The fourth dimension

124 THE FOURTH DIMENSION

with it o of the kind j; and then, that we take o of the kind ¢ and with it 1 of the kind j.

Thus we get a pair of positions lying in the straight

CG line BC, fig. 64. We can call this pair 10

01 and 01 if we adopt the plan of mentally,

adding an 7@ to the first and aj to the

4 5 second of the symbols written thus—01 is a short expression for 02, 1).

Coming now to our space, we have three

dimensions, so we take three positions on each. These

positions I will suppose to be at equal distances along each

fig. 64.

®

axis. The three axes and the three positions on each are shown in the accompanying diagrams, fig. 65, of which the first represents a cube with the front faces visible, the second the rear faces of the same cube; the positions I will call 0,1,2; the axes, 7,7,k. I take the base anc as the starting place, from which to determine distances in the & direction, and hence every point in the base anc will be an ok position, and the base anc can be called an ok plane.

In the same way, measuring the distances from the face ADC, we see that every position in the face apc is a o7 position, and the whole plane of the face may be called an ot plane, Thus we see that with the introduction of a