'Project' is Latin for 'thrown forward' — casting an idea into the future. Plans as projectiles.
A planned undertaking or scheme; to throw or cast forward; to extend outward; to present or communicate an image or idea to others.
From Latin prōiectum (something thrown forth, a plan), the neuter perfect passive participle of prōicere (to throw forward, to fling out, to protrude), composed of prō- (forward, before, in front of) and iacere (to throw, to hurl), from PIE *yeh₁- (to throw). The PIE root *yeh₁- yielded Latin iacere, giving English inject, reject, eject, subject, object, adjacent, and trajectory (a throwing across). The same prō- prefix (PIE *per- in its forward-pointing sense) appears in provide, produce, and promote