In geometry, an even or level surface, like plain in popular language.

In astronomy, an imaginary surface supposed to pass through any of the curves described on the celestial sphere; as the plane of the ecliptic; the plane of a planet’s orbit; the plane of a great circle.

In mechanics.

In joinery and cabinet work, an instrument consisting of a smooth piece of wood, with an aperture, through which passes obliquely a piece of edged steel or chisel, used in paring or smoothing boards or wood of any kind.

To make smooth; to pare off the inequalities of the surface of a board or other piece of wood by the use of a plane.

To free from inequalities of surface.