late 14c., "movable joint of a gate or door," not found in Old English, cognate with Middle Dutch henghe "hook, handle," Middle Low German henge "hinge," from Proto-Germanic *hanhan (transitive), *hangen (intransitive), from PIE *konk- "to hang" (see hang (v.)). The notion is the thing from which a door hangs. Figurative sense of "that on which events, etc., turn" is from c.1600. Stamp-collecting sense is from 1883.
1610s, "suitcase, soldier's kit bag," from French valise (16c.), from Italian valigia, a word of uncertain origin. Attested in Medieval Latin forms valisia (early 15c.), valixia (late 13c.). "The name is generally given to a leather case of moderate size, opening wide on a hinge or like a portfolio ...." [Century Dictionary]
"pin on which a wheel or other object turns," 1610s, from French pivot, from Old French pivot "hinge pin, pivot" (12c.), also "penis," a word of uncertain origin. Pevetsheres, evidently some kind of shears, is mentioned in a will registered in York in 1398. Figurative sense of "turning point, that on which some matter hinges or depends" is recorded from 1813.
"chief, pivotal," early 14c., from Latin cardinalis "principal, chief, essential," a figurative use, literally "pertaining to a hinge," from cardo (genitive cardinis) "that on which something turns or depends; pole of the sky," originally "door hinge," which is of unknown origin. Related: Cardinally.
The cardinal numbers (1590s) are "one, two, three," etc. as opposed to ordinal numbers "first, second, third," etc.; they are so called because they are the principal numbers and the ordinals depend on them.
The cardinal points (1540s) are north, south, east, west. The cardinal sins (c. 1600) are too well known to require rehearsal. The cardinal virtues (c. 1300) were divided into natural (justice, prudence, temperance, fortitude) and theological (faith, hope, charity). The natural ones were the original classical ones, which were amended by Christians. But typically in Middle English only the first four were counted as the cardinal virtues:
Of þe uour uirtues cardinales spekeþ moche þe yealde philosofes. ["Ayenbite of Inwyt," c. 1340]
By analogy of this, and cardinal winds (late 14c.), cardinal signs (four zodiacal signs marking the equinoxes and the solstices, late 14c.), etc., the adjective in Middle English acquired an association with the number four.
Meaning "thread or cord composed of two or more fibers" is recorded from 1550s. Meaning "act or action of turning on an axis" is attested from 1570s. Sense of "beverage consisting of two or more liquors" is first attested c. 1700. Meaning "thick cord of tobacco" is from 1791. Meaning "curled piece of lemon, etc., used to flavor a drink" is recorded from 1958. Sense of "unexpected plot development" is from 1941.
The popular rock 'n' roll dance craze is from 1961, so called from the motion involved, but twist was used to describe popular dances in 1894 and again in the 1920s. To get one's knickers in a twist "be unduly agitated" is British slang first attested 1971.