c.1400, "a plan, draft, scheme," from Latin proiectum "something thrown forth," noun use of neuter of proiectus, past participle of proicere "stretch out, throw forth," from pro- "forward" (see pro-) + combining form of iacere (past participle iactus) "to throw" (see jet (v.)).
Meaning "scheme, proposal, mental plan" is from c.1600. Meaning "group of low-rent apartment buildings" first recorded 1935, American English, short for housing project (1932). Related: Projects. Project manager attested from 1913.