Etymology
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Words related to anaerobic

an- (1)
privative prefix, from Greek an-, "not, without," from PIE root *ne- "not"). The Greek prefix is a fuller form of the one represented in English by a- (3).
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air (n.1)

c. 1300, "invisible gases that surround the earth," from Old French air "atmosphere, breeze, weather" (12c.), from Latin aer "air, lower atmosphere, sky," from Greek aēr (genitive aeros) "mist, haze, clouds," later "atmosphere" (perhaps related to aenai "to blow, breathe"), which is of unknown origin. It is possibly from a PIE *awer- and thus related to aeirein "to raise" and arteria "windpipe, artery" (see aorta) on notion of "lifting, suspended, that which rises," but this has phonetic difficulties.

In Homer mostly "thick air, mist;" later "air" as one of the four elements. Words for "air" in Indo-European languages tend to be associated with wind, brightness, sky. In English, air replaced native lyft, luft (see loft (n.)). In old chemistry, air (with a qualifying adjective) was used of any gas.

To be in the air "in general awareness" is from 1875; up in the air "uncertain, doubtful" is from 1752. To build castles in the air "entertain visionary schemes that have no practical foundation" is from 1590s (in 17c. English had airmonger "one preoccupied with visionary projects"). Broadcasting sense (as in on the air, airplay) first recorded 1927. To give (someone) the air "dismiss" is from 1900. Air pollution is attested by 1870. Air guitar is by 1983. Air traffic controller is from 1956.

*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."
*wer- (1)

Proto-Indo-European root meaning "to raise, lift, hold suspended." 

It forms all or part of: aerate; aeration; aerial; aero-; aerobics; aerophyte; aerosol; air (n.1) "invisible gases that surround the earth;" airy; aorta; anaerobic; aria; arterial; arterio-; arteriosclerosis; arteriole; artery; aura; malaria; meteor

It is the hypothetical source of/evidence for its existence is provided by: Greek aerein "to lift, raise up;" Lithuanian svarus "heavy," sverti "to lift, weigh;" Old English swar, Old Norse svarr, Old High German swar, German schwer "heavy."