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early 15c., "act of looking into the distance," from Latin prospectus "distant view, look out; sight, faculty of sight," noun use of past participle of prospicere "look out on, look forward," from pro- "forward" (see pro-) + specere "look at" (see scope (n.1)). Meaning "extensive view of the landscape" is from 1530s; transferred sense of "mental view or survey" is from 1620s. Sense of "person or thing considered promising" is from 1922. Prospects "expectations, things looked forward to" is from 1660s.
"explore for gold, examine land with a view to a mining claim," 1841, from prospect (n.) in specialized sense of "spot giving prospects of ore" (1832). Earlier in a sense "look forth, look out over" (1550s), from Latin prospectare. Related: Prospected; prospecting.