"flat surface, simplest of all geometrical surfaces," c. 1600, from Latin planum "flat surface, plane, level, plain," noun use of neuter of adjective planus "flat, level, even, plain, clear," from PIE *pla-no- (source also of Lithuanian plonas "thin;" Celtic *lanon "plain;" perhaps also Greek pelanos "sacrificial cake, a mixture offered to the gods, offering (of meal, honey, and oil) poured or spread"), suffixed form of root *pele- (2) "flat; to spread."
Introduced (perhaps by influence of French plan in this sense) to differentiate the geometrical senses from plain, which in mid-16c. English also meant "geometric plane." The figurative sense, in reference to inanimate things, is attested from 1850.
c. 1300, "to devise, plan;" early 14c. as "to surround, contain, envelop, enclose;" from Anglo-French cumpasser, Old French compasser "to go around, measure (with a compass), divide equally, calculate; plan" (12c.), from Vulgar Latin *compassare "to pace out" (source of Italian compassare, Spanish compasar), from Latin com "with, together" (see com-) + passus "a step" (from PIE root *pete- "to spread"). Related: Compassed; compassing.
1716, transitive, "reduce to a scheme;" 1767, "devise a scheme, plot, plan," from scheme (n.). Intransitive sense of "form plans, contrive" is by 1842. Related: Schemed; scheming.