Hence there are eleven tetractys. The first is that which subsists according to the composition of numbers. The second, according to the multiplication of numbers. The third subsists according to magnitude. The fourth is of the simple bodies. The fifth is of figures. The sixth is of things rising into existence through the vegetative life. The seventh is of communities. The eighth is the judicial power. The ninth is of the parts of the animal. The tenth is of the seasons of the year. And the eleventh is of the ages of man. All of them however are proportional to each other. For what the monad is in the first and second tetractys, that a point is in the third; fire in the fourth; a pyramid in the fifth; seed in the sixth; man in the seventh; intellect in the eighth; and so of the rest. Thus, for instance, the first tetractys is 1. 2. 3. 4. The second is the monad, a side, a square, and a cube. The third is a point, a line, a superficies, and a solid. The fourth is fire, air, water, earth. The fifth the pyramid, the octaedron, the icosaedron, and the cube. The sixth, seed, length, breadth and depth. The seventh, man, a house, a street, a city. The eighth, intellect, science, opinion, sense. The ninth, the rational, the irascible, and the epithymetic parts, and the body. The tenth, the spring, summer, autumn, winter. The eleventh, the infant, the lad, the man, and the old man.
The world also, which is composed from these tetractys, is perfect, being elegantly arranged in geometrical, harmonical, and arithmetical proportion; comprehending every power, all the nature of number, every magnitude, and every simple and composite body. But it is perfect, because all things are the parts of it, but it is not itself the part of any thing. Hence, the Pythagoreans are said to have first used the before-mentioned oath, and also the assertion that “all things are assimilated to number.”
[P. 111.] This number is the first that partakes of every number, and when divided in every possible way, receives the power of the numbers subtracted, and of those that remain.
Because 6 consists of 1, 2 and 3, the two first of which are the principles of all number, and also because 2 and 3 are the first even and odd, which are the sources of all the species of numbers; the number 6 may be said to partake of every number. In what Iamblichus afterwards adds, I suppose he alludes to 6 being a perfect number and therefore equal to all its parts.
[P. 134.] Not to step above the beam of the balance.
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.”