Etymology
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viva (interj.)
1640s, from Italian viva "(long) live, may he (or she) live," third person singular present subjunctive of vivere "to live," from Latin vivere "to live," from PIE root *gwei- "to live." Probably reborrowed (1836) from Spanish viva, from vivir "to live," from Latin vivere. Sometimes also in Latin form vivat (1660s).
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vive (interj.)
1590s (in vive le roi), from French, literally "long live ______!" It is the French equivalent of viva (q.v.). The opposite is à bas "down! down with!" Jocular phrase vive la différence in reference to the difference between men and women is recorded from 1963. Also in vive la bagatelle, literally "long live nonsense," denoting a carefree attitude to life.
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qui vive 

1726, in on the qui vive "on the alert," from French être sur le qui vive "be on the alert," from the phrase qui voulez-vous qui vive? sentinel's challenge, "whom do you wish to live?" In other words "(long) live who?" meaning "whose side are you on?" (The answer might be Vive la France, Vive le roi, etc.). From qui (from Latin qui "who") + vive, third person singular present subjunctive of vivre, from Latin vivere "to live" (see viva).

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viva voce 
also viva-voce, "by word of mouth," 1580s, Latin, literally "living-voice," ablative of viva vox.
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*gwei- 
also *gweie-, Proto-Indo-European root meaning "to live."

It forms all or part of: abiogenesis; aerobic; amphibian; anaerobic; azo-; azoic; azotemia; bio-; biography; biology; biome; bionics; biopsy; biota; biotic; cenobite; Cenozoic; convivial; couch-grass; epizoic; epizoon; epizootic; macrobiotic; Mesozoic; microbe; Protozoa; protozoic; quick; quicken; quicksand; quicksilver; quiver (v.) "to tremble;" revive; survive; symbiosis; viable; viand; viper; vita; vital; vitamin; victuals; viva; vivace; vivacious; vivarium; vivid; vivify; viviparous; vivisection; whiskey; wyvern; zodiac; Zoe; zoetrope; zoic; zoo-; zoolatry; zoology; zoon; zoophilia; zoophobia; zooplankton.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit jivah "alive, living;" Old Persian *jivaka- "alive," Middle Persian zhiwak "alive;" Greek bios "one's life, course or way of living, lifetime," zoe "animal life, organic life;" Old English cwic, cwicu "living, alive;" Latin vivus "living, alive," vita "life;" Old Church Slavonic zivo "to live;" Lithuanian gyvas "living, alive," gyvata "(eternal) life;" Old Irish bethu "life," bith "age;" Welsh byd "world."
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quicklime (n.)

"caustic lime, lime not yet slaked with water," late 14c., from quick (adj.) "living" + lime (n.1). A loan-translation of Latin calx viva. So called perhaps for being unquenched, or for the vigorousness of its qualities; compare Old English cwicfyr "sulfur."

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quicksilver (n.)

common popular designation of metallic mercury, Middle English quik-silver, from late Old English cwicseolfor, literally "living silver," so called for its mobility, translating Latin argentum vivum (source also of Italian argento vivo), "living silver;" so called from its liquid mobility. See quick (adj.) + silver (n.). Similar formation in Dutch kwikzilver, Old High German quecsilbar, German quecksilber, French vif-argent, Italian argenta viva.

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bon-vivant (n.)
also bon vivant, "jovial companion, one fond of good living," 1690s, French (see bon); the fem. is bonne vivante.
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vivace (adv.)
1680s, from Italian vivace "brisk, lively," from Latin vivac-, stem of vivax "lively, vigorous; long-lived, enduring," from PIE root *gwei- "to live."
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vivarium (n.)
c. 1600, "game park," from Latin vivarium "enclosure for live game, park, warren, preserve, fish pond," noun use of neuter singular of vivarius "pertaining to living creatures," from vivus "alive, living" (from PIE root *gwei- "to live"). Meaning "glass bowl for studying living creatures" is from 1853.
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