1670s as a technical term in perspective drawing; more generally by 1706 as "the representation of anything drawn on a plane; a drawing, sketch, or diagram of any object," from French plan "ground plot of a building, map," literally "plane surface" (mid-16c.), from Latin planum "level or flat surface," noun use of adjective planus "level, flat" (from PIE root *pele- (2) "flat; to spread").
The notion is of "a drawing on a flat surface." A doublet of plain via a later, learned French form. The meaning "scheme of action, formulated scheme for the accomplishment of some object or attainment of an end" is by 1713.
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