The full deployment of internalisation, swapping and extra diagonals helps determine the image of any transversal line in space thanks to a bevy of auxiliary points, two of which are strategically located within the Black Box (a” and a”’). The same metrical equivalence between red and blue dotted lines applies, and space folds like an accordion. Desargues’s use of the Black Box
Desargues’s use of the Black Box (and the three geometric expedients shown in Figure 8) to determine the image (projection) of a line T2 located two times further than the observer from the picture plane (but on the opposite side). All geometric moves will take place within rectangle GG0F0F. The length of the red dotted line is equal to that of the blue one, providing a vivid and accurate visual account of the folding of outer space within the confines of the Black Box. Figure 9. in, and their image will be determined without reference to any external points. Like an inward reflection, the lines meeting the boundaries of the back box will bounce back
The same operation as in Figure 9, assuming that the transversal line is now located three times further than the observer from the picture plane.