Life of Pythagoras — Iamblichus, trans. Thomas Taylor (1818)

The fourth tetractys is of the simple bodies fire, air, water, and earth, which have an analogy according to numbers. For what the monad was in the first tetractys, that fire is in this. But the duad is air, the triad is water, and the tetrad is earth. For such is the nature of the elements according to tenuity and density of parts. Hence fire has to air the ratio of 1 to 2; but to water, the ratio of I to 3; and to earth, the ratio of

1 Instead of wepirrovrat, it is necessary to read mwepardvrac; the necessity of which emendation, I wonder the learned Bullialdus did not observe.

p. 238

1 to 4. In other respects also they are analogous to each other.

The fifth tetractys is of the figures of the simple bodies. For the pyramid, indeed, is the figure of fire; the octaedron, of air; the icosaedron, of water; and the cube, of earth.

The sixth tetractys is of things rising into existence through the vegetative life. And the seed, indeed, is analogous to the monad anda point. But if it increases in length it is analogous to the duad and a line; if in breadth, to the triad and a superficies; but if in thickness, to the tetrad and a solid.

The seventh tetractys is of communities; of which the principle indeed, and as it were monad, is man; the duad is a house; the triad a street; and the tetrad acity. Fora nation consists of these. And these indeed are the material and sensible tetractys.

The eighth tetractys consists of the powers which form a judgment of things material and sensible, and which are of a certain intelligible nature. And these are, intellect, science, opinion, and sense. And intellect, indeed, corresponds in its essence to the monad; but science to the duad; for science is the science of a certain thing. Opinion subsists between science and ignorance; but sense is as the tetrad. For the touch which is common to all the senses being fourfold, all the senses energize according to contact.

The ninth tetractys is that from which the animal is composed, the soul and the body. For the parts of the soul, indeed, are the rational, the irascible, and the epithymetic, or that which desires external good; and the fourth is the body in which the soul subsists.

The tenth tetractys is of the seasons of the year, through which all things rise into existence, viz. the spring, the summer, the autumn, and the winter.

And the eleventh is of the ages of man, viz. of the infant, the lad, the man, and the old man.

Hence there are eleven tetractys. The first is that

p. 239

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 1s I. 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, acity. 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.