Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

6X 1 and +1= 7 the 2ndj
6X 7 and +1= 43 the 8th octangular gnomon.
6X 18 and +1=109 the 19th J
&c.
CHAPTER XVI
On the properties of the hebdomad.
THE hebdomad possesses many admirable properties, and is
of a venerable nature as its name implies. Concerning these
properties much has been transmitted to us by the ancients, but
they have been discussed by none so copiously as by Philo the
Jew, who in his treatise De Mundi Opificio, has written the
following eulogium on this number :
"I know not whether any one can sufficiently celebrate the
nature of the hebdomad, which is too excellent to be described
by the power of words; yet it is not proper to be silent though
what is said about it is of the most wonderful nature, but we
should endeavour, if we cannot relate all and its most principal
excellencies, to render manifest at least such of its properties
as are accessible by our reasoning power. The hebdomad
then, is spoken of in a twofold respect; one indeed, subsisting
within the decad, which is seven times measured by the monad
alone, and consists of seven monads; but the other is external
to the decad, of which the principle is entirely the monad, according
to double, or triple, or in short, analogous numbers;
and such are the numbers of 64 and 729; the former indeed increasing
by a duplication from unity, but the other by a triplication.
Each species however ought not to be negligently considered.
The second species indeed, has a most manifest prerogative.
For the hebdomad which is compounded from double,
or triple, or analogous numbers from the monad, is both
a cube and a square, comprehending both species, viz. of the