (whence ambiguous, ambient, ambassador), in Old English ymbe, in Sanskrit abhí, in Old Church Slavonic obŭ, and in Celtic forms surviving in Welsh am. The same prefix hides in amphibian ("both lives," land and water), amphora ("handles on both sides"), amphibole (a mineral group whose twinned crystals confused early mineralogists), and amphiboly (a grammatical ambiguity). Greek was fond of describing things by what flanked them, and the prefix gave scientists a ready tool for new compounds well into the nineteenth century.
The word entered English in the fourteenth century through the Latin scholarship of the late medieval universities. Chaucer did not use it, but it appears in John Trevisa's 1398 translation of Bartholomew's De proprietatibus rerum, describing the ruined Roman arenas that medieval travellers still gawked at. For two centuries it was a bookish Latinism used only for ancient buildings. The Renaissance revived it as a live architectural term: Inigo Jones drafted plans for a Stuart amphitheatre in 1611, and by the eighteenth century the word had broadened to mean any large oval gathering-space, from surgical theatres at Padua to the tiered lecture rooms of the Enlightenment academies.
Noah Webster's 1828 American Dictionary of the English Language dropped the final -re in favour of -er, one piece of his programme to rationalise English spelling along American lines. British English kept amphitheatre. The Atlantic has been spelling it two ways ever since. Both forms are correct; neither is older; the split is purely a nineteenth-century political choice about which tradition to honour.
Latin Roots
Cognates across Europe follow the Latin form almost everywhere: French amphithéâtre, Italian anfiteatro, Spanish anfiteatro, German Amphitheater, Dutch amfitheater, Romanian amfiteatru, Polish amfiteatr, Russian амфитеатр (amfiteatr). The Romance languages tend to soften the ph cluster to f and the th to t, reflecting regular sound changes from Late Latin into the medieval vernaculars; the Germanic and Slavic forms preserve the Greek spelling more faithfully through direct learned borrowing. What none of them preserve is any distinction between the Greek original and the Roman amphitheatre — European architectural vocabulary inherited both through Latin, and the earlier semicircular shape was subsumed into the rounder word.
Modern English has extended the term far beyond architecture. A natural amphitheatre is a landform — a cirque in the Alps, a glacial hollow in Snowdonia — whose rough semicircle of cliffs suggests the seating of the built form. Surgical amphitheatre was standard nineteenth-century usage for an operating room surrounded by student galleries; the tiered design persists in modern teaching hospitals. Concert amphitheatres — the Hollywood Bowl, Red Rocks — borrow the word for outdoor venues that are in fact closer to Greek theatres than to Roman arenas, a terminological slippage nobody has bothered to correct.