"structure (in a building, bridge, etc.) in the shape of a curve that stands when supported only a the extremities," c. 1300, from Old French arche "arch of a bridge, arcade" (12c.), from Latin arcus "a bow" (see arc (n.)). Replaced native bow (n.1).
Originally architectural in English; transferred by early 15c. to anything having a curved form (eyebrows, feet, etc.). The commemorative or monumental arch is attested in English from late 14c. Compare Middle English Seinte Marie Chirche of the Arches (c. 1300) in London, later known as St. Mary-le-Bow, site of an ecclesiastical court, so called for the arches that supported its steeple (the modern church is by Sir Christopher Wren, rebuilt after the Great Fire of 1666).
1540s, "chief, principal," from separate use of the prefix arch-, which is attested from late Old English (in archangel, archbishop, etc.). The prefix figured in so many derogatory uses (arch-rogue, arch-knave, etc.) that by mid-17c. it had acquired a meaning of "roguish, mischievous," softened by 19c. to "saucy." The shifting sense is exemplified by archwife (late 14c.), variously defined as "a wife of a superior order" or "a dominating woman, virago." Related: Archly; archness.
early 14c., "to form an arch" (implied in arched); c. 1400 in transitive sense "furnish with an arch," from arch (n.). Related: Arching.