Etymology
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contract (v.)

late 14c., "to draw into a smaller compass, become smaller, shrink" (intransitive); early 15c. "make an agreement, enter into a contract, agree or establish to undertake mutually," from Old French contracter and directly from Latin contractus, past participle of contrahere "to draw several objects together; draw in, shorten, lessen, abridge," metaphorically "make a bargain, make an agreement," from assimilated form of com "with, together" (see con-) + trahere "to draw" (see tract (n.1)). Related: Contracted; contracting.

Meaning "to acquire as by habit or contagion, become infected with" is from 1590s. Transitive sense of "make narrow, draw together the parts (of something) to cause it to shrink" is from c. 1600. Grammatical sense of "to shorten (a word or syllable) by combining or eliding concurrent elements" is from c. 1600. Transitive sense of "arrange for by contract" is from 1897.

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scamp (v.)

"do in a hasty manner, perform in a slipshod or perfunctory way," 1837, probably from a dialect word, perhaps from a Scandinavian source (OED compares Old Norse skemma "to shorten, make shorter," from skammr "short; brief; lately"), or a blend of scant and skimp [Klein], or a back-formation from scamper. Related: Scamped; scamping.

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scant (adj.)

mid-14c., "short or insufficient in quantity, rather less than is wanted for the purpose," from a Scandinavian source such as Old Norse skamt, neuter of skammr "short, brief," from Proto-Germanic *skamma- (source also of Old English scamm "short," Old High German skemmen "to shorten"), perhaps ultimately "hornless" (from PIE *kem- (1) "hornless;" see hind (n.)).

Also in Middle English as a noun, "dearth, scant supply, scarcity," from Old Norse.

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logarithm (n.)

a mathematical function used to shorten calculation, 1610s, logarithmus, coined in Modern Latin by Scottish mathematician John Napier (1550-1617), literally "ratio-number," from Greek logos "proportion, ratio, word" (see Logos) + arithmos "number" (from PIE *erei-dhmo-, suffixed variant form of root *re- "to reason, count"). Napier invented them and published a table in 1614; the kind now chiefly in use were invented by his contemporary Henry Briggs (1561-1630), a professor of geometry at Gresham College, London.

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*mregh-u- 
Proto-Indo-European root meaning "short."

It forms all or part of: abbreviate; abbreviation; abridge; amphibrach; brace; bracelet; brachio-; brachiopod; brachiosaurus; brachy-; brassiere; breviary; brevity; brief; brumal; brume; embrace; merry; mirth; pretzel; vambrace.

It is the hypothetical source of/evidence for its existence is provided by: Greek brakhys "short;" Latin brevis "short, low, little, shallow;" Old Church Slavonic bruzeja "shallow places, shoals;" Gothic gamaurgjan "to shorten."
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cut-off (n.)

also cutoff, 1640s, "act of cutting off," also "portion cut off," from verbal phrase cut off (see cut (v.) + off (adv.)). Sense of "new and shorter channel formed on a river" (especially the Mississippi) is from 1773; of road that cut off or shorten a route, from 1806; of clothing (adj.), from 1840. Cutoffs "jeans or other long pants trimmed down to be shorts" is by 1967.

The verbal phrase is attested from late 14c. as "detach by cutting;" from 1570s as "exclude from access" and "bring to an abrupt end;" and from 1590s as "intercept, stop the flow or passage of."

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contract (n.)

early 14c., "agreement between two or more persons to do or not do some particular thing," originally especially of marriage, from Old French contract (Modern French contrat), from Latin contractus "a drawing together, a shrinking; a contract, an agreement," from past participle of contrahere "to draw several objects together; draw in, shorten, lessen, abridge," metaphorically "make a bargain, make an agreement," from assimilated form of com "with, together" (see con-) + trahere "to draw" (see tract (n.1)).

In reference to the writing which contains the agreement and its terms and conditions, 1610s. U.S. underworld sense of "arrangement to kill someone" first recorded 1940.

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pucker (v.)

1590s, intransitive, "become irregularly ridged or wrinkled," possibly a frequentative form of pock, dialectal variant of poke "bag, sack" (see poke (n.1)), which would give it the same notion as in purse (v.). OED writes that it was "prob. earlier in colloquial use." "Verbs of this type often shorten or obscure the original vowel; compare clutter, flutter, putter, etc." [Barnhart]. Transitive sense of "draw up or contract into irregular folds or wrinkles" is from 1610s. Related: Puckered; puckering.

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precise (adj.)

mid-15c., "neither more nor less than, with no error; exactly stated or marked off; definitely or strictly expressed; distinguished with precision from all others," from Old French précis "condensed, cut short" (14c.) and directly from Medieval Latin precisus, from Latin praecisus "abrupt, abridged, cut off," past participle of praecidere "to cut off, shorten," from prae "before" (see pre-) + -cidere, combining form of caedere "to cut" (from PIE root *kae-id- "to strike"). For the Latin vowel change, see acquisition. Related: Precisely (late 14c.).

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contractor (n.)

1540s, "one who enters into a contract," from Late Latin contractor "one who makes a contract," agent noun from past-participle stem of Latin contrahere "to draw several objects together; draw in, shorten, lessen, abridge," metaphorically "make a bargain, make an agreement," from assimilated form of com "with, together" (see con-) + trahere "to draw" (see tract (n.1)).

From 1680s as "a muscle which contracts a part." Specifically "one who enters into a contract to provide work, services, or goods at a certain price or rate" is from 1724.

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