Then consider this white line with its terminal points itself to move in a second dimension, each of the points traces out a line, the line itself traces out an area, and gives two lines as well, its initial and its final position. Thus, if we call “a region” any element of the figure, such as a point, or a line, etc., every “region” in moving traces out a new kind of region, “a higher region,” and gives two regions of its own kind, an initial and a final position. The “higher region” means a region with another dimension in it. Now the square can move and generate a cube. The square light yellow moves and traces out the mass of the cube. Letting the addition of red denote the region made by the motion in the upward direction we get an ochre solid. The light yellow face in its initial and terminal positions give the two square boundaries of the cube above and below. Then each of the four lines of the light yellow square—white, yellow, and the white, yellow opposite them—trace out a bounding square. So there are in all six bounding squares, four of these squares being designated in colour by adding red to the colour of the generating lines. Finally, each point moving in the up direction gives rise to a line coloured null + red, or red, and then there are the initial and terminal positions of the points giving eight points. The number of the lines is evidently twelve, for the four lines of this light yellow square give four lines in their initial, four lines in their final position, while the four points trace out four lines, that is altogether twelve lines. Now the squares are each of them separate boundaries of the cube, while the lines belong, each of them, to two squares, thus the red line is that which is common to the orange and pink squares. Now suppose that there is a direction, the fourth dimension, which is perpendicular alike to every one of the space dimensions already used—a dimension perpendicular, for instance, to up and to right hand, so that the pink square moving in this direction traces out a cube. A dimension, moreover, perpendicular to the up and away directions, so that the orange square moving in this direction also traces out a cube, and the light yellow square, too, moving in this direction traces out a cube. Under this supposition, the whole cube moving in the unknown dimension, traces out something new—a new kind of volume, a higher volume. This higher volume is a four-dimensional volume, and we designate it in colour by adding blue to the colour of that which by moving generates it. It is generated by the motion of the ochre solid, and hence it is of the colour we call light brown (white, yellow, red, blue, mixed together). It is represented by a number of sections like 2 in fig. 103.