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plane 1  (plān)n.1. Mathematics A surface containing all the straight lines that connect any two points on it.2. A flat or level surface.3. A level of development, existence, or achievement: scholarship on a high plane.4. An airplane or hydroplane.5. A supporting surface of an airplane; an airfoil or wing.adj.1. Mathematics Of or being a figure lying in a plane: a plane curve.2. Flat; level. See Synonyms at level.[Latin plānum, flat surface, from neuter of plānus, flat; see pelə- in Indo-European roots. N., sense 4, short for aeroplane.]plane′ness n.plane2carpentry planeplane 2  (plān)n.1. A carpenter's tool with an adjustable blade for smoothing and leveling wood.2. A trowel-shaped tool for smoothing the surface of clay, sand, or plaster in a mold.v. planed, plan·ing, planes v.tr.1. To smooth or finish with a plane: planed the door.2. To remove with a plane: plane off the rough edges on a board.v.intr. To work with a plane.[Middle English, from Old French, from Late Latin plāna, from plānāre, to plane, from plānus, flat; see pelə- in Indo-European roots.]plane 3  (plān)intr.v. planed, plan·ing, planes 1. To rise partly out of the water, as a