Pohlke's theorem is the fundamental theorem of axonometry. It was established 1853 by the German painter and teacher of descriptive geometry Karl Wilhelm Pohlke. The first proof of the theorem was published 1864 by the German mathematician Hermann Amandus Schwarz, who was a student of Pohlke. Therefore the theorem is sometimes called theorem of Pohlke and Schwarz, too.
in a plane originating at point 
, which are not contained in a line, can be considered as the parallel projection of three edges 
of a cube.
For a mapping of a unit cube, one has to apply an additional scaling either in the space or in the plane. Because a parallel projection and a scaling preserves ratios one can map an arbitrary point 
Pohlke's theorem can be stated in terms of linear algebra as:
Pohlke's theorem is the justification for the following easy procedure to construct a scaled parallel projection of a 3-dimensional object using coordinates,:[2][3]
of a point is determined by the three steps, starting at point :
in
-direction, then
in
-direction, then
in
-direction and.In order to get undistorted pictures, one has to choose the images of the axes and the forshortenings carefully (see Axonometry). In order to get an orthographic projection only the images of the axes are free and the forshortenings are determined. (see de:orthogonale Axonometrie).
Schwarz formulated and proved the more general statement:
and used a theorem of L’Huilier:
