Etymology
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ratchet (n.)

"pivoted piece designed to fit into the teeth of a ratchet-wheel, permitting the wheel to rotate in one direction but not in the other," 1650s, rochet, from French rochet "bobbin, spindle," from Italian rocchetto "spool, ratchet," diminutive of rocca "distaff," possibly from a Germanic source (compare Old High German rocko "distaff," Old Norse rokkr), from Proto-Germanic *rukka-, from PIE root *ruk- "fabric, spun yarn." Compare rocket (n.2). The current spelling in English dates from 1721, influenced by synonymous ratch, which perhaps is borrowed from German Rätsche "ratchet."

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ratify (v.)

mid-14c., ratifien, "confirm, approve, sanction, validate by formal act of approval," from Old French ratifier (13c.), from Medieval Latin ratificare "confirm, approve," literally "fix by reckoning," from Latin ratus "fixed by calculation; determined; approved; certain, sure; valid" (past-participle adjective from reri "to reckon, think;" from PIE root *re- "to reason, count") + combining form of facere "to make" (from PIE root *dhe- "to set, put"). Related: Ratified; ratifying.

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rating (n.1)

1530s, "a fixing of rates, proportionate distribution of charge or compensation," verbal noun from rate (v.2). Meaning "a classification according to grade or rank" is from 1764.

Ratings "statistical estimate of the size of an audience for a particular broadcast," originally radio programs, began in 1930 in U.S. under a system set up by pollster and market researcher Archibald M. Crossley (1896-1985), and were called Crossley ratings or Crossleys until ratings began to be preferred c. 1947.

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ratiocination (n.)

"process of reasoning, mental process of passing from the cognition of premises to the cognition of the conclusion," 1520s, from Latin ratiocinationem (nominative ratiocinatio) "a reasoning, calm reasoning," noun of action from past-participle stem of ratiocinari "to reckon, compute, calculate; to deliberate, meditate; to reason, argue, infer." This is a compound of ratio "reckoning, calculation," also "judgment, reason" (see ratio) + -cinari, which probably is related to conari "to endeavor, to try," from PIE *kona-, from root *ken- "to hasten, set oneself in motion" (see deacon).

Most writers make ratiocination synonymous with reasoning. J.S. Mill and others hold that the word is usually limited to necessary reasoning. [Century Dictionary]
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death-rattle (n.)

"sound sometimes heard in the last labored breathing of a dying person," 1805, from death + rattle (n.).

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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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poor-rate (n.)

"assessment or tax imposed by law for the relief or support of the poor in a particular community," c. 1600, from poor (n.) + rate (n.).

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ratherish (adj.)

"slightly, to a small extent," 1835, from rather + -ish.

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rating (n.2)

"a reproving," 1570s, verbal noun from rate (v.1).

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pro rata 

"in proportion," from Medieval Latin pro rata (parte) "according to the calculated (share)," from pro "for, in accordance with" (see pro-) + rata, ablative singular of ratus, past participle of reri "to count, reckon" (see rate (n.)).

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