Etymology
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meat (n.)

Middle English mēte, from Old English mete "food, nourishment, sustenance" (paired with drink), "item of food; animal food, fodder," also "a meal, repast," from Proto-Germanic *mati (source also of Old Frisian mete, Old Saxon meti, Old Norse matr, Old High German maz, Gothic mats "food," Middle Dutch, Dutch metworst, German Mettwurst "type of sausage"), from PIE *mad-i-, from root *mad- "moist, wet," also with reference to food qualities, (source also of Sanskrit medas- "fat" (n.), Old Irish mat "pig;" see mast (n.2)).

Narrower sense of "flesh of warm-blooded animals killed and used as food" is attested from c. 1300 (earlier this was flesh-meat, early 12c.). There is a similar sense evolution in French viande "meat," originally "food." In Middle English, vegetables still could be called grene-mete (15c.) and white meat was "a dairy food or product" (early 15c.). Figurative sense of "essential part" is from 1901.

Dark meat and light meat in reference to the meat of fowls, based on the color when cooked, were popularized 19c., supposedly as euphemisms for leg or thigh and breast, but earliest sources use both sets of terms without apparent embarrassment.

The choicest parts of a turkey are the side bones, the breast, and the thigh bones. The breast and wings are called light meat; the thigh-bones and side-bones dark meat. When a person declines expressing a preference, it is polite to help to both kinds. [Lydia Maria Child, "The American Frugal Housewife," Boston, 1835]

First record of meat loaf is from 1876. Meat-market "place where one looks for sex partners" is from 1896 (meat in various sexual senses of "penis, vagina, body regarded as a sex object, prostitute" are attested from 1590s; Old English for "meat-market" was flæsccyping ('flesh-cheaping')); slang meat wagon "ambulance" is from 1920, American English slang, said to date from World War I (in a literal sense by 1857). Meat-grinder is by 1858 in the literal sense "device for grinding meat;" in the figurative sense it is attested by 1951. Meat-hook is by 1812; in the colloquial transferred sense "arm" it is attested by 1919.

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fire (n.)

Old English fyr "fire, a fire," from Proto-Germanic *fūr- (source also of Old Saxon fiur, Old Frisian fiur, Old Norse fürr, Middle Dutch and Dutch vuur, Old High German fiur, German Feuer "fire"), from PIE *perjos, from root *paewr- "fire." Current spelling is attested as early as 1200, but did not fully displace Middle English fier (preserved in fiery) until c. 1600.

PIE apparently had two roots for fire: *paewr- and *egni- (source of Latin ignis). The former was "inanimate," referring to fire as a substance, and the latter was "animate," referring to it as a living force (compare water (n.1)).

Brend child fuir fordredeþ ["The Proverbs of Hendyng," c. 1250]

English fire was applied to "ardent, burning" passions or feelings from mid-14c. Meaning "discharge of firearms, action of guns, etc." is from 1580s. To be on fire is from c. 1500 (in fire attested from c. 1400, as is on a flame "on fire"). To play with fire in the figurative sense "risk disaster, meddle carelessly or ignorantly with a dangerous matter" is by 1861, from the common warning to children. Phrase where's the fire?, said to one in an obvious hurry, is by 1917, American English.

Fire-bell is from 1620s; fire-alarm as a self-acting, mechanical device is from 1808 as a theoretical creation; practical versions began to appear in the early 1830s. Fire-escape (n.) is from 1788 (the original so-called was a sort of rope-ladder disguised as a small settee); fire-extinguisher is from 1826. A fire-bucket (1580s) carries water to a fire. Fire-house is from 1899; fire-hall from 1867, fire-station from 1828. Fire company "men for managing a fire-engine" is from 1744, American English. Fire brigade "firefighters organized in a body in a particular place" is from 1838. Fire department, usually a branch of local government, is from 1805. Fire-chief is from 1877; fire-ranger from 1887.

Symbolic fire and the sword is by c. 1600 (translating Latin flamma ferroque absumi); earlier yron and fyre (1560s), with suerd & flawme (mid-15c.), mid fure & mid here ("with fire and armed force"), c. 1200. Fire-breathing is from 1590s. To set the river on fire, "accomplish something surprising or remarkable" (usually with a negative and said of one considered foolish or incompetent) is by 1830, often with the name of a river, varying according to locality, but the original is set the Thames on fire (1796). The hypothetical feat was mentioned as the type of something impossibly difficult by 1720; it circulated as a theoretical possibility under some current models of chemistry c. 1792-95, which may have contributed to the rise of the expression.

[A]mong other fanciful modes of demonstrating the practicability of conducting the gas wherever it might be required, he anchored a small boat in the stream about 50 yards from the shore, to which he conveyed a pipe, having the end turned up so as to rise above the water, and forcing the gas through the pipe, lighted it just above the surface, observing to his friends "that he had now set the river on fire." ["On the Origins and Progress of Gas-lighting," in "Repertory of Patent Inventions," vol. III, London, 1827]
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run (v.)

Old English, "move swiftly by using the legs, go on legs more rapidly than walking," also "make haste, hurry; be active, pursue or follow a course," and, of inanimate things, "to move over a course."

The modern verb is a merger of two related Old English words, in both of which the initial two letters sometimes switched places. The first is intransitive rinnan, irnan "to run, flow, run together" (past tense ran, past participle runnen), which is cognate with Middle Dutch runnen, Old Saxon, Old High German, Gothic rinnan, German rinnen "to flow, run."

The second is Old English transitive weak verb ærnan, earnan "ride, run to, reach, gain by running" (probably a metathesis of *rennan), from Proto-Germanic *rannjanan, causative of the root *ren- "to run." This is cognate with Old Saxon renian, Old High German rennen, German rennen, Gothic rannjan.

Watkins says both are from PIE *ri-ne-a-, nasalized form of root *rei- "to run, flow," but Boutkan's sources find this derivation doubtful based on the poor attestation of supposed related forms, and he lists it as of "No certain IE etymology."

Of streams, etc., "to flow," from late Old English. From c. 1200 as "take flight, retreat hurriedly or secretly." Phrase run for it "take flight" is attested from 1640s.

Also from c. 1200 as "compete in a race." Extended to "strive for any ends," especially "enter a contest for office or honors, stand as a candidate in an election" (1826, American English).

Of any sort of hurried travel, c. 1300. From early 13c. as "have a certain direction or course." By c. 1300 as "keep going, extend through a period of time, remain in existence." Specifically of theater plays by 1808. Of conveyances, stage lines, etc., "perform a regular passage from place to place" by 1817.

Of machinery or mechanical devices, "go through normal or allotted movements or operation," 1560s. Of colors, "to spread in a fabric when exposed to moisture," 1771. Of movie film, "pass between spools," hence "be shown," by 1931.

The meaning "carry on" (a business, etc.) is by 1861, American English; hence extended senses of "look after, manage." As "publish or print in a newspaper or magazine," by 1884. 

Many senses are via the notion of "pass into or out of a certain state." To run dry "cease to yield water or milk" (1630s). In commerce, "be of a specified price, size, etc.," by 1762. To run low "be nearly exhausted" is by 1712; to run short "exhaust one's supply" is from 1752; to run out of in the same sense is from 1713. To run on "keep on, continue without pause or change" is from 1590s.

The transitive sense of "cause to run" was in Old English. By late 15c. as "to pierce, stab," hence 1520s as "thrust through or into something." The meaning "enter (a horse) in a race" is from 1750. The sense of "cause a mechanical device to keep moving or working" is by 1817.

Many figurative uses are from horseracing or hunting (such as to run (something) into the ground "carry to excess, exhaust by constant pursuit," 1836, American English).

To run across "meet by chance, fall in with" is attested from 1855, American English. To run into in this sense is by 1902. To run around with "consort with" is from 1887.

In reference to fevers by 1918. To run a (red) traffic signal is by 1933. Of tests, experiments, etc., by 1947. Of computers by 1952. Time has been running out since c. 1300. To run in the family is by 1771. The figurative expression run interference (1929) is from U.S. football. To run late is from 1954.

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