A null point moving in a direction away generates a yellow line, and the yellow line ends in a null point. We suppose, that is, a point to move and mark out the products of this motion in such a manner. Now suppose this whole line as thus produced to move in an upward direction; it traces out the two-dimensional solid, and the plane being gets an orange square. The null point moves in a red line and ends in a null point, the yellow line moves and generates an orange square and ends in a yellow line, the farther null point generates a red line and ends in a null point. Thus, by movement in two successive directions known to him, he can imagine his two-dimensional solid produced with all its boundaries. Now we tell him: “This whole two-dimensional solid can move in a third or unknown dimension to you. The null point moving in this dimension out of your world generates a white line and ends in a null point. The yellow line moving generates a light yellow two-dimensional solid and ends in a yellow line, and this two-dimensional solid, lying end on to your plane world, is bounded on the far side by the other yellow line. In the same way each of the lines surrounding your square traces out an area, just like the orange area you know. But there is something new produced, something which you had no idea of before; it is that which is produced by the movement of the orange square. That, than which you can imagine nothing more solid, itself moves in a direction open to it and produces a three-dimensional solid. Using the addition of white to symbolise the products of this motion this new kind of solid will be light orange or ochre, and it will be bounded on the far side by the final position of the orange square which traced it out, and this final position we suppose to be coloured like the square in its first position, orange with yellow and red boundaries and null corners.” This product of movement, which it is so easy for us to describe, would be difficult for him to conceive. But this difficulty is connected rather with its totality than with any particular part of it. Any line, or plane of this, to him higher, solid we could show to him, and put in his sensible world. We have already seen how the pink square could be put in his world by a turning of the cube about the red line. And any section which we can conceive made of the cube could be exhibited to him. You have simply to turn the cube and push it through, so that the plane of his existence is the plane which cuts out the given section of the cube, then the section would appear to him as a solid. In his world he would see the contour, get to any part of it by digging down into it. THE PROCESS BY WHICH A PLANE BEING WOULD GAIN A NOTION OF A SOLID.