Hinton - The Fourth Dimension.pdf

124
THE FOURTH DIMENSION
with it o of the kind j; and then, that we take o of the
kind i and with it 1 of the kind j.
Thus we get a pair of positions lying in the straight
C line BC, fig. 64. We call this part 10 and 01
01 if we adopt the plan of mentally adding an
i to the first and a j to the second of the
B
symbols written thus—01 is a short
10
expression for 0i, 1j.
Fig. 64.
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
i
201
D
200
B C
k
ji
Fig. 65.
001
000
k
D
100 A
B C
axis. The three axes and the three positions on each are
shown in the accompanying diagram, 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, i, j, k. I take the base ABC as
the starting place, from which to determine distances in
the k direction, and hence every point in the base ABC
will be an ok position, and the base ABC can be called an
ok plane.
In the same way, measuring the distance from the face
ADC, we see that every position in the face ADC is an oi
position, and the whole plane of the face may be called an
oi plane. Thus we see that with the introduction of a
j