Etymology
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bequeath (v.)

Old English becweðan "to say, speak to, exhort, blame," also "leave by will;" from be- + cweðan "to say," from Proto-Germanic *kwithan (see quoth). The simple verb cweðan became obsolete, but its old, strong past tense survived through Middle English as quoth.

The original sense of "say, utter" died out 13c., leaving the word with only the legal sense of "transfer by legacy." Compare bequest. "An old word kept alive in wills" [OED 1st ed.]. Old English bequeðere meant "interpreter, translator." Related: Bequeathed; bequeathing.

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bequest (n.)

c. 1300, "act of bequeathing," from be- + *cwis, *cwiss "saying" (related to quoth, from Proto-Germanic *kwessiz, from PIE root *gwet- "to say, speak"). Also compare bequeath. With unetymological -t (as in behest). The meaning "legacy, that which is bequeathed" is recorded from late 15c.

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quoth (v.)

"to say, say as follows," from Middle English quoth, from Old English cweþ (Mercian), cwæþ (Northumbrian), third person singular past tense of cweoþan, cweoþa "to say, speak; name, call; declare, proclaim" (Middle English quethan), from Proto-Germanic *kwethanan (source also of Old Saxon quethan, Old Norse kveða, Old Frisian quetha, Old High German quedan, Gothic qiþan).

This is often traced to PIE root *gwet- "to say, speak," but Boutkan, on the grounds of formal objection to proposed cognates (Sanskrit gadati "speaks," Old Welsh guetid "say," Latin vetare "not allow"), has it as of "no (certain) IE etymology," and writes, "This is complicated."

Related to bequeath and bequest. Compare also archaic interjection quotha "forsooth, indeed," originally "said he," 1510s in sarcastic use, "originally a parenthetical phrase used in repeating the words of another with more or less contempt or disdain" [Century Dictionary], from Middle English, from Old English cwæðe ge.

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lease (n.)

late 14c., "legal contract conveying property, usually for a fixed period of time and with a fixed compensation," from Anglo-French les (late 13c.), Old French lais, lez "a lease, a letting, a leaving," verbal noun from Old French laissier "to let, allow, permit; bequeath, leave" (see lease (v.)). Figuratively from 1580s, especially of life. Modern French equivalent legs is altered by erroneous derivation from Latin legatum "bequest, legacy."

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legate (n.)

mid-12c., "authorized representative of the Pope," from Old French legat and directly from Latin legatus "ambassador, envoy," originally "provided with a commission," past participle of legare "send as a deputy, send with a commission, charge, bequeath," possibly literally "engage by contract" and related to lex (genitive legis) "contract, law," from PIE root *leg- (1) "to collect, gather." General sense of "ambassador, delegate, messenger of a state or authority" is from late 14c. in English. Related: Legator; legatee; legatine.

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assign (v.)

c. 1300, "to transfer, convey, bequeath (property); appoint (to someone a task to be done); order, direct (someone to do something); fix, settle, determine; appoint or set (a time); indicate, point out," from Old French assigner "assign, set (a date, etc.); appoint legally; allot" (13c.), from Latin assignare/adsignare "to mark out, to allot by sign, assign, award," from ad "to" (see ad-) + signare "make a sign," from signum "identifying mark, sign" (see sign (n.)). Its original use was in legal transfers of personal property. Related: Assigned; assigning.

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lease (v.)

late 15c., "to take a lease," from Anglo-French lesser (13c.), Old French laissier "to let, let go, let out, leave" "to let, allow, permit; bequeath, leave," from Latin laxare "loosen, open, make wide," from laxus "loose" (from PIE root *sleg- "be slack, be languid"). Medial -x- in Latin tends to become -ss- or -s- in French (compare cuisse from coxa). The Latin verb also is the source of Spanish laxar; Italian lasciare "leave," lassare "loosen."

Compare release (v.). Meaning "to grant the temporary possession of at a fixed rate" is from 1560s. Related: Leased; leasing. The form has been influenced by the noun, and the modern sense of "to take a lease" might be a new 19c. formation. Lessor, lessee in contract language preserve the Anglo-French vowel.

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relegate (v.)

1590s "to banish (someone), send to an obscure or remote place, send away or out of the way," from Latin relegatus, past participle of relegare "remove, dismiss, banish, send away, schedule, put aside," from re- "back" (see re-) + legare "send as a deputy, send with a commission, charge, bequeath," which is possibly literally "engage by contract" and related to lex (genitive legis) "contract, law" (from PIE root *leg- (1) "to collect, gather").

All senses are from a specific meaning in Roman law: "send into exile, cause to move a certain distance from Rome for a certain period." The meaning "place (someone) in a position of inferiority" is recorded from 1790. Of subjects, things, etc., "assign to some specific category, domain, etc.," by 1866. Related: Relegated; relegating; relegable.

[Relegatio] allowed the expulsion of a citizen from Rome by magisterial decree. All examples of relegation were accomplished by magistrates with imperium, and lesser magistrates probably did not possess this power. Any number of individuals could be relegated under a single decree, and they even could be directed to relocate to a specific area. This act was generally used to remove undesirable foreigners from Rome, as when Greek philosophers were expelled from Rome in 161 and two Epicureans, Philiscus and Alcaeus, were banished seven years later. [Gordan P. Kelly, "A History of Exile in the Roman Republic," Cambridge: 2006]
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leave (v.)

Old English læfan "to allow to remain in the same state or condition; to let remain, allow to survive; to have left (of a deceased person, in reference to heirs, etc.); to bequeath (a heritage)," from Proto-Germanic *laibjanan (source also of Old Frisian leva "to leave," Old Saxon farlebid "left over"), causative of *liban "remain" (source of Old English belifan, German bleiben, Gothic bileiban "to remain"), from PIE root *leip- "to stick, adhere."

The Germanic root seems to have had only the sense "remain, continue" (which was in Old English as well but has since become obsolete), which also is in Greek lipares "persevering, importunate." But this usually is regarded as a development from the primary PIE sense of "adhere, be sticky" (compare Lithuanian lipti, Old Church Slavonic lipet "to adhere," Greek lipos "grease," Sanskrit rip-/lip- "to smear, adhere to."

Originally a strong verb (past participle lifen), it early switched to a weak form. Meaning "go away, take one's departure, depart from; leave behind" (c. 1200) comes from notion of "leave behind" (as in to leave the earth "to die;" to leave the field "retreat"). From c. 1200 as "to stop, cease; give up, relinquish, abstain from having to do with; discontinue, come to an end;" also "to omit, neglect; to abandon, forsake, desert; divorce;" also "allow (someone) to go."

Colloquial use for "let, allow" is by 1840, said by OED to be chiefly American English. Not related to leave (n.). To leave out "omit" is from late 15c. To leave (something) alone is from c. 1400; to leave (something) be is from 1825. To leave (something/nothing) to be desired is from 1780. To leave it at that is from 1902. Leave off is from c. 1400 as "cease, desist" (transitive); early 15c. as "stop, make an end" (intransitive).

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let (v.)

Old English lætan (Northumbrian leta) "to allow; to leave behind, depart from; leave undone; bequeath," also "to rent, put to rent or hire" (class VII strong verb; past tense let, leort, past participle gelæten), from Proto-Germanic *letan (source also of Old Saxon latan, Old Frisian leta, Dutch laten, Old High German lazan, German lassen, Gothic letan "to leave, let"), from PIE *led-, extended form of root *‌‌lē- "to let go, slacken." If that derivation is correct, the etymological sense might be "let go through weariness, neglect."

The idea of slackening lies at the root of both applications of the term. When we speak of letting one go, letting him do something, we conceive him as previously restrained by a band, the loosening or slackening of which will permit the execution of the act in question. ... At other times the slackness is attributed to the agent himself, when let acquires the sense of being slack in action, delaying or omitting to do. [Hensleigh Wedgwood, "A Dictionary of English Etymology," 1859] 

He points to similar developments in French laisser "to let" from Latin laxare "to slacken," German lassen "to permit, to let," from dialectal lass "loose."

"The shortening of the root vowel ... has not been satisfactorily explained" [OED]. Of blood, from late Old English. Other Old and Middle English senses include "regard as, consider; behave toward; allow to escape; pretend;" to let (someone) know and to let fly (arrows, etc.) preserve the otherwise obsolete sense of "to cause to."

To let (someone) off "allow to go unpunished, excuse from service" is from 1814. To let on is from 1725 as "allow (something) to be known, betray one's knowledge of," 1822 as "pretend" (OED finds a similar use in the phrase never let it on him in a letter from 1637). To let out is late 12c. as "allow to depart" (transitive); intransitive use "be concluded," of schools, meetings, etc., is from 1888, considered by Century Dictionary (1895) to be "Rural, U.S." Of garments, etc., late 14c.

Let alone "abstain from interfering with" is in Old English; the phrase in the sense "not to mention, to say nothing of" is from 1812. To let (something) be "leave it alone" is from c. 1300; let it be "let it pass, leave it alone" is from early 14c. To let go is from c. 1300 as "allow to escape," 1520s as "cease to restrain," 1530s as "dismiss from one's thoughts." Let it go "let it pass, no matter" is as old as Chaucer's Wife of Bath: "But age allas Hath me biraft my beautee Lat it go, far wel, the deuel go ther with!" [c. 1395]. Let me see "show me" is from c. 1300.

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