Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

friendship, and which consequently is founded in virtue, so
these numbers are perspicuous images of the friendship sub
sisting among vicious characters; such of them whose parts are
less than the whole, adumbrating the friendship between those
who fall short of the medium in which true virtue consists;
and those whose parts are greater than the whole, exhibiting
an image of the friendship of such as exceed this medium. As
likewise, of the vicious characters situated on each side of the
medium, those that exceed it are more allied to virtue, than
those that fall short of it, and being more allied to virtue are
more excellent, and being more excellent, are more rarely to be
found;-thus also in these numbers, the pairs whose parts are
less than the whole numbers, are far more numerous than those
whose parts are greater than the wholes of which they are the
parts.
CHAPTER XXXVII
On the series of unevenly-even numbers.
THE series of these numbers is as follows: 12, 20, 24, 28, 36,
40, 44, 48, 52, 56,60, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108,
112, 116, 120, 124, 132, 136, 140, 144, 1489 152, 156, 160, 164,
168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216,
220, 224, 228, 232, 236, 240, 244, 248, 252, 260, &c.
In this series, it is observable in the first place, that the difference
between the terms is every where either 8 or 4. Thus
the, difference between 12 and 20 is 8; but between 20 and 24,
and 24 and 28 is 4. Again, the difference between 28 and 36
is 8; but between 36 and 40, 40 and 44, 44 and 48, 48 and
52, 52 and 56, 56 and 60, is 4. And again the difference between
60 and 68 is 8; but between 68 and 72 is 4, and so on,
till we arrive at 124 and 132, the difference between which is 8.