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.

air (n.2)

1590s, "manner, appearance" (as in an air of mystery); 1650s, "assumed manner, affected appearance" (especially in phrase put on airs, 1781), from French air "look, appearance, mien, bearing, tone" (Old French aire "reality, essence, nature, descent, extraction" (12c.); compare debonair), which is perhaps from Latin ager "place, field, productive land" (from PIE root *agro- "field") on notion of "place of origin."

But some French sources connect this Old French word with the source of air (n.1), and it also is possible these senses in English developed from or were influenced by air (n.1); compare sense development of atmosphere and Latin spiritus "breath, breeze," also "high spirit, pride," and the extended senses of anima.

air (n.3)

"melody, tune, connected rhythmic succession of distinct musical sounds," 1580s, nativized from Italian aria (see aria), perhaps via French.

air (v.)

1520s, "expose to open air," 1520s, from air (n.1). Figurative sense of "expose ostentatiously, make public" is from 1610s of objects, 1862 of opinions, grievances, etc. Meaning "to broadcast" (originally on radio) is from 1933. Related: Aired; airing.

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Definitions of air
air (n.)
a mixture of gases (especially oxygen) required for breathing; the stuff that the wind consists of;
open a window and let in some air
a smell of chemicals in the air
I need some fresh air
air pollution
air (n.)
the region above the ground;
he threw the ball into the air
her hand stopped in mid air
air (n.)
a distinctive but intangible quality surrounding a person or thing;
an air of mystery
the house had a neglected air
Synonyms: aura / atmosphere
air (n.)
a slight wind (usually refreshing);
as he waited he could feel the air on his neck
Synonyms: breeze / zephyr / gentle wind
air (n.)
the mass of air surrounding the Earth;
it was exposed to the air
Synonyms: atmosphere
air (n.)
once thought to be one of four elements composing the universe (Empedocles);
air (n.)
a succession of notes forming a distinctive sequence;
she was humming an air from Beethoven
Synonyms: tune / melody / strain / melodic line / line / melodic phrase
air (n.)
medium for radio and television broadcasting;
the program was on the air from 9 til midnight
Synonyms: airwave
air (n.)
travel via aircraft;
if you've time to spare go by air
Synonyms: air travel / aviation
air (v.)
expose to fresh air;
Synonyms: air out / aerate
air (v.)
be broadcast;
This show will air Saturdays at 2 P.M.
air (v.)
broadcast over the airwaves, as in radio or television;
We cannot air this X-rated song
Synonyms: send / broadcast / beam / transmit
air (v.)
make public;
She aired her opinions on welfare
Synonyms: publicize / publicise / bare
air (v.)
expose to warm or heated air, so as to dry;
air (v.)
expose to cool or cold air so as to cool or freshen;
air out the smoke-filled rooms
air the old winter clothes
Synonyms: vent / ventilate / air out