c. 1600, "resembling a mitre, of or pertaining to a mitre," from French mitral, from Modern Latin mitralis, from Latin mitra (see mitre). The mitral valve of the heart is so called from 1705, from Modern Latin mitrales valvulae.
1560s, "quinsy," from choke (v.). Meaning "action of choking" is from 1839. Meaning "valve which controls air to a carburetor" first recorded 1926; earlier it meant "constriction in the bore of a gun" (1875).
in various mechanical senses, such as "turn-valve of a faucet" (early 15c.), of uncertain connection with cock (n.1). Perhaps all are based on real or fancied resemblances not now obvious; German has hahn "cock" in many of the same senses.
The cock of a firearm, which when released by the action of the trigger discharges the piece, is from 1560s. Hence "position into which the hammer is brought by being pulled back to the catch" (1745). For half-cocked, see cock (v.).