Etymology
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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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fire (v.)

c. 1200, furen, "arouse, inflame, excite" (a figurative use); literal sense of "set fire to" is attested from late 14c., from fire (n.). The Old English verb fyrian "to supply with fire" apparently did not survive into Middle English. Related: Fired; firing.

Meaning "expose to the effects of heat or fire" (of bricks, pottery, etc.) is from 1660s. Meaning "to discharge artillery or a firearm" (originally by application of fire) is from 1520s; extended sense of "to throw (as a missile)" is from 1580s. Fire away in the figurative sense of "go ahead" is from 1775.

The sense of "sack, dismiss from employment" is recorded by 1877 (with out; 1879 alone) in American English. This probably is a play on the two meanings of discharge (v.): "to dismiss from a position," and "to fire a gun," influenced by the earlier general sense "throw (someone) out" of some place (1871). To fire out "drive out by or as if by fire" (1520s) is in Shakespeare and Chapman. Fired up "angry" is from 1824 (to fire up "become angry" is from 1798).

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catch (n.)

late 14c., "device to hold a latch of a door," also "a trap;" also "a fishing vessel," from catch (v.). The meaning "action of catching" is attested from 1570s. The meaning "that which is caught or worth catching" (later especially of spouses) is from 1590s. The sense of "hidden cost, qualification, etc.; something by which the unwary may be entrapped" is slang first attested 1855 in writings of P.T. Barnum.

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catch (v.)

c. 1200, "to take, capture," from Anglo-French or Old North French cachier "catch, capture" animals (Old French chacier "hunt, pursue, drive" animals, Modern French chasser "to hunt"), from Vulgar Latin *captiare "try to seize, chase" (also source of Spanish cazar, Italian cacciare), from Latin captare "to take, hold," frequentative of capere "to take, hold" (from PIE root *kap- "to grasp"). A doublet of chase (v.).

Its senses in early Middle English also included "to chase, hunt," which later went with chase (v.). Of sleep, etc., from early 14c.; of infections from 1540s; of fire from 1734 (compare Greek aptō "fasten, join, attach, grasp, touch," also "light, kindle, set on fire, catch on fire"). Related: Catched (obsolete); catching; caught.

The meaning "act as a catcher in baseball" is recorded from 1865. To catch on "apprehend, understand" is by 1884, American English colloquial. To catch the eye "draw the attention" is attested by 1718. Catch as catch can has roots in late 14c. (cacche who that cacche might).

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catch-all (n.)

also catchall, "something used as a general receptacle for odds and ends," 1838, from catch (v.) + all.

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Catch-22 (n.)

from the title of Joseph Heller's 1961 novel, but the phrase became widespread after release of the movie based on the book in 1970. The catch (n.) is that a bomber pilot is insane if he flies combat missions without asking to be relieved from duty, and thus he is eligible to be relieved from duty. But asking to be relieved from duty indicates sanity and thus he must keep flying missions.

There was only one catch and that was Catch-22, which specified that a concern for one's safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.
"That's some catch, that Catch-22," he observed.
"It's the best there is," Doc Daneeka agreed.
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fire-walker (n.)

one who walks barefoot over hot coals without injury, as an entertainment, etc., 1895, from fire (n.) + agent noun from walk (v.). Related: Fire-walking.

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fire-ant (n.)

1796, from fire (n.) + ant. So called for their bite.

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cease-fire (n.)

also ceasefire, "a cessation of shooting," 1916, from the verbal phrase cease fire, attested from 1847 as a military command (formerly also signaled by bugles), from cease (v.) + fire (n.) in the gunnery sense. Generally written as two words until after mid-20c.

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catch-phrase (n.)

also catchphrase, "phrase caught up and repeated," 1837, from catch (v.) + phrase (n.). The notion is of words that will "catch" in the mind (compare catchword, which is older and might have suggested this word; also catchy). From the first in a political context, also of lines from plays that became popular.

This new experiment consists in a "divorce of bank and State." This is a mere catch-phrase, which was originally introduced by artful and designing politicians to impose upon the credulity and honesty of the people. Many have adopted it without reflecting or inquiring as to its import, or its consequences. [Sen. Talmage (Georgia), U.S. Senate debate on the Sub-Treasury Bill, Sept. 22, 1837]
In political or partisan squibs, the introduction of such phrases may be properly allowed, though sparingly ; for they are most undoubtedly a species of ornament that soon nauseates upon repetition. There is a still lower species of "slang," consisting of the "catch phrase of the day," in great vogue among the gods at the minor theatres, that we only mention to reprobate entirely ; and which, as common sense is no ingredient in its concoction, is as destitute of energy as it is abhorrent to a cultivated ear. ["T.A.," "Guide for the Writing-Desk; or, Young Author's and Secretary's Friend," etc., London, 1846]
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