Etymology
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temperate (adj.)
late 14c., of persons, "modest, forbearing, self-restrained, not swayed by passion;" of climates or seasons, "not liable to excessive heat or cold," from Latin temperatus "restrained, regulated, limited, moderate, sober, calm, steady," from past participle of temperare "to moderate, regulate" (see temper (v.)). Related: Temperately; temperateness. Temperate zone is attested from 1550s.
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quiet (n.)

c. 1300, "freedom from disturbance or conflict; calm, stillness," from Old French quiete "rest, repose, tranquility" and directly from Latin quies (genitive quietis) "a lying still, rest, repose, peace" (from PIE root *kweie- "to rest, be quiet").

From late 14c. as "inactivity, rest, repose;" from c. 1400 as "absence of noise."

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coy (adj.)

early 14c., "quiet, modest, demure," from Old French coi, earlier quei "quiet, still, placid, gentle," ultimately from Latin quietus "free; calm, resting" (from PIE root *kweie- "to rest, be quiet"). Meaning "shy, bashful" emerged late 14c. Meaning "unwilling to commit" is by 1961. Related: Coyly; coyness.

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tranquility (n.)
also tranquillity, late 14c., from Old French tranquilite "peace, happiness" (12c.), from Latin tranquillitatem (nominative tranquillitas) "quietness, stillness; serenity," from tranquillus "quiet, calm, still," perhaps from trans- "over" (here perhaps in its intensive sense of "exceedingly") and an adjective from PIE root *kweie- "be quiet," but de Vaan finds this "semantically vague" and phonetically disputable.
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peaceful (adj.)

early 14c., pesful, peesfull, paisful, "inclined to peace, friendly, pacific;" mid-14c. as "tranquil, calm, full of peace;" from peace + -ful. In reference to nonviolent methods of effecting social change, it is attested from 1876. Related: Peacefully; peacefulness. Peaceful coexistence (1920) originally was in regard to Soviet policy toward the capitalist West.

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assure (v.)
late 14c., "reassure, give confidence to; make secure or safe, protect; bind by a pledge, give a promise or pledge (to do something)," from Old French asseurer "to reassure, calm, protect, to render sure" (12c., Modern French assurer), from Vulgar Latin *assecurar, from assimilated form of Latin ad "to" (see ad-) + securus "safe, secure" (see secure (adj.)). Related: Assured; assuring.
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serenity (n.)

mid-15c., serenite, "fair, calm, clear weather," from Old French (Modern French sérénité) and directly from Latin serenitatem (nominative serenitas) "clearness, serenity," from serenus (see serene). Of persons, "tranquility of mind or temper," by 1590s. Also formerly used as a title of honor for kings (mid-15c.), probably from the similar use of Latin serenitas, which was applied to Roman emperors and later to popes.

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quit (adj.)

c. 1200, "excused, exempt, free, clear" (of debt, obligation, penalty, etc.), from Old French quite, quitte "free, clear, entire, at liberty; discharged; unmarried," and directly from Medieval Latin quitus, quittus, from Latin quietus "free" (in Medieval Latin "free from war, debts, etc."), also "calm, resting" (from PIE root *kweie- "to rest, be quiet").

From mid-13c. as "deprived of." From c. 1300 of real property, "exempt from taxes or other dues or claims."

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assuage (v.)
"to soften," usually figuratively, of pain, anger, passion, grief, etc., c. 1300, from Anglo-French assuager, Old French assoagier "soften, moderate, alleviate, calm, soothe, pacify," from Vulgar Latin *adsuaviare, from Latin ad "to" (see ad-) + suavis "sweet, agreeable," from PIE root *swād- "sweet, pleasant" (see sweet (adj.)). For sound development in French, compare deluge from Latin diluvium, abridge from abbreviare. Related: Assuaged; assuaging.
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lull (v.)
early 14c., lullen "to calm or hush to sleep," probably imitative of lu-lu sound used to lull a child to sleep (compare Swedish lulla "to hum a lullaby," German lullen "to rock," Sanskrit lolati "moves to and fro," Middle Dutch lollen "to mutter"). Figurative use from 1570s; specifically "to quiet (suspicion) so as to delude into a sense of security" is from c. 1600. Related: Lulled; lulling.
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