Entries linking to air-pump
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.
"one of several kinds of apparatus for forcing liquid or air," early 15c., pumpe, which is probably from Middle Dutch pompe "water conduit, pipe," or Middle Low German pumpe "pump" (Modern German Pumpe), both from some North Sea sailors' word, possibly imitative of the sound of the plunger in the water.
Earliest English uses are in reference to a device to raise and expel bilge water from ships. Late Old French pompe probably is from Germanic. Pumps themselves are very ancient, which makes the late appearance of the Germanic word odd. From 1670s as "an act of pumping." Pump-action in reference to a type of repeating firearm is attested in advertisements for them from 1912.