The grade of parallelism depends on the planeness of the surface worked first.    From Wordnik.com.  [3. Preparing face and parallel milling] Reference

Size of the permissible tolerances of workpiece surfaces, planeness, parallelism and dimensions as well as surface finish.    From Wordnik.com.  [3. Preparing face and parallel milling] Reference

After the finished size has been achieved, the workpiece is unclamped, deburred at the cutting edges and checked for planeness, accuracy to size and surface finish.    From Wordnik.com.  [4. Face milling] Reference

When all requirements as to accuracy to size, planeness and roughness are fulfilled, all the workpieces are milled, de-burred and checked according to the task set.    From Wordnik.com.  [4. Face milling] Reference

But then this smoothness and uniformity, or, in other words, this planeness of the picture, is not perceived immediately by vision: for it appeareth to the eye various and multiform.    From Wordnik.com.  [A Essay Towards a New Theory of Vision] Reference