project (n.)
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" (from PIE root *ye- "to throw, impel").

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.
project (v.)
late 15c., "to plan," from Latin proiectus, past participle of proicere "stretch out, throw forth," from pro- "forward" (from PIE root *per- (1) "forward") + combining form of iacere (past participle iactus) "to throw" (from PIE root *ye- "to throw, impel").

Sense of "to stick out" is from 1718. Meaning "to cast an image on a screen" is recorded from 1865. Psychoanalytical sense, "attribute to another (unconsciously)" is from 1895 (implied in a use of projective). Meaning "convey to others by one's manner" is recorded by 1955. Related: Projected; projecting.