Etymology
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vague (adj.)

"uncertain as to specifics," 1540s, from French vague "empty, vacant; wild, uncultivated; wandering" (13c.), from Latin vagus "strolling, wandering, rambling," figuratively "vacillating, uncertain," perhaps from PIE *Huog-o-  and cognate with Old Norse vakka "to stray, hover," Old High German wankon "to totter, stagger," Old High German winkan "to waver, stagger, wink," Old English wincian "to nod" [de Vaan]. Related: Vagueness.

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vagus (n.)
plural vagi, 1840, "pneumogastric nerve," the long, widely distributed nerve from the brain to the upper body, from Latin vagus "wandering, straying" (see vague).
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vagabond (adj.)
early 15c. (earlier vacabond, c. 1400), from Old French vagabond, vacabond "wandering, unsteady" (14c.), from Late Latin vagabundus "wandering, strolling about," from Latin vagari "wander" (from vagus "wandering, undecided;" see vague) + gerundive suffix -bundus.
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noctivagant (adj.)

"rambling or wandering in the night," 1620s, from Latin noct-, stem of nox "night" (see noct-) + vagantem (nominative vagans), present participle of vagari "to wander, stroll about, roam, be unsettled, spread abroad," from vagus "roving, wandering" (see vague). Related: Noctivagation; noctivagous.

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evagation (n.)
"action of wandering," 1650s, from French évagation, from Latin evagationem (nominative evagatio), noun of action from past participle stem of evagari, from assimilated form of ex "out, out of" (see ex-) + vagari, from vagus "roving, wandering" (see vague).
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vagary (n.)
1570s, "a wandering, a roaming journey," from Italian vagare or directly from Latin vagari "to wander, stroll about, roam, be unsettled, spread abroad," from vagus "roving, wandering" (see vague). The infinitive appears to have been adopted in English as a noun and conformed to nouns in -ary, "but this can hardly be explained except as an orig. university use" [Century Dictionary]. Current meaning of "eccentric notion or conduct" (1620s) is from notion of mental wandering. Related: Vagaries.
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extravagant (adj.)

late 14c., in constituciouns extravagaunt, a term in Canon Law for papal decrees not originally included or codified in the Decretals, from Medieval Latin extravagantem (nominative extravagans), present participle of extravagari "wander outside or beyond," from Latin extra "outside of" (see extra-) + vagari "wander, roam" (see vague).

In 15c. it also could mean "rambling, irrelevant; extraordinary, unusual." Extended sense of "excessive, extreme, exceeding reasonable limits" first recorded 1590s, probably via French; that of "wasteful, lavish, exceeding prudence in expenditure" is from 1711. Related: Extravagantly. Wordsworth ("Prelude") used extravagate (v.).

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New Wave 
1960, of cinema (from French Nouvelle Vague, late 1950s); 1976 as a name for the more restrained and melodic alternative to punk rock.
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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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