The second point of view under which we regard numbers is as equal,
so that they make one unity, and of such there is an annumeration or
sum before us. To tell the tale of these is Multiplication. It makes
no matter in the process, how the functions of Sum and Unity are
distributed between the two numbers, or factors of the product; either
may be Sum and either may be Unity.
The third and final point of view is the equality of Sum (amount) and
Unity. To number together numbers when so characterised is Involution;
and in the first instance raising them to the square power. To
raise the number to ä higher power means in point of form to go on
multiplying a number with itself an indefinite amount of times.--Since
this third type of calculation exhibits the complete equality of the
sole existing distinction in number, viz. the distinction between Sum
or amount and Unity, there can be no more than these three modes of
calculation. Corresponding to the integration we have the dissolution
of numbers according to the same features. Hence besides the three
species mentioned, which may to that extent be called positive, there
are three negative species of arithmetical operation.
Number, in general, is the quantum in its complete specialisation.
Hence we may employ it not only to determine what we call discrete, but
what are called continuous magnitudes as well. For that reason even
geometry must call in the aid of number, when it is required to specify
definite figurations of space and their ratios.
(c) _Degree._
103.] The limit (in a quantum) is identical with the whole of the
quantum itself. As _in itself_ multiple, the limit is Extensive
magnitude; as in itself _simple_ determinateness (qualitative
simplicity), it is Intensive magnitude or Degree.
The distinction between Continuous and Discrete magnitude differs
from that between Extensive and Intensive in the circumstance that
the former apply to quantity in general, while the latter apply to
the limit or determinateness of it as such. Intensive and Extensive
magnitude are not, any more than the other, two species, of which the
one involves a character not possessed by the other: what is Extensive
magnitude is just as much Intensive, and _vice versâ._