Abstract: This paper describes the process of proving the sole existence of an orthographic projection for a 3-dimentional geometry based on the projection theorem in the optimal theory, and proposes a new method of calculating the orthographically projective transformation of an object. It includes: ①An orthographic projection of a 3-dimentional geometry is defined again with the mathematical concepts; ②In order to apply the projection theorem, a series of propositions related to the orthographic projection are proved sequentially, and then the sole existence of an orthographic projection for a 3-dimentional object is strictly testified and the orthographically projective transformation of an object is found with respect to the Fourier series; ③The advantages of the method of calculating the orthographically projective transformation are concluded.