c. 1400, "to put a cap on," from cap (n.); meaning "cover as with a cap" is from c. 1600. Figurative sense of "complete, consummate, bring to a climax" is from 1580s; that of "go one better, outdo, excel" is by 1821. Related: Capped; capping. To cap verses (1610s) was "to quote alternately verses each beginning with the same letter with which the last ended."
The capping of Latin verses is a common game in classical schools. No verse may be used twice, and no hesitation or delay is permitted; so that a moderate proficiency in the game supposes several thousand verses arranged in the memory alphabetically. [Century Dictionary, 1895]
late Old English cæppe "hood, head-covering, cape," a general Germanic borrowing (compare Old Frisian and Middle Dutch kappe, Old High German chappa) from Late Latin cappa "a cape, hooded cloak" (source of Spanish capa, Old North French cape, French chape), a word of uncertain origin. Possibly a shortened from capitulare "headdress," from Latin caput "head" (from PIE root *kaput- "head").
The Late Latin word apparently originally meant "a woman's head-covering," but the sense was transferred to "hood of a cloak," then to "cloak" itself, though the various senses co-existed. Old English took in two forms of the Late Latin word, one meaning "head-covering," the other "ecclesiastical dress" (see cape (n.1)). In most Romance languages, a diminutive of Late Latin cappa has become the usual word for "head-covering" (such as French chapeau).
Meaning "soft, small, close-fitted head covering" in English is from early 13c., originally for women; extended to men late 14c. Extended to cap-like coverings on the ends of anything (such as hubcap) from mid-15c. Meaning "contraceptive device" is first recorded 1916.
Meaning "cap-shaped piece of copper lined with gunpowder and used to ignite a firearm" is by 1825, hence cap-gun (1855); extended to paper version used in toy pistols, 1872 (cap-pistol is from 1879).
Figurative thinking cap is from 1839 (considering cap is 1650s). Cap and bells (1781) was the insignia of a fool; cap and gown (1732) of a scholar. To set one's cap at or for (1773) means "use measures to gain the regard or affection of," usually in reference to a woman seeking a man's courtship.
by c. 1200 as an emphatic form of Old English of (see of), employed in the adverbial use of that word. The prepositional meaning "away from" and the adjectival sense of "farther" were not firmly fixed in this variant until 17c., but once they were they left the original of with the transferred and weakened senses of the word. Meaning "not working" is from 1861.
Off the cuff "extemporaneously, without preparation" (1938) is from the notion of speaking from notes written in haste on one's shirt cuffs. In reference to clothing, off the rack (adj.) "not tailored, not made to individual requirements, ready-made" is by 1963, on the notion of buying it from the rack of a clothing store; off the record "not to be publicly disclosed" is from 1933; off the wall "crazy" is 1968, probably from the notion of a lunatic "bouncing off the walls" or else in reference to carom shots in squash, handball, etc.
a type of woman's indoor cap with a bag-shaped crown and a broad band and frills, 1795 (as simply mob, 1748), from cap (n.) + obsolete mob (n.) "negligent attire" (1660s), earlier "a strumpet" (earlier form mab, 1550s), which is related to the obsolete verb mob "to tousle the hair, to dress untidily" (1660s), and perhaps is ultimately from mop (n.), but has been influenced by Mab as a female name. Dutch has a similar compound, mopmuts, but the relationship between it and the English word is uncertain.
slang, "perform male masturbation," by 1896, from jerk (v.) denoting rapid pulling motion + off (adv.). Compare come off "experience orgasm" (17c.). Farmer and Henley ("Slang and Its Analogues") also lists as synonyms jerk (one's) jelly and jerk (one's) juice. The noun jerk off or jerkoff as an emphatic form of jerk (n.2) is attested by 1968. As an adjective from 1957.