Iamblichus' Life of Pythagoras, or Pythagoric Life / Accompanied by Fragments of the Ethical Writings of certain Pythagoreans in the Doric dialect; and a collection of Pythagoric Sentences from Stobaeus and others, which are omitted by Gale in his Opuscula Mythologica, and have not been noticed by any editor

by Iamblichus

In these numbers the more perfect ratios of symphonies are found; and in these also a tone is comprehended. The monad, however, contains the productive principle of a point. But the second numbers 2 and 3 contain the principle of a side, since they are incomposite, and first, are measured by the monad, and naturally measure a right line. The third terms are 4 and 9, which are in power a square superficies, since they are equally equal. And the fourth terms 8 and 27 being equally equally equal, are in power a cube. Hence from these numbers, and this tetractys, the increase takes place from a point to a solid. For a side follows after a point, a superficies after a side, and a solid after a superficies. In these numbers also, Plato in the Timæus constitutes the soul. But the last of these seven numbers, i. e. 27, is equal to all the numbers that precede it; for 1 + 2 + 3 + 4 + 8 + 9 = 27. There are, therefore, two tetractys of numbers, one of which subsists by addition, but the other by multiplication, and they comprehend musical, geometrical, and arithmetical ratios, from which also the harmony of the universe consists.

But the third tetractys is that which according to the same analogy or proportion comprehends the nature of all magnitude. For what the monad was in the former tetractys, that a point is in this. What the numbers 2 and 3, which are in power a side, were in the former tetractys, that the extended species of a line, the circular and the right, are in this; the right line indeed subsisting in conformity to the even number, since it is terminated[107] by two points; but the circular in conformity to the odd number, because it is comprehended by one line which has no end. But what in the former tetractys the square numbers 4 and 9 were, that the two-fold species of planes, the rectilinear and the circular, are in this. And what the cube numbers 8 and 27 were in the former, the one being an even, but the other an odd number, that the two solids, one of which has a hollow superficies, as the sphere and the cylinder, but the other a plane superficies, as the cube and pyramid, are in this tetractys. Hence, this is the third tetractys, which gives completion to every magnitude, from a point, a line, a superficies, and a solid.

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 1 to 3; and to earth, the ratio of 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 and a 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 a city. For a 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.