air-brake (n.)

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) is by 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.

mid-15c., "instrument for crushing or pounding," from Middle Dutch braeke "flax brake," from breken "to break" (see break (v.)). The word was applied to many crushing implements, especially the tool for breaking up the woody part of flax to loosen the fibers. It also was applied to the ring through the nose of a draught ox. It was influenced in sense by Old French brac, a form of bras "an arm," thus the sense "a lever or handle," which was being used in English from late 14c., and "a bridle or curb" (early 15c.).

One or the other sense or a convergence of all of them yielded the main modern meaning "mechanical device for arresting the motion of a wheel," which is attested by 1772.