"flat surface," 1604, from L. plantum "flat surface," properly neut. of adj. planus "flat, level, plain, clear," from PIE *pla-no- (cf. Lith. plonas "thin;" Celtic *lanon "plain;" perhaps also Gk. pelanos "sacrificial cake, a mixture offered to the gods, offering (of meal, honey, and oil) poured or spread"), suffixed form of base *pele- "to spread out, broad, flat" (cf. O.C.S. polje "flat land, field," Rus. polyi "open;" O.E., O.H.G. feld, M.Du. veld "field"). Fig. sense is attested from 1850. The verb meaning "soar, glide on motionless wings" is first recorded 1611, from M.Fr. planer (16c.), from L. planum on notion of bird gliding with flattened wings. Of boats, etc., "to skim over the surface of water" it is first found 1913.
"tool for smoothing surfaces," 1349, from O.Fr. plane, earlier plaine (14c.), from L.L. plana, from planare "make level," from L. planus "level, flat" (see plane (1)). The verb meaning "to make smooth" is c.1320, from O.Fr. planer (12c.), from L.L. planare.
"tree of the genus Platanus," 1382, from O.Fr. plane, earlier plasne (14c.), from L. platanus, from Gk. platanos, earlier platanistos "plane tree," a species from Asia Minor, associated with platys "broad," in reference to its leaves (see place (n.)). Applied since 1778 in Scotland and northern England to the sycamore, whose leaves somewhat resemble those of the true plane tree.