Now, the whole of this red, yellow, blue, or brown cube appears as a series of faces on the successive sections of the tesseract starting from the ochre cube and letting the blue axis run in the fourth dimension. Hence the plane traced out by the red line appears as a series of lines in the successive sections, in our ordinary way of representing the tesseract; these lines are in different places in each successive section.
Fig. 114.
Thus drawing our initial cube and the successive sections, calling them b0, b1, b2, b3, b4, [fig. 115], we have the red line subject to this movement appearing in the positions indicated.
We will now investigate what positions in the tesseract another line in the pink face assumes when it is moved in a similar manner.
Take a section of the original cube containing a vertical line, 4, in the pink plane, [fig. 115]. We have, in the section, the yellow direction, but not the blue.
From this section a cube goes off in the fourth dimension, which is formed by moving each point of the section in the blue direction.
Fig. 115.
