Hinton - The Fourth Dimension.pdf

198
THE FOURTH DIMENSION
would be small; if it were to pass farther, we should
have a different figure, the outlines of which can be
determined in a similar manner.
The preceding method is open to the objection that
it depends rather on our inferring what must be, than
our seeing what is. Let us therefore consider our
sectional space as consisting of a number of planes, each
very close to the last, and observe what is to be found
in each place.
The corresponding method in the case of two dimen-
Null r. l.y.
p.
or.
Red
Null y.
x
Null Null wh.
Fig. 124.
sions is as follows:--the plane
being can see that line of the
sectional plane through null
y., null b., null r., which lies
in the orange plane. Let him
now suppose the cube and the
section plane to pass half way
though his plane. Replacing
the red and yellow axes are lines parallel to them, sections
of the pink and light yellow faces.
Where will the section plane cut these parallels to
the red and yellow axes?
Let him suppose the cube, in the position of the
drawing, fig. 124, turned so that the pink face lies
against his plane. He can see the line from the null r.
point to the null wh. point, and can see (compare fig. 119)
that it cuts as a parallel to his red axis, drawn at a point
half way along the white line, in a point n., half way up.
I shall speak of the axis as having the length of an edge
of the cube. Similarly, by letting the cube turn so that
the light yellow square swings in against his plane, he can
see (compare fig. 119) that a parallel to his yellow axis
drawn from a point half-way along the white axis, is cut
at half its length by the trace of the section plane in the
light yellow face.