Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
are at a distance 0 from our space in the fourth dimension,
the second showing all those that are at a distance 1,
and so on.
These figures will each be cubes. The first two are
drawn showing the front faces, the second two the rear
faces. We will mark the points 0, 1, 2, 3, putting points
at those distances along each of these axes, and suppose
i
k
D
B C
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j
0h 1h
E2 E
2h 3h
Fig. 71.
all the points thus determined to be contained in solid
models of which our drawings in fig. 71 are representations.
Here we notice that as on the plane 0i meant
the whole line from which the distance in the i direction
was measured, and as in space 0i means the whole plane
from which distances in the i direction are measured, so
now 0h means the whole space in which the first cube
stands—measuring away from that space by a distance
of one we come to the second cube represented.