Etymology
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trade (n.)

late 14c., "path, track, course of action," introduced by the Hanse merchants, from Middle Dutch or Middle Low German trade "track, course" (probably originally of a ship), cognate with Old English tredan (see tread (v.)).

Sense of "one's habitual business" (1540s) developed from the notion of "way, course, manner of life" (mid-15c.); sense of "buying and selling, exchange of commodities" is from 1550s. Meaning "act of trading" is from 1829. Trade-name is from 1821; trade-route is from 1873; trade-war is from 1899. Trade union is attested from 1831. Trade wind (1640s) has nothing to do with commerce, but preserves the obsolete sense of "in a habitual or regular course."

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trade (v.)
1540s, "to tread a path," from trade (n.). Meaning "to occupy oneself (in something)" is recorded from c. 1600. Meaning "to barter" is by 1793. The U.S. sports team sense of "to exchange one player for another" is attested from 1899. Related: Traded; trading. To trade down is attested from 1942; trade up from 1959. Trade places "exchange situations" is from 1917. Trading post is recorded from 1796. Trading stamp, given by merchants and exchangeable for goods, is from 1897.
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rat (v.)

1812, "to desert one's party, go over from a losing cause;" 1847 as "to work for less than current wages, refuse to join a labor strike;" 1864 as "to catch or kill rats;" 1910 as "to peach on, inform on, behave dishonestly toward;" from rat (n.). All but the third are extended from the proverbial belief that rats leave a ship about to sink or a house about to fall. Related: Ratted; ratting.

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rat (n.)

"a rodent of some of the larger species of the genus Mus," late Old English ræt "rat," a word of uncertain origin. Similar words are found in Celtic (Gaelic radan), Romanic (Medieval Latin ratus, Italian ratto, Spanish rata, Old French rat) and Germanic (Old Saxon ratta; Middle Dutch ratte, Dutch rat; German Ratte, dialectal Ratz; Swedish råtta, Danish rotte) languages, but their connection to one another and the ultimate source of the word are unknown. In its range and uncertain origin, it is much like cat.

Perhaps from Vulgar Latin *rattus, but Weekley thinks this is of Germanic origin, "the animal having come from the East with the race-migrations" and the word passing thence to the Romanic languages. American Heritage and Tucker connect Old English ræt to Latin rodere and thus to PIE root *red- "to scrape, scratch, gnaw," source of rodent (q.v.). Klein says there is no such connection and suggests a possible cognate in Greek rhine "file, rasp." Weekley connects the English noun and the Latin verb with a question mark and OED says it is "probable" that the rat word spread from Germanic to Romanic, but takes no position on further etymology. The common Middle English form was ratton, from augmented Old French form raton. Applied to rat-like species on other continents from 1580s.

The distinction between rat and mouse, in the application of the names to animals everywhere parasitic with man, is obvious and familiar. But these are simply larger and smaller species of the same genus, very closely related zoologically, and in the application of the two names to the many other species of the same genus all distinction between them is lost. [Century Dictionary]

Applied since 12c. (in surnames) to persons held to resemble rats or share some characteristic or quality with them. Specific sense of "one who abandons his associates for personal advantage" (1620s) is from the belief that rats leave a ship about to sink or a house about to fall, and this led to the meaning "traitor, informant" (1902).

To smell a rat "to be put on the watch by suspicion as the cat by the scent of a rat; to suspect danger" [Johnson] is from 1540s.  _____-rat, "person who frequents _____" (in earliest reference dock-rat) is from 1864.

RATS. Of these there are the following kinds: a black rat and a grey rat, a py-rat and a cu-rat. ["Dictionary of the Vulgar Tongue," Grose, 1788]  
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trade-in (n.)
1917, in reference to used cars, from verbal phrase, from trade (v.) + in (adv.).
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rat-terrier (n.)

"small, active dog used to kill rats," by 1852, American English, from rat (n.) + terrier.

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trade-off (n.)
also tradeoff, "sacrifice of one benefit for another," 1959, from verbal phrase to trade off; see trade (v.) + off (adv.).
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rat-a-tat (n.)

"a rattling sound or effect," 1680s, echoic, originally of a cooper hammering tubs.

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rat-race (n.)

also rat race, 1934 in reference to aviation training, from rat (n.) + race (n.1).

A rat race is ... a simple game of "follow the leader" in fighter planes. The leader does everything he can think of — Immelmanns, loops, snap rolls, and turns, always turns, tighter and tighter. [Popular Science, May 1941]

In the 1930s actual rat races of some sort are frequently mentioned among popular carnival and gambling attractions. Meaning "fiercely competitive struggle," especially to maintain one's position in work or life is by 1939. Rat-run is from 1870 in the sense of "maze-like passages by which rats move about their territory," but originally and usually in a derogatory transferred sense.

[Matthew] Milton was not, at the period we write of [c. 1811], at all in the ring ; for in the following March he was steward of a rat-race, held at a public-house in Shepherd's-market, where four of these "varmin," decorated with different coloured ribands, were started for a sweepstakes, round the clubroom, before a host of sportsmen. ["Sporting Incidents at Home and Abroad," The Sporting Review, May 1848]
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rat-catcher (n.)

"one whose business is the catching of rats, a ratter," 1590s, from rat (n.) + catcher.

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