late 15c., precipitacioun, "a casting down" (of the evil angels from heaven), also, in alchemy "separation of a solid substance from a solution," from Old French precipitation (15c.) and directly from Latin praecipitationem (nominative praecipitatio) "act or fact of falling headlong, haste," noun of action from past-participle stem of praecipitare "to throw or dive headlong; be hasty," from praeceps (genitive praecipitis) "steep, headlong, headfirst," from prae "before, forth" (see pre-) + caput "head" (from PIE root *kaput- "head").
The meaning "sudden haste" is from c. 1500. The meaning "act of falling from a height" is attested from 1610s. The meteorological sense of "rain, snow, dew, frost, hail, etc.; moisture from the atmosphere deposited on the earth's surface" is from 1670s.