Etymology
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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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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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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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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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quietus (n.)

"release or discharge from debt, a final clearing of accounts," 1530s, short for Medieval Latin phrase quietus est "he is quit," from quietus "free" (in Medieval Latin "free from war, debts, etc."), also "calm, resting" (from PIE root *kweie- "to rest, be quiet"). The full Latin phrase was used in English from early 15c. Hence, "death" (i.e. "final discharge"), c. 1600. Latin quies also was used for "the peace of death."

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sober (adj.)
mid-14c., "moderate in desires or actions, temperate, restrained," especially "abstaining from strong drink," also "calm, quiet, not overcome by emotion," from Old French sobre "decent; sober" (12c.), from Latin sobrius "not drunk, temperate, moderate, sensible," from a variant of se- "without" (see se-) + ebrius "drunk," of unknown origin. Meaning "not drunk at the moment" is from late 14c.; also "appropriately solemn, serious, not giddy." Related: Soberly; soberness. Sobersides "sedate, serious-minded person" is recorded from 1705.
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sedative (adj.)

in medicine, "tending to calm or soothe," early 15c. (Chauliac), sedatif, from Old French sedatif and directly from Medieval Latin sedativus "calming, allaying," from sedat-, past participle stem of Latin sedare, causative of sedere "to sit" (from PIE root *sed- (1) "to sit").

The noun derivative meaning "a sedative drug" is attested by 1797, short for sedative salt, etc.; earlier it was used in a figurative or non-medical sense (1785), "whatever soothes or allays."

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