Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

duced, the name of the multiple being always one more than
that of the terms which are omitted.
And all the double terms indeed are always even. But of
the triple terms, one is always found to be odd, and another
even. Again, the quadruple terms always preserve an even
quantity; and they are formed from the fourth number, one
of the prior even numbers being omitted in order; first the
even number 2; then 6 being omitted, 8 follows as the next
quadruple term; and after 8, the quadruple number 12 follows,
the even number 10 being omitted. And so on in the
rest. But the quintuple resembles the triple multiple; for in
this the even and odd terms have an alternate arrangement.
CHAPTER XVIII.
On the superpartictllar nrcm ber, its species, and the generation
of them, etc.
W ~ N one number contains the whole of another in itself,
and some part of it besides, it is called superparticular. And
if the part of the less which it contains is the half, it is called
sesquialter; if the third part, sesquitertian; if the fourth, sesquiquartan;
if the fifth, sesquiquintan. And the like names
being employed to infinity, the form of superparticular numbers
will also proceed infinitely. And the greater numbers,
indeed, are thus denominated. But of the less, the wholes of
which are contained in the greater, and a certain part of them
besides ; one is called subsesquialter ; another subsesquitertian ;
another subsesquiquartan; another subsesquiquintan; and so
on according to the rule and multitude of the greater numbers.
The greater numbers also are called leaders, but the less
attendants.
Of superparticular numbers likewise, the multitude is infinite;
because the progression of their species is boundless.