Projection
mid 16th century (in projection (sense 6)): from Latin projectio(n- ), from proicere ‘throw forth’ (see project).
wiktionary
From either the Middle French projection or its etymon, the Classical Latin prōiectiō (stem: prōiectiōn-), from prōiciō. Compare the Modern French projection, the German Projektion, and the Italian proiezione.
etymonline
projection (n.)
late 15c., projeccioun, in alchemy, "transmutation by casting a powder on molten metal," from Old French projeccion and directly from Latin proiectionem (nominative proiectio) "a throwing forward, a stretching out," noun of action from past-participle stem of proicere "stretch out, throw forth" (see project (v.)).
From 1560s in the cartographical sense of "system of continuous correspondence between the points of a spherical surface and those of a plane." From 1590s as "action of projecting." From 1756 as "that which projects or juts out."