1580s, "characterized by looking to the future," from obsolete French prospectif and directly from Medieval Latin prospectivus "affording a prospect; pertaining to a prospect," from Latin prospect-, past-participle stem of prospicere "look out on, look forward," from pro "forward" (see pro-) + specere "look at" (from PIE root *spek- "to observe"). The sense of "being in prospect or expectation, looked forward to" is by 1829.
Also used as a noun in various senses: "outlook, prospect, view" (1590s); "spy glass, telescope" (17c.), from the adjectival sense of "suitable for viewing at a distance" (c. 1600). Related: Prospectively.