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Middle English merger of Old English dor (neuter; plural doru) "large door, gate," and Old English duru (fem., plural dura) "door, gate, wicket;" both from Proto-Germanic *dur- (cf. Old Saxon duru, Old Norse dyrr, Danish dør, Old Frisian dure, Old High German turi, German Tür).
The Germanic words are from PIE *dhwer- "a doorway, a door, a gate" (cf. Greek thura, Latin foris, Gaulish doro "mouth," Gothic dauro "gate," Sanskrit dvárah "door, gate," Old Persian duvara- "door," Old Prussian dwaris "gate," Russian dver' "a door").
The base form is frequently in dual or plural, leading to speculation that houses of the original Indo-Europeans had doors with two swinging halves. Middle English had both dure and dor; form dore predominated by 16c., but was supplanted by door.
A door is what a dog is perpetually on the wrong side of. [Ogden Nash]