This is the 14th Symbol in the Protreptics of Iamblichus, whose
explanation of it is as follows: “This symbol exhorts us to the exercise
of justice, to the honoring equality and moderation in an admirable
degree, and to the knowledge of justice as the most perfect virtue, to
which the other virtues give completion, and without which none of the
rest are of any advantage. It also admonishes us, that it is proper to
know this virtue not in a careless manner, but through theorems and
scientific demonstrations. But this knowledge is the business of no
other art and science than the Pythagoric philosophy alone, which in a
transcendent degree honors disciplines before every thing else.”
The following extract also from my Theoretic Arithmetic, (p. 194.), will
in a still greater degree elucidate this symbol. The information
contained in it is derived from the anonymous author of a very valuable
work entitled Θεολογουμενα Αριθμητικης _Theologumena Arithmeticæ_, and
which has lately been reprinted at Leipsic, “The Pythagoreans called the
pentad providence and justice, because it equalizes things unequal,
justice being a medium between excess and defect, just as 5 is the
middle of all the numbers that are equally distant from it on both sides
as far as to the decad, some of which it surpasses, and by others is
surpassed, as may be seen in the following arrangement:
1. 4. 7.
2. 5. 8.
3. 6. 9.
“For here, as in the middle of the beam of a balance, 5 does not depart
from the line of the equilibrium, while one scale is raised, and the
other is depressed.
“In the following arrangement also, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9, it
will be found that the sum of the numbers which are posterior, is triple
the sum of those that are prior to 5; for 6 + 7 + 8 + 9 = 30; but 1 + 2
+ 3 + 4 = 10. If therefore the numbers on each side of 5 represent the
beam of a balance, 5 being the tongue of it, when a weight depresses the
beam, an obtuse angle is produced by the depressed part with the tongue,
and an acute angle by the elevated part of the beam. Hence it is worse
to do than to suffer an injury: and the authors of the injury verge
downward as it were to the infernal regions; but the injured tend upward
as it were to the Gods, imploring the divine assistance. Hence the
meaning of the Pythagoric symbol is obvious, “Pass not above the beam of
the balance.” Since however injustice pertains to inequality, in order
to correct this, equalization is requisite, that the beam of the balance
may remain on both sides without obliquity. But equalization is effected
by addition and subtraction. Thus if 4 is added to 5, and 4 is also
taken from 5, the number 9 will be produced on one side, and 1 on the
other, each of which is equally distant from 5. Thus too, if 3 is added
to 5, and is also subtracted from it, on the one side 8 will be
produced, and on the other 2. If 2 is added to 5, and likewise taken
from it, 7 and 3 will be produced. And by adding 1 to 5, and subtracting
3 from it, 6 and 4 will be the result; in all which instances, the
numbers produced are equidistant from 5, and the sum of each couple is
equal to 10.”