rces, centrifugal and centripetal, are
symbolized in the operations of addition and subtraction. Within them
is embraced the whole of computation; but because every number, every
aggregation of units, is also a new unit capable of being added
or subtracted, there are also the operations of multiplication and
division, which consists in one case of the addition of several equal
numbers together, and in the other, of the subtraction of several
equal numbers from a greater until that is exhausted. In order to
think correctly it is necessary to consider the whole of numeration,
computation, and all mathematical processes whatsoever as _the
division of the unit_ into its component parts and the establishment
of relations between these parts.

[Illustration 73]

[Illustration 74]

The progression and retrogression of numbers in groups expressed by
the multiplication table gives rise to what may be termed "numerical
conjunctions." These are analogous to astronomical conjunctions: the
planets, revolving around the sun at different rates of speed, and
in widely separated orbits, at certain times come into line with one
another and with the sun. They are then said to be in conjunction.
Similarly, numbers, advancing toward infinity singly and in groups
(expressed by the multiplication table), at certain stages of their
progression come into relation with one another. For example, an
important conjunction occurs in 12, for of a series of twos it is
the sixth, of threes the fourth, of fours the third, and of sixes the
second. It stands to 8 in the ratio of 3:2, and to 9, of 4:3. It is
related to 7 through being the product of 3 and 4, of which numbers 7
is the sum. The numbers 11 and 13 are not conjunctive; 14 is so in
the series of twos, and sevens; 15 is so in the series of fives and
threes. The next conjunction after 12, of 3 and 4 and their first
multiples, is in 24, and the next following is in 36, which numbers
are respectively the two and three of a series of twelves, each end
being but a new beginning.

[Illustration 75]

It will be seen that this discovery of numerical conjunctions consists
merely of resolving numbers into their prime factors, and that a
conjunctive number is a common multiple; but by naming it so, to
dismiss the entire subject as known and exhausted, is to miss a
sense of the wonder, beauty and rhythm of it all: a mental impression
analogous to that made upon the eye by the swift-glancing balls of a