Where one segment of a straight line leaves off and another begins is a point, and the straight line itself can be generated by the motion of the point.
One portion of a plane is bounded from another by a straight line, and the plane itself can be generated by the straight line moving in a direction not contained in itself.
Again, two portions of solid space are limited with regard to each other by a plane; and the plane, moving in a direction not contained in itself, can generate solid space.
Thus, going on, we may say that space is that which limits two portions of higher space from each other, and that our space will generate the higher space by moving in a direction not contained in itself.
Another indication of the nature of four-dimensional space can be gained by considering the problem of the arrangement of objects.
If I have a number of swords of varying degrees of brightness, I can represent them in respect of this quality by points arranged along a straight line.
Fig. 1.
If I place a sword at A, [fig. 1], and regard it as having a certain brightness, then the other swords can be arranged in a series along the line, as at A, B, C, etc., according to their degrees of brightness.
