Perspective, with the Reason of Shadows and Mirrors

A perspective diagram showing a tall building with windows labeled B and C. Lines of sight originate from a human figure on the left, passing through a vertical plane (the "cut line") marked with points F, G, D, H, I, and M. A semi-circle arc illustrates the projection of angles from the eye to the building's height.

Theoresme Ninth.

THE VISIBLE THING PARALLEL TO THE CUT LINE GIVES ITS OWN FORESHORTENING.

Let there be, for example, two squares B C and D E in foreshortening. Now, B C is further from the eye than D E, and also the said side B C is seen from the side and not from the front. For these reasons, it seems that it should be smaller on the foreshortened plane, but if the cut line is parallel to the said sides, the foreshortening will be equal, that is to say, L M will be equal to N O. And to see by how much L M is smaller than N O, let the semi-circle F G H I be drawn. Thus, the side B C, or L M, will appear under the size F G, and the side D E, or N O, under the size H I.

A second perspective diagram below the text, showing a top-down or plan view of the same geometric principle. It features two squares in perspective labeled with points B, L, M, E, N, D, and O. A "cut line" intersects the visual rays. At the bottom, a "point of distance" (poinct d'eslongnement) serves as the vertex for a semi-circle arc with points F, G, H, and I, demonstrating the angular measurement of the objects.