A line, on the other hand, is a continuous quantity, for it is possible
to find a common boundary at which its parts join. In the case of the
line, this common boundary is the point; in the case of the plane, it
is the line: for the parts of the plane have also a common boundary.
Similarly you can find a common boundary in the case of the parts of a
solid, namely either a line or a plane.
Space and time also belong to this class of quantities. Time, past,
present, and future, forms a continuous whole. Space, likewise, is a
continuous quantity; for the parts of a solid occupy a certain space,
and these have a common boundary; it follows that the parts of space
also, which are occupied by the parts of the solid, have the same
common boundary as the parts of the solid. Thus, not only time, but
space also, is a continuous quantity, for its parts have a common
boundary.
Quantities consist either of parts which bear a relative position each
to each, or of parts which do not. The parts of a line bear a relative
position to each other, for each lies somewhere, and it would be
possible to distinguish each, and to state the position of each on the
plane and to explain to what sort of part among the rest each was
contiguous. Similarly the parts of a plane have position, for it could
similarly be stated what was the position of each and what sort of
parts were contiguous. The same is true with regard to the solid and to
space. But it would be impossible to show that the parts of a number had
a relative position each to each, or a particular position, or to state
what parts were contiguous. Nor could this be done in the case of time,
for none of the parts of time has an abiding existence, and that which
does not abide can hardly have position. It would be better to say that
such parts had a relative order, in virtue of one being prior to
another. Similarly with number: in counting, 'one' is prior to 'two',
and 'two' to 'three', and thus the parts of number may be said to
possess a relative order, though it would be impossible to discover any
distinct position for each. This holds good also in the case of speech.
None of its parts has an abiding existence: when once a syllable is
pronounced, it is not possible to retain it, so that, naturally, as the
parts do not abide, they cannot have position. Thus, some quantities
consist of parts which have position, and some of those which have not.