"rope fastened to one of the lower corners of a sail to control it," late 13c., shete, shortened from Old English sceatline "sheet-line," from sceata "lower part of sail," originally "piece of cloth," from same Proto-Germanic source as sheet (n.1). Compare Old Norse skaut, Dutch schoot, German Schote "rope fastened to a sail."

The rope sense of sheet probably is that in the phrase three sheets to the wind "drunk and disorganized," which is recorded by 1812 (in the form three sheets in the wind), an image of a sloop-rigged sailboat whose three sheet-lines have slipped through the blocks are lost to the wind, thus "out of control." Apparently there was an early 19c. informal drunkenness scale in use among sailors and involving one, two, and three sheets, three signifying the highest degree of inebriation; there is a two sheets in the wind from 1813.

It must not be wondered at that the poor, untutored, savage Kentuckyan got "more than two thirds drunk," that is, as the sailors term it, three sheets in the wind and the fourth shivering, before the dinner was ended. [Niles' Weekly Register, May 2, 1812]

c. 1200, autorite, auctorite "authoritative passage or statement, book or quotation that settles an argument, passage from Scripture," from Old French autorité, auctorité "authority, prestige, right, permission, dignity, gravity; the Scriptures" (12c.; Modern French autorité), from Latin auctoritatem (nominative auctoritas) "invention, advice, opinion, influence, command," from auctor "master, leader, author" (see author (n.)).

It usually was spelled with a -c- in English before 16c. but the letter was dropped in imitation of French, then with a -th-, probably by influence of authentic.

It is attested from c. 1300 in the general sense of "legal validity," also "authoritative doctrine" (opposed to reason or experience), also "author whose statements are regarded as correct." It is from mid-14c. as "right to rule or command, power to enforce obedience, power or right to command or act."

In Middle English it also meant "power derived from good reputation; power to convince people, capacity for inspiring trust." It is attested from c. 1400 as "official sanction, authorization." The meaning "persons in authority" is from 1610s; the authorities "those in charge, those with police powers" is recorded from mid-19c.

early 14c., allouen, "to commend, praise; approve of, be pleased with; appreciate the value of;" also, "take into account or give credit for," also, in law and philosophy, "recognize, admit as valid" (a privilege, an excuse, a statement, etc.). From late 14c. as "sanction or permit; condone;" in business, of expenses, etc., by early 15c.

The Middle English word is from Anglo-French alouer, Old French aloer, alloiier (13c.) "to place, situate, arrange; allot, apportion, bestow, assign," from Latin allocare "allocate" (see allocate). This word in Old French was confused and ultimately merged with aloer; alloer "to praise, commend, approve," from Latin allaudare, adlaudare, a compound of ad "to" (see ad-) + laudare "to praise" (see laud).

Between the two primary significations there naturally arose a variety of uses blending them in the general idea of assign with approval, grant, concede a thing claimed or urged, admit a thing offered, permit, etc., etc. [OED].

From the first word came the sense preserved in allowance "money granted;" from the second came allowance "permission based on approval." The 19c. U.S. colloquial meaning "assert, say," also was in English dialect and goes back to 1570s. Related: Allowed; allowing.

1756, "special vocabulary of tramps or thieves" or any set of persons of low character, later "jargon of a particular profession" (1801). The sense of "very informal language characterized by vividness and novelty" is by 1818.

Anatoly Liberman writes here an extensive account of the established origin of the word from the Northern England noun slang "a narrow piece of land running up between other and larger divisions of ground" and the verb slanger "linger, go slowly," which is of Scandinavian origin (compare Norwegian slenge "hang loose, sling, sway, dangle," Danish slænge "to throw, sling"). "Their common denominator seems to be 'to move freely in any direction' " [Liberman]. Noun derivatives of these (Danish slænget, Norwegian slenget) mean "a gang, a band," and Liberman compares Old Norse slangi "tramp" and slangr "going astray" (used of sheep). He writes:

It is not uncommon to associate the place designated for a certain group and those who live there with that group’s language. John Fielding and the early writers who knew the noun slang used the phrase slang patter, as though that patter were a kind of talk belonging to some territory.

So the sense evolution would be from slang "a piece of delimited territory" to "the territory used by tramps for their wandering," to "their camping ground," and finally to "the language used there." The sense shift then passes through itinerant merchants:

Hawkers use a special vocabulary and a special intonation when advertising their wares (think of modern auctioneers), and many disparaging, derisive names characterize their speech; charlatan and quack are among them.

Liberman concludes: 

[Slang] is a dialectal word that reached London from the north and for a long time retained the traces of its low origin. The route was from "territory; turf" to "those who advertise and sell their wares on such a territory," to "the patter used in advertising the wares," and to "vulgar language" (later to “any colorful, informal way of expression”).

The association of the word with thieves and low life faded in the 19c.

[S]lang is a conscious offence against some conventional standard of propriety. A mere vulgarism is not slang, except when it is purposely adopted, and acquires an artificial currency, among some class of persons to whom it is not native. The other distinctive feature of slang is that it is neither part of the ordinary language, nor an attempt to supply its deficiencies. The slang word is a deliberate substitute for a word of the vernacular, just as the characters of a cipher are substitutes for the letters of the alphabet, or as a nickname is a substitute for a personal name. [Henry Bradley, from "Slang," in Encyclopedia Britannica, 11th ed.]

"all right, correct," 1839, only survivor of a slang fad in Boston and New York c. 1838-9 for abbreviations of common phrases with deliberate, jocular misspellings (such as K.G. for "no go," as if spelled "know go;" N.C. for "'nuff ced;" K.Y. for "know yuse"). In the case of O.K., the abbreviation is of "oll korrect."

Probably further popularized by use as an election slogan by the O.K. Club, New York boosters of Democratic president Martin Van Buren's 1840 re-election bid, in allusion to his nickname Old Kinderhook, from his birth in the N.Y. village of Kinderhook. Van Buren lost, the word stuck, in part because it filled a need for a quick way to write an approval on a document, bill, etc.

Spelled out as okeh, 1919, by Woodrow Wilson, on assumption that it represented Choctaw okeh "it is so" (a theory which lacks historical documentation); this spelling was ousted quickly by okay after the appearance of that form in 1929. Greek immigrants to America who returned home early 20c. having picked up U.S. speech mannerisms were known in Greece as okay-boys, among other things.

The noun is first attested 1841, "endorsement, approval, authorization" (especially as indicated by the letters O.K.); the verb, "to approve, agree to, sanction," is by 1888. Okey-doke is student slang first attested 1932.

early 13c., "of or pertaining to the head," from Old French capital, from Latin capitalis "of the head," hence "capital, chief, first," from caput (genitive capitis) "head" (from PIE root *kaput- "head"). The meaning "main, principal, chief, dominant, first in importance" is from early 15c. in English. The modern informal sense of "excellent, first-rate" is by 1754 (as an exclamation of approval, OED's first example is 1875), perhaps from earlier use of the word in reference to ships, "first-rate, powerful enough to be in the line of battle," attested from 1650s, fallen into disuse after 1918. Related: Capitally.

A capital letter "upper-case latter," of larger face and differing more or less in form (late 14c.) is so called because it stands at the "head" of a sentence or word. Capital gain is recorded from 1921. Capital goods is recorded from 1899.

A capital crime or offense (1520s) is one that involves the penalty of death and thus affects the life or "head" (capital had a sense of "deadly, mortal" from late 14c. in English, as it did earlier in Latin). The felt connection between "head" and "life, mortality" also existed in Old English: as in heafodgilt "deadly sin, capital offense," heafdes þolian "to forfeit life." Capital punishment was in Blackstone (1765) and classical Latin capitis poena.

1758, genus name of a type of eight-armed cephalopod mollusks, from Latinized form of Greek oktōpous, literally "eight-foot," from oktō "eight" (see eight) + pous "foot," from PIE root *ped- "foot."

The more usual Greek word seems to have been polypous (also pōlyps), from polys "many" + pous, but for this word Thompson ["Glossary of Greek Fishes," 1947] suggests folk-etymology and a non-Hellenic origin.

The classically correct Greek plural (had the word been used in this sense in ancient Greek) would be octopodes. Octopi (1817) regards the -us in this word as the Latin noun ending that takes -i in plural. Like many modern scientific names of creatures, it was formed in Modern Latin from Greek elements, so it might be allowed to partake of Latin grammar in forming the plural. But it probably is best to let such words follow the grammar of the language that uses them, and octopuses probably works best in English (unless one wishes also to sanction diplodoci for the dinosaurs).

Used figuratively since at least 1882 of powers having far-reaching influence (usually as considered harmful and destructive). To the ancients, the octopus was crafty and dangerous, thrifty (stores food in its nest), and proverbial of clever and adaptable men, based on the animal's instinct of changing color when frightened or for disguise.

It also was thought to be amphibious and to climb trees near shores to steal grapes and olives (the giant ones were said to raid whole warehouses). Thompson writes that "the eggs look remarkably like ripe olives; hence the story." 

c. 1200, prēven, pruven, proven "to try by experience or by a test or standard; evaluate; demonstrate in practice," from Old French prover, pruver "show; convince; put to the test" (11c., Modern French prouver), from Latin probare "to make good; esteem, represent as good; make credible, show, demonstrate; test, inspect; judge by trial" (source also of Spanish probar, Italian probare, and English probe), from probus "worthy, good, upright, virtuous."

This is from PIE *pro-bhwo- "being in front," from *pro-, extended form of root *per- (1) "forward," hence "in front of," + root *bhu- "to be," source also of Latin fui "I have been," futurus "about to be;" Old English beon "to be;" see be.

From early 13c. as "render certain, put out of doubt," also "establish the validity or authenticity of a will, etc." By c. 1300 as "test and find worthy, virtuous, false, etc.," also "find out, discover, ascertain; prove by argument." By mid-14c. as "check the accuracy of." The meaning "be found to be (a hero, coward, etc.) by experience or trial" is by late 14c.

The word had many more senses and broader application in Middle English than Modern English: "to experience; to strive, endeavor; act, accomplish; thrive, succeed." Also in Middle English in a now-obsolete sense of "approve, sanction, praise" (c. 1300; compare approve). Related: Proved; proven; proving. Proving ground "place used for firing cannons for making ballistics tests and testing powder" is by 1837.

Old English fyrst "foremost, going before all others; chief, principal," also (though rarely) as an adverb, "at first, originally," superlative of fore; from Proto-Germanic *furista- "foremost" (source also of Old Saxon fuirst "first," Old High German furist, Old Norse fyrstr, Danish første, Old Frisian ferist, Middle Dutch vorste "prince," Dutch vorst "first," German Fürst "prince"), from PIE *pre-isto-, superlative of *pre-, from root *per- (1) "forward," hence "in front of, before, first, chief."

The usual Old English superlative word was not fyrst, but forma, which shows more clearly the connection to fore. Forma became Middle English firme "first, earliest," but this has not survived.

First aid is that given at the scene, pending the arrival of a doctor. First lady as an informal title for the wife of a U.S. president was in use by 1908, short for First lady of the land (by 1863 with reference to the president's wife); the earlier title was simply Lady (1841). First name is attested from mid-13c. First base "a start" in any sense (1938) is a figurative use from baseball.

First fruits is from late 14c. as "earliest productions of the soil;" 1590s as "first results" of any activity or endeavor. First love is from 1741 as "one's first experience of romantic love;" 1971 as "one's favorite occupation or pastime." First floor is from 1660s as "story built on or just above the ground" (now U.S.); 1865 as "story built next above the ground."

Old English halig "holy, consecrated, sacred; godly; ecclesiastical," from Proto-Germanic *hailaga- (source also of Old Norse heilagr, Danish hellig, Old Frisian helich "holy," Old Saxon helag, Middle Dutch helich, Old High German heilag, German heilig, Gothic hailags "holy"), from PIE *kailo- "whole, uninjured" (see health). Adopted at conversion for Latin sanctus.

The primary (pre-Christian) meaning is not possible to determine, but probably it was "that must be preserved whole or intact, that cannot be transgressed or violated," and connected with Old English hal (see health) and Old High German heil "health, happiness, good luck" (source of the German salutation Heil). Holy water was in Old English.

Holy is stronger and more absolute than any word of cognate meaning. That which is sacred may derive its sanction from man ; that which is holy has its sanctity directly from God or as connected with him. Hence we speak of the Holy Bible, and the sacred writings of the Hindus. He who is holy is absolutely or essentially free from sin; sacred is not a word of personal character. The opposite of holy is sinful or wicked; that of sacred is secular, profane, or common. [Century Dictionary, 1895]

Holy has been used as an intensifying word from 1837; in expletives since 1880s (such as holy smoke, 1883, holy mackerel, 1876, holy cow, 1914, holy moly etc.), most of them euphemisms for holy Christ or holy Moses. Holy Ghost was in Old English (in Middle English often written as one word). Holy League is used of various European alliances; the Holy Alliance was that formed personally by the sovereigns of Russia, Austria, and Prussia in 1815; it ended in 1830.