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). 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.
word-forming element making adjectives from verbs, meaning "pertaining to, tending to; doing, serving to do," in some cases from Old French -if, but usually directly from Latin adjectival suffix -ivus (source also of Italian and Spanish -ivo). In some words borrowed from French at an early date it has been reduced to -y (as in hasty, tardy).