Life of Pythagoras — Iamblichus, trans. Thomas Taylor (1818)
The text is shown on its own: no facing layer is held for this issue.
In consequence, however, of the great veneration paid to the tetractys by the Pythagoreans, it will be proper to give it a more ample discussion, and for this purpose to show from Theo of Smyrna,+ how many tetractys there are: “‘The tetractys,” says he, “‘was not only principally honored by the Pythagoreans, because all symphonies are found to exist within it, but also because it appears to contain the nature of all things.” Hence the dollowine was their oath: “Not by him who delivered to our soul the tetractys, which contains the fountain and root of everlasting nature.” But by him who delivered the tetractys they mean Pythagoras; for the doctrine concerning it appears to have been his invention. The above-mentioned tetractys, therefore, is seen in the composition of the first numbers I. 2. 3. 4. But the second tetractys arises from the increase by multiplication of even and odd numbers beginning from the monad.
Of these, the monad is assumed as the first, because,
1 In Mathemat. p. 147.
p. 236
as we have before observed, it is the principle of all even, odd, and evenly-odd numbers, and the nature of it is simple. But the three successive numbers receive their composition according to the even and the odd; because every number is not alone even, nor alone odd. Hence the even and the odd receive two tetractys, according to multiplication; the even indeed, in a duple ration; for 2 is the first of even numbers, and increases from the monad by duplication. But the odd number is increased in a triple ratio; for 3 is the first of odd numbers, and is itself increased from the monad by triplication. Hence the monad is common to both these, being itself even and odd. The second number, however, in even and double numbers is 2; but in odd and triple numbers 3. The third among even numbers is 4; but among odd numbers is 9. And the fourth among even numbers is 8; but among odd numbers is 27.
{h 2. 4. oy Is. 3s -Q..- 27.
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 9g, which are in power a square superficies, since they are equally equal. And the fourth terms 8 and 27 being equally equal, are in power a cube. Hence from these numbers, and this tetractys, the increase takes place from a point toa solid. Fora side follows after a point, a superficies after a side, and a solid after a superficies. In these numbers also, Plato in the Timzus 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. Therep. 237 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 ! by two points; but the circular in conformity to the odd number, because it is comprehended by one line which has noend. But what in the former tetractys the square numbers 4 and g 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 curd tetractys, which gives completion to every magnitude, from a point, a line, a superficies, and a solid.
No commentary for this page under the selected tracks.
There is commentary on page 1.