Etymology
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rate (n.)

early 15c., "estimated value or worth, proportional estimation according to some standard; monetary amount; a proportional part," from Old French rate "price, value" and directly from Medieval Latin rata (pars) "fixed (amount)," from Latin rata "fixed, settled," fem. past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").

Meaning "degree of speed" (properly ratio between distance and time) is attested from 1650s. Currency exchange sense of "basis of equivalence upon which one currency is exchanged for another" is recorded by 1727. Meaning "fixed public tax assessed on property for some local purpose" is by 1712.

First-rate, second-rate, etc. are 1640s, from British Navy division of ships into six classes based on size and strength. Phrase at any rate originally (1610s) meant "at any cost," hence "positively, assuredly." weakened sense of "at least" is attested by 1760. Rate-payer "one who is assessed and pays a local tax" is by 1825.

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track (n.)
late 15c., "footprint, mark left by anything," from Old French trac "track of horses, trace" (mid-15c.), possibly from a Germanic source (compare Middle Low German treck, Dutch trek "drawing, pulling;" see trek). Meaning "lines of rails for drawing trains" is from 1805. Meaning "branch of athletics involving a running track" is recorded from 1905. Meaning "single recorded item" is from 1904, originally in reference to phonograph records. Meaning "mark on skin from repeated drug injection" is first attested 1964.

Track record (1955) is a figurative use from racing, "performance history" of an individual car, runner, horse, etc. (1907, but the phrase was more common in sense "fastest speed recorded at a particular track"). To make tracks "move quickly" is American English colloquial first recorded 1835; to cover (one's) tracks in the figurative sense first attested 1898; to keep track of something is attested from 1883. American English wrong side of the tracks "bad part of town" is by 1901. Track lighting attested from 1970.
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stamp (v.)
Old English stempan "to pound in a mortar," from Proto-Germanic *stamp- (source also of Old Norse stappa, Danish stampe, Middle Dutch stampen, Old High German stampfon, German stampfen "to stamp with the foot, beat, pound," German Stampfe "pestle"), from nasalized form of PIE root *stebh- "to support, place firmly on" (source also of Greek stembein "to trample, misuse;" see staff (n.)). The vowel altered in Middle English, perhaps by influence of Scandinavian forms.

Sense of "strike the foot forcibly downwards" is from mid-14c. The meaning "impress or mark (something) with a die" is first recorded 1550s. Italian stampa "stamp, impression," Spanish estampar "to stamp, print," French étamper (13c., Old French estamper) "to stamp, impress" are Germanic loan-words. Related: Stamped; stamping. To stamp out originally was "extinguish a fire by stamping on it;" attested from 1851 in the figurative sense. Stamping ground "one's particular territory" (1821) is from the notion of animals. A stamped addressed envelope (1873) was one you enclosed in a letter to speed or elicit a reply.
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stake (n.2)

"that which is placed at hazard as a wager, the sum of money or other valuable consideration which is deposited as a pledge or wager to be lost or won according to the issue of a contest or contingency," 1530s, perhaps from stake (v.2), which is attested a few years earlier, but both the noun and verb are of uncertain origin. Perhaps literally "that which is fixed or put up," either from a particular use of stake (n.1) "stake, pole," or from the notion of "a post on which a gambling wager was placed" (but OED points out there is "no evidence of the existence of such a custom"). Weekley suggests "there is a tinge of the burning or baiting metaphor" in this usage.

Meaning "the prize in a contest of strength, skill, speed, etc." is by 1620s; plural stakes, "sum of money to be won in a (horse) race," is recorded by 1690s (compare sweepstakes). Meaning "an interest, something to gain or lose" is by 1580s; hence have a stake in "have an interest in the turn of events, have something to gain or lose" (1784). The phrase at stake "state of being laid or pledged as a wager; state of being at hazard or in peril" is from c. 1600.

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race (n.1)

[act of running] late Old English, also rase, "a narrative, an account;" c. 1300, "an act of swift running, a hurried attack," also "a course of life or conduct, a swift current;" from Old Norse rās "a running, a rush (of water)," cognate with Old English ræs "a running, a rush, a leap, jump; a storming, an attack;" or else a survival of the Old English word with spelling and pronunciation influenced by the Old Norse noun and the verb. The Norse and Old English words are from Proto-Germanic *res- (source also of Middle Dutch rasen "to rave, rage," German rasen, Old English raesettan "to rage" (of fire)), from a variant form of PIE *ers- (1) "be in motion" (see err).

Originally a northern word, it became general in English c. 1550. Formerly used more broadly than now, of any course which has to be run, passed over, or gone through, such as the course of time or events or a life (c. 1300) or the track of a heavenly body across the sky (1580s). To rue (one's) race (15c.) was to repent the course one has taken.

Meaning "contest of speed involving two or more competitors; competitive trial in running, riding, etc." is from 1510s. For the sense of "artificial stream leading water to a mill, etc.," see race (n.3). Meaning "electoral contest for public office" is by 1827.

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assembly (n.)

c. 1300, "a gathering of persons, a group gathered for some purpose," from Old French asemblee, assemblee "assembly, gathering; union, marriage," noun use of fem. past participle of assembler "to assemble" (see assemble). The meaning "a gathering together" is recorded from early 15c.; that of "act of assembling parts or objects" is from 1914, as is assembly line.

Perhaps the most interesting department in the whole factory, to the visitor, is the final assembly. In this division, all the assembled units meet the assembly conveyor at the point where they are needed. At the start of the track a front axle unit, a rear axle unit and a frame unit are assembled. This assembly is then started in motion by means of a chain conveyor, and as it moves down the room at a constant speed of eight feet per minute, each man adds one part to the growing chassis or does one operation, which is assigned to him, so that when the chassis reaches the end of the line, it is ready to run on its own power. ["The Story of an Automobile Factory," in "Universal Book of Knowledge and Wonders," 1917]

The school sense, "gathering of all students for a presentation," is from 1932. Attested from mid-14c. as "a gathering for deliberation," hence its use as the name of the lower house in some state (earlier colonial) legislatures in America (1680s). In 17c.-18c., assemblies "dancing balls 'among polite persons of both sexes,' often paid for by subscription of the participants" were a prominent feature of social life.

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pace (n.)

late 13c., "a step in walking," also "rate of motion; the space traveled by the foot in one completed movement in walking," from Old French pas "a step, pace, trace," and directly from Latin passus, passum "a step, pace, stride," noun use of past participle of pandere "to stretch (the leg), spread out," probably from PIE *pat-no-, nasalized variant form of root *pete- "to spread."

It also was, from late 14c., a lineal measurement of vague and variable extent, representing the space naturally traversed by the adult human foot in walking. In some places and situations it was reckoned as the distance from the place where either foot is taken up, in walking, to that where the same foot is set down again (a great pace), usually 5 feet or a little less. The pace of a single step (military pace) is about 2.5 feet.

To keep pace (with) "maintain the same speed, advance at an equal rate" is from 1580s. Pace-setter "one who establishes trends in fashion," is by 1895; it also had literal meanings.

It is customary for the contractor to employ some expert as a pace setter. A man who can thin an acre of beets a day commands as high as $2.00 per day as a pace setter. The other employees are paid in the proportion their work bears to that of the pace setter. The weak, lazy and unskillful get the smallest wage. Besides that the contractor runs a commissary department and feeds the gang. They sleep in tents or in the shade of trees near where they work. [report on Oxnard, Calif., beet harvesting in "The Louisiana Planter and Sugar Manufacturer," May 13, 1899] 
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wait (v.)

c. 1200, "to watch with hostile intent, lie in wait for, plot against," from Anglo-French and Old North French waitier "to watch" (Old French gaitier "defend, watch out, be on one's guard; lie in wait for;" Modern French guetter), from Frankish *wahton or another Germanic source, from Proto-Germanic *waht- (source also of Dutch wacht "a watching," Old High German wahten, German wachten "to watch, to guard;" Old High German wahhon "to watch, be awake," Old English wacian "to be awake"), from PIE root *weg- "to be strong, be lively." General sense of "remain in some place" is from late 14c.; that of "to see to it that something occurs" is late 14c. Meaning "to stand by in attendance on" is late 14c.; specific sense of "serve as an attendant at a table" is from 1560s. Related: Waited; waiting.

To wait (something) out "endure a period of waiting" is recorded from 1849. Waiting room is attested from 1680s. Waiting list is recorded from 1841; the verb wait-list "to put (someone) on a waiting list" is recorded from 1960. Waiting game is recorded from 1835, originally in horse-racing.

When speed, not stoutness, is the best of a horse, quite a contrary system is practised. With such a horse, the jockey plays a waiting game; that is, he carefully nurses him through the race, so as not to distress him by overpacing him; as the finish approaches, he creeps up to his horses by degrees, but does not quit them to go in front till he sees that the pace has made them "safe," — when he lets loose and wins. [James Christie Whyte, "History of the British Turf," London, 1840]
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