Quantity is either discrete or continuous. Moreover, some
quantities are such that each part of the whole has a relative
position to the other parts: others have within them no such
relation of part to part.
Instances of discrete quantities are number and speech; of
continuous, lines, surfaces, solids, and, besides these, time and
In the case of the parts of a number, there is no common boundary
at which they join. For example: two fives make ten, but the two
fives have no common boundary, but are separate; the parts three
and seven also do not join at any boundary. Nor, to generalize,
would it ever be possible in the case of number that there should
be a common boundary among the parts; they are always separate.
Number, therefore, is a discrete quantity.
The same is true of speech. That speech is a quantity is evident:
for it is measured in long and short syllables. I mean here that
speech which is vocal. Moreover, it is a discrete quantity for
its parts have no common boundary. There is no common boundary at
which the syllables join, but each is separate and distinct from
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.