arch

Etymology 1

From Middle English arch, arche, from Old French arche (“an arch”), a feminine form of arc, from Latin arcus (“a bow, arc, arch”). Doublet of arc and arco. Displaced native Old English bīeġels.

noun

1. An inverted U shape.
2. An arch-shaped arrangement of trapezoidal stones, designed to redistribute downward force outward.
3. (architecture) An architectural element having the shape of an arch
4. Any place covered by an arch; an archway.
   to pass into the arch of a bridge
5. (archaic, geometry) An arc; a part of a curve.
6. A natural arch-shaped opening in a rock mass.
7. (anatomy) The curved part of the bottom of a foot.

verb

1. To form into an arch shape.
   The cat arched its back
2. To cover with an arch or arches.

Etymology 2

From the prefix arch-. "Principal" is the original sense; "mischievous" is via onetime frequent collocation with rogue, knave, etc.

adj

1. Knowing, clever, mischievous.
   I attempted to hide my emotions, but an arch remark escaped my lips.
   A certain melancholy that touched her countenance must have been of recent birth, for it had not yet altered the fine and youthful contours of her cheek, nor subdued the arch though resolute curve of her lips. 1906, O. Henry, By Courier
   When you're watching a Wes Anderson film, you know it. Within seconds, you spot the symmetrical compositions, the horizontal camera moves, the blocks of garish colour, the san-serif lettering, the arch, wordy, vaguely melancholy humour and all the other elements that distinguish his comedies from everyone else's. July 12 2021, Nicholas Barber, “The French Dispatch: Four stars for Wes Anderson's latest”, in BBC
   Ms. Brier specializes in point of view, or P.O.V., videos that confront relatable, often hateable characters, with a subtle sneer, gleefully rubbery body and arch delivery of generational catchphrases like “slay, queen” and “I got you,” often repeated for effect. 2023-03-14, Alexandra Jacobs, “Your Annoying Roommate Is Slaying on TikTok”, in The New York Times
2. Principal; primary.
   They were arch enemies.
   Challenger the super scientist, Challenger the arch-pioneer, Challenger the first man of all men whom Mother Earth had been compelled to recognize. 1929, Sir Arthur Conan Doyle, When the World Screamed

noun

1. (obsolete) chief