late 14c., perspectif, "the science of optics," from Old French perspective and directly from Medieval Latin perspectiva ars "science of optics," from fem. of perspectivus "of sight, optical" from Latin perspectus "clearly perceived," past participle of perspicere "inspect, look through, look closely at," from per "through" (from PIE root *per- (1) "forward," hence "through") + specere "look at" (from PIE root *spek- "to observe"). The English word is also attested from early 15c. as an adjective, "pertaining to the science of optics."
The sense of "the art of drawing solid objects on a flat surface so as to give appearance of distance or depth" is attested by 1590s, probably by influence of Italian prospettiva, an artists' term. The meaning "proper or just proportion, appropriate relation in the mind of the parts of a subject to one another" is recorded by c. 1600, hence the figurative meaning "mental outlook over time" (1762).