same size. In accordance with Euclidean geometry we can place them
above, beside, and behind one another so as to fill a part of space
of any dimensions; but this construction would never be finished;
we could go on adding more and more cubes without ever finding
that there was no more room. That is what we wish to express when
we say that space is infinite. It would be better to say that space
is infinite in relation to practically-rigid bodies, assuming that
the laws of disposition for these bodies are given by Euclidean
geometry.

Another example of an infinite continuum is the plane. On a plane
surface we may lay squares of cardboard so that each side of any
square has the side of another square adjacent to it. The construction
is never finished; we can always go on laying squares--if their laws
of disposition correspond to those of plane figures of Euclidean
geometry. The plane is therefore infinite in relation to the
cardboard squares. Accordingly we say that the plane is an infinite
continuum of two dimensions, and space an infinite continuum of
three dimensions. What is here meant by the number of dimensions,
I think I may assume to be known.

Now we take an example of a two-dimensional continuum which is
finite, but unbounded. We imagine the surface of a large globe and
a quantity of small paper discs, all of the same size. We place
one of the discs anywhere on the surface of the globe. If we move
the disc about, anywhere we like, on the surface of the globe,
we do not come upon a limit or boundary anywhere on the journey.
Therefore we say that the spherical surface of the globe is an
unbounded continuum. Moreover, the spherical surface is a finite
continuum. For if we stick the paper discs on the globe, so that