Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

fect number is produced as follows: from the addition of 1, 2
and 4 arises 7, which is a first and incomposite number, and
this being multiplied by 4 the last of the evenly-even numbers,
the perfect number 28 is produced. Since therefore these two
perfect numbers 6 and 28 are found, others must be investigated
after the same manner. Thus, in order to find the next
perfect number, add 1, 2, 4, and 8 together; but the sum of
these is 15. This however is a second and composite number;
for it has a third and a fifth part, besides a fifteenth part, unity,
which is denominated from itself. This therefore must be
passed by, and the next evenly-even number, viz. 16, must be
added to it, and the sum will be 31, which is a first and incomposite
number. Let this then be multiplied by 16 the last of
the evenly-even numbers, and the product will be 496 the next
perfect number after 28. The monad therefore is in power
though not in energy itself a perfect number. For if it is first
assumed in the order of numbers, it will be found to be primary
and incomposite, and if multiplied by itself, the same
unity is produced. But this is equal to its parts in power alone.
Hence the monad is perfect by its own proper virtue, is first
and incomposite, and preserves itself unchanged when multiplied
by itself.
The way however in which perfect numbers are generated,
will immediately become manifest by the following table.
Odd numh pro-
I
duced by the
addition of the 3 7 IS 31 63 127 255 511 1023 2047 4095 8191
even1 yeven
numben
Perfect numberr . . . 1 6 28 4% 8128 + 33550336
The asterisks in this table signify that the odd numbers
above them produced by the addition of the evenly-even numbers,
are composite, and therefore unfit to form perfect numbers.