Finding the eye's height and distance in a perspective square
A construction to locate a random point a in a foreshortened square, and a cube-in-corner method
Given a plane shown in perspective with a point a marked at random and only the length of its front edge told to him, Leonardo claims he can determine how far the viewpoint stood from the square, its height, and the position of point a. The analytical figure extends the sides a-b and c-d until they meet at f, the height of the eye, and uses a perspective screen a-n and a distance point g to build a square grid in perspective and locate a. A closing sketch of a sphere balanced on a right-angled corner accompanies a note on depicting a cube in the corner of a wall by first making it in its proper form and then raising it onto a perspective screen shaped like the corner.
On this page
Locating a random point a in a foreshortened square
If a plane is shown with a point marked on it at random and only the length of the first face is given, Leonardo can tell how many braccia the viewpoint was from the square and how far away the random point a lies. He directs the reader to the demonstration below.
Sides a b and c d meet at f, the height of the eye
Extending line a b and line d c to their intersection at f gives the height of the eye. Drawing line c to g on line g f gives the distance point, after which the braccia markers a, r, S, t and c are joined to f and to g to complete the plane and reveal the position of point a.
Depicting a cube in the corner of a wall
To render a cube in the corner of a wall, first make the thing in its proper form and then lift it onto a perspective screen that resembles the corner where the body is to be depicted. A sphere resting on a right-angled corner illustrates the setup.