Etymology
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nail (n.)

Old English negel "tapering metal pin," nægl "fingernail (handnægl), toenail," from Proto-Germanic *naglaz (source also of Old Norse nagl "fingernail," nagli "metal nail;" Old Saxon and Old High German nagel, Old Frisian neil, Middle Dutch naghel, Dutch nagel, German Nagel "fingernail; small metal spike"), from PIE root *(o)nogh "nail of the finger or toe" (source also of Greek onyx "claw, fingernail;" Latin unguis "fingernail, claw;" Old Church Slavonic noga "foot," noguti "fingernail, claw;" Lithuanian naga "hoof," nagutis "fingernail;" Old Irish ingen, Old Welsh eguin "fingernail, claw").

The "fingernail" sense seems to be the original one, but many figurative uses are from the "small metal spike" sense: hard as nails is from 1828. To hit the nail on the head "say or do just the right thing" is by 1520s; in Middle English driven in the nail (c. 1400) was "to drive home one's point, clinch an argument," and smiten the nail on the hed was "tell the exact truth" (mid-15c.). Phrase on the nail "on the spot, exactly" is from 1590s, of obscure origin; OED says it is not certain it belongs to this sense of nail.

As a unit of English cloth measure (about 2 1/4 inches) from late 14c.; perhaps from a nail being used to mark that length on the end of a yardstick.

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odd (adj.)

c. 1300, odde, "constituting a unit in excess of an even number," from Old Norse oddi "third or additional number," as in odda-maðr "third man, odd man (who gives the casting vote)," odda-tala "odd number." The literal meaning of Old Norse oddi is "point of land, angle" (related via notion of "triangle" to oddr "point of a weapon"); from Proto-Germanic *uzdaz "pointed upward" (source also of Old English ord "point of a weapon, spear, source, beginning," Old Frisian ord "point, place," Dutch oord "place, region," Old High German ort "point, angle," German Ort "place"), from PIE *uzdho- (source also of Lithuanian us-nis "thistle"). None of the other languages, however, shows the Old Norse development from "point" to "third number." Used from late 14c. to indicate a surplus over any given sum.

Sense of "strange, peculiar" first attested 1580s from notion of "odd one out, unpaired one of three" (attested earlier, c. 1400, as "singular" in a positive sense of "renowned, rare, choice"). An odd job "casual, disconnected piece of work" (1728) is so called from notion of "not regular." Odd lot "incomplete or random set" is from 1897. The international order of Odd Fellows began as local social clubs in England, late 18c., with Masonic-type trappings; formally organized 1813 in Manchester, England.

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degree (n.)

c. 1200, "a step, a stair," also "a position in a hierarchy," and "a stage of progress, a single movement toward an end," from Old French degré (12c.) "a step (of a stair), pace, degree (of relationship), academic degree; rank, status, position," which is said to be from Vulgar Latin *degradus "a step," from Latin de- "down" (see de-) + gradus "a step; a step climbed;" figuratively "a step toward something, a degree of something rising by stages" (from PIE root *ghredh- "to walk, go").

A word of wide use in Middle English; in 14c. it also meant "way, manner; condition, state, standing." Most extended senses in Middle English are from the notion of a hierarchy of steps. Genealogical sense of "a certain remove in the line of blood" is from mid-14c.; educational sense of "an academic rank conferred by diploma" is from late 14c. By degrees "gradually, by stages" is from late 14c.

Other transferred senses are from the notion of "one of a number of subdivisions of something extended in space or time," hence "intensive quality, measure, extent." The meaning "1/360th of a circle" is from late 14c. (The division of the circle into 360 degrees was known in Babylon and Egypt; the number is perhaps from the daily motion of the sun through the zodiac in the course of a year.) From 1540s as "a measure of heat;" the specific use as a unit of temperature on a thermometer is by 1727. In reference to crime, by 1670s as "one of certain distinctions of culpability;" in U.S. use by 1821 as "one of the phases of the same kind of crime."

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nation (n.)
Origin and meaning of nation

c. 1300, nacioun, "a race of people, large group of people with common ancestry and language," from Old French nacion "birth, rank; descendants, relatives; country, homeland" (12c.) and directly from Latin nationem (nominative natio) "birth, origin; breed, stock, kind, species; race of people, tribe," literally "that which has been born," from natus, past participle of nasci "be born" (Old Latin gnasci), from PIE root *gene- "give birth, beget," with derivatives referring to procreation and familial and tribal groups.

The word is used in English in a broad sense, "a race of people an aggregation of persons of the same ethnic family and speaking the same language," and also in the narrower sense, "a political society composed of a government and subjects or citizens and constituting a political unit; an organized community inhabiting a defined territory within which its sovereignty is exercised."

In Middle English it is not easy to distinguish them, but the "political society" sense emerged by 16c., perhaps late 14c. and it has gradually predominated. The older sense is preserved in the application of nation to the native North American peoples (1640s). Nation-building "creation of a new nation" is attested by 1907 (implied in nation-builder). Nation-state "sovereign country the inhabitants of which are united by language, culture, and common descent" is from 1918.

A nation is an organized community within a certain territory; or in other words, there must be a place where its sole sovereignty is exercised. [Theodore D. Woolsey, "Introduction to the Study of International Law," 1864] 
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boilerplate (n.)

1831, "iron rolled in large, flat plates for use in making steam boilers," from boiler + plate (n.). In newspaper (and now information technology) slang, the sense of "unit of writing that can be used over and over without change" is attested by 1887. The connecting notion probably is the permanence of the prepared plate compared to set type: From the 1870s to the 1950s, publicity items were cast or stamped in metal ready for the printing press and distributed to country newspapers as filler. An early provider was the American Press Association (1882). The largest supplier later was Western Newspaper Union.

An older name for it was plate-matter "type cast in a number of stereotype plates for insertion in different newspapers" (1878). Plate (n.) is attested by 1824 in printing as "a cast of a page of composed movable types." 

WITHIN the past ten years, "plate matter" has become more and more popular among out-of-town papers, and the more enterprising are discarding the ready prints and are using plate matter instead. For a long time there was a prejudice against "Boiler Plates," but editors of small, and even of prosperous papers, began to discover that better matter was going out in the plates than they could afford, individually, to pay for. It was found that the reading public did not care, so long as the reading columns were bright and newsy, whether they were set up in the local office or in New York. ["The Journalist Souvenir," 1887]
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set (n.2)

"act of setting; state or condition of being set" (originally of the sun or another heavenly body), mid-14c., from set (v.) or its identical past participle. Old English had set "seat," in plural "camp; stable," but OED finds it "doubtful whether this survived beyond OE." Compare set (n.1).

Disparate senses collect under this word because of the many meanings given the verb. The sense of "manner or position in which something is set" is by 1530s, hence "general movement, direction, drift, tendency, inclination" (of mind, character, policy, etc.), by 1560s.

The meaning "permanent change of shape caused by pressure; a bend, warp, kink" is by 1812; that of "action of hardening," by 1837. Hence "action or result of fixing the hair when damp so that it holds the desired style" (1933).

"Something that has been set" (1510s), hence the use in tennis, "set of six games which counts as a unit" (1570s) and set-point "state of the game at which one side or player needs only one point to win the set" (by 1928).

The theatrical meaning "scenery for an individual scene in a play, etc.," is by 1859, from the past-participle adjective. It later was extended in movie and television production to the place or area where filming takes place.

Set (n.1) and set (n.2) are not always distinguished in dictionaries; OED has them as two entries, Century Dictionary as one. The difference of opinion seems to be whether the set meaning "group, grouping" (here (n.2)) is a borrowing of the unrelated French word that sounds like the native English one, or a borrowing of the sense only, which was absorbed into the English word.

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night (n.)

late Old English niht (West Saxon neaht, Anglian næht, neht) "the dark part of a day; the night as a unit of time; darkness," also "absence of spiritual illumination, moral darkness, ignorance," from Proto-Germanic *nahts (source also of Old Saxon and Old High German naht, Old Frisian and Dutch nacht, German Nacht, Old Norse natt, Gothic nahts).

The Germanic words are from PIE *nekwt- "night" (source also of Greek nyx "a night," Latin nox, Old Irish nochd, Sanskrit naktam "at night," Lithuanian naktis "night," Old Church Slavonic nosti, Russian noch', Welsh henoid "tonight"), according to Watkins, probably from a verbal root *neg- "to be dark, be night." For spelling with -gh- see fight.  The vowel indicates that the modern English word derives from oblique cases (genitive nihte, dative niht).

The fact that the Aryans have a common name for night, but not for day (q.v.), is due to the fact that they reckoned by nights. [Weekley]

Thus in Old English combinations night was "the night before (a certain day or feast day);" compare German Weihnachten "Christmas," literally "holy night." In early times, the day was held to begin at sunset, so Old English monanniht "Monday night" was the night before Monday, or what we would call Sunday night; so saeterniht "Friday night." The Greeks, by contrast, counted their days by mornings.

To work nights preserves the Old English genitive of time. Night soil "excrement" (1770) is so called because it was removed (from cesspools, etc.) after dark. Night train is attested from 1838; night-school from 1520s; night-life "habitual nocturnal carousing" is attested from 1852.

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ace (n.)

c. 1300, "one at dice," from Old French as "one at dice" (12c.), from Latin as "a unit, one, a whole, unity;" also the name of a small Roman coin (originally a rectangular bronze plaque weighing one pound, it eventually was reduced by depreciation to half an ounce; in imperial times it became a round coin). The Latin word also is the source of Spanish as, Italian asso, German ass, Dutch aas, Danish es. It is perhaps originally Etruscan and related to Greek heis "one" (from PIE root *sem- (1) "one, as one"), or it might have been taken directly into Latin from the Greek word.

In English, it meant the side of the die with only one mark before it meant the playing card with one pip (1530s). Because this was the lowest roll at dice, ace was used metaphorically in Middle English for "bad luck" or "something of no value;" but as the ace often is the highest playing card, the extended senses based on "excellence, good quality" arose 18c. as card-playing became popular. Ace in the hole in the figurative sense of "concealed advantage" is attested from 1904, from crooked stud-poker deals.

The meaning "outstanding pilot" dates from 1917 (technically, in World War I aviators' jargon, one who has brought down 10 enemy planes, though originally in reference to 5 shot down), from French l'ace (1915), which, according to Bruce Robertson (ed.) "Air Aces of the 1914-1918 War" was used in prewar French sporting publications for "top of the deck" boxers, cyclists, etc. The sports meaning "point scored" (1819) led to sense of "unreturnable serve" (by 1889).

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quarter (n.1)

c. 1300, "one-fourth of anything; one of four equal parts or divisions into which anything is or may be divided;" often in reference to the four parts into which a slaughtered animal is cut, from Old French quartier, cartier (12c.), from Latin quartarius "fourth part," from quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four"). One of the earliest dated references in English is to "parts of the body as dismembered during execution" (c. 1300).

Used of the phases of the moon from early 15c. The phrase quarter of an hour is attested from mid-15c. In Middle English quarter also meant "one of the four divisions of a 12-hour night" (late 14c.), and the quarter of the night meant "nine o'clock p.m." (early 14c.). As a period of time in a football game, from 1911. 

From late 14c. as "one of the four quadrants of the heavens;" hence, from the notion of the winds, "a side, a direction" (c. 1400). In heraldry from mid-14c. as "one of the four divisions of a shield or coat of arms."

Meaning "region, locality, area, place" is from c. 1400. Meaning "distinct portion of a town" (identified by the class or race of people who live there) is first attested 1520s. For military sense, see quarters.

The coin (one fourth of a dollar, originally silver) is peculiar to U.S. and dates to 1783. But quarter could mean "a farthing" (one quarter of a penny) in Middle English (late 14c.), and compare quadrant "a farthing" (c. 1600), and classical Latin quadrans, the name of a coin worth a quarter of an as (the basic unit of Roman currency).

Quarter horse, bred strong for racing on quarter-mile tracks, is recorded by 1834. The word's connection with "four" loosened in Middle English and by 15c. expressions such as six-quartered for "six-sided" are found.  

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