Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

consequence of moving circularly* and producing light.
Whence also it is called light. But it is the privation of strife,
because it constitutes and unites all things which were before
separated by interiral, and on account of the association and
friendship of the two forms (of numbers, i.e. of the even and
the odd, the pentad consisting of 3 and 2). And it is justice,
because the pentad in the most eminent degree unfolds justice
into light." But Alexander Aphrodisiensis in his Comment on
the 7th chapter of the first book of Aristotle's Metaphysics,
assigns the following reason why the pentad was called by tnc
Pythagoreans the unconquered. "Because," says he, "in the first
right-angled triangle whose sides are effable,? one of the sides
is 3, another is 4, and the base is 5, and the base is in power
equal to both the other sides; hence is was said by the Pythagoreans
that it was victorious, and the two other sides were
conquered. The pentad therefore, was denominated by them
unconquered as not being surpassed, and as being superior."
The anonymous author too, unfolds the meaning of this appellation
as follows: "The Pythagoreans," says he, "called the
pentad unconquered, not only because the fifth element, ether,
which is arranged analogous to the pentad, and which has an
invariable sameness of subsistence, terminates the strife and
mutation of the elements which subsist under it as far as
to the earth, but also it amicably connects and unites the
first two differing, and not similar species of numbers, the odd
and the even (i.e. 2 and 3.) becoming itself the system of their
association."
The same author likewise thus explains the reason why the
pentad was called the smallest extremity of vitality. "Since,"
says he, "according to physiologists there arc three things
+ For 5 is eminently a circular and spherical number, in every multiplication
terminating in, or restoring itsdf.
t See this explained in the chapter on the properties of the heptad.