"moved or played by means of air; of or pertaining to air or gases," 1650s, from Latin pneumaticus "of the wind, belonging to the air," from Greek pneumatikos "of wind or air" (which is attested mainly as "of spirit, spiritual"), from pneuma (genitive pneumatos) "the wind," also "breath" (see pneuma). Earlier was pneumatical (c. 1600). The pneumatic-dispatch tube was so called by 1859 (in Paris, pneumatique).
"cause to mix with carbonic acid or other gas," 1794 (implied in aerated), from aer/aër (used in old science for specific kinds of air, a sense later given to gas (n.1)), from Latin aer (see air (n.1)) + verbal suffix -ate (2). Meaning "expose to air" is from 1799, probably a back-formation from aeration. Related: Aerating.