Etymology
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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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*aiw- 

also *ayu-, Proto-Indo-European root meaning "vital force, life; long life, eternity."

It forms all or part of: age; aught (n.1) "something; anything;" aye (adv.) "always, ever;" Ayurvedic; coetaneous; coeval; each; eon; eternal; eternity; ever; every; ewigkeit; hygiene; longevity; medieval; nay; never; no; primeval; sempiternal; tarnation; utopia

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit ayu- "life;" Avestan aiiu "age, life(time);" Greek aiōn "age, vital force; a period of existence, a lifetime, a generation; a long space of time," in plural, "eternity;" Latin aevum "space of time, eternity;" Gothic aiws "age, eternity," Old Norse ævi "lifetime," German ewig "everlasting," Old English a "ever, always."  

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*leip- 

Proto-Indo-European root meaning "to stick, adhere; fat."

It forms all or part of: adipose; beleave; delay; leave (v.); lebensraum; life; liparo-; lipo- (1) "fat;" lipoma; liposuction; lively; live (v.); liver (n.1) "secreting organ of the body;" Olaf; relay.

It is the hypothetical source of/evidence for its existence is provided by: Greek liparein "to persist, persevere," aleiphein "anoint with oil," lipos "fat;" Old English lifer "liver," læfan "to allow to remain."

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*ane- 

Proto-Indo-European root meaning "to breathe."

It forms all or part of: anemo-; anemometer; anemone; anima; animadversion; animadvert; animal; animalcule; animalistic; animate; animation; animatronic; anime; animism; animosity; animus; Enid; equanimity; longanimity; magnanimous; pusillanimous; unanimous.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit aniti "breathes;" Greek anemos "wind;" Latin animus "rational soul, mind, life, mental powers, consciousness, sensibility; courage, desire," anima "living being, soul, mind, disposition, passion, courage, anger, spirit, feeling;" Old Irish anal, Welsh anadl "breath," Old Irish animm "soul;" Gothic uzanan "to exhale," Old Norse anda "to breathe," Old English eðian "to breathe;" Old Church Slavonic vonja "smell, breath;" Armenian anjn "soul."

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rat-race (n.)

also rat race, 1934 in reference to aviation training, from rat (n.) + race (n.1).

A rat race is ... a simple game of "follow the leader" in fighter planes. The leader does everything he can think of — Immelmanns, loops, snap rolls, and turns, always turns, tighter and tighter. [Popular Science, May 1941]

In the 1930s actual rat races of some sort are frequently mentioned among popular carnival and gambling attractions. Meaning "fiercely competitive struggle," especially to maintain one's position in work or life is by 1939. Rat-run is from 1870 in the sense of "maze-like passages by which rats move about their territory," but originally and usually in a derogatory transferred sense.

[Matthew] Milton was not, at the period we write of [c. 1811], at all in the ring ; for in the following March he was steward of a rat-race, held at a public-house in Shepherd's-market, where four of these "varmin," decorated with different coloured ribands, were started for a sweepstakes, round the clubroom, before a host of sportsmen. ["Sporting Incidents at Home and Abroad," The Sporting Review, May 1848]
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