1520s, "to hurl or fling down" (from a precipice or height), a back formation from precipitation or else from Latin praecipitatus, past participle 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").
Earliest use in English is figurative, "to hurl or cause (someone) to fall (into some state or condition). Â Meaning "to cause to happen suddenly, hurry the beginning of" is recorded from 1620s. The chemical sense "cause to fall as a sediment to the bottom of a vessel" is from 1620s (intransitive sense from 1640s). The meteorological sense (intransitive) is attested by 1863. Related: Precipitated; precipitating.