Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

Here it is evident in the first instance, that 3, 2, and 1, are
all the possible parts of 6. For 3 is the half, 2 the third, and 1
the sixth part of 6. And it is likewise manifest that 14,7,4, 2,
and 1, are all the parts of 28. Thus too, in the division of 495
into its parts, 465 is the sum of the parts that are the quotients
arising from the division by 2 and its powers. And as the half
of 496 is 248, it is the same thing to divide 248 by 2, as to divide
4% by 4. For the same reason it is the same thing to
divide 124, the half of 248, by 2, as to divide 496 bv 8. And
to divide 62, the half of 124, by 2, as to divide 496 by 16.
Hence the divisors of 496 are 2, 4, 8, 16, and the sum of these
added to 1 and to 465, is 496. In a similar manner in the
fourth instance, 8001 is the aggregate of the parts that are the
quotients arising from the division by 2 and its powers. And
the divisors of 8128 are 2, 4, 8, 1.6, 32, 64, the sum of which
added to 1, and to 8001, is equal to 8128,. And so in the other
instances.
Only eight perfect numbers have as yet been found, owing to
the difficulty of ascertaining in very great terms, whether a
number is a prime or not. And these eight are as. follow,
230584308139952128. By an evolution of the expression
twenty terms, the reader will see at what dis-
tance these perfect numbers are from each other. But these
twenty terms are as follow, those that are perfect numbers being
designated by a star: