Eurytus

The Pythagorean Eurytus and his followers beheld the images of things themselves in numbers. They rightly attributed certain numbers to certain things, according to their peculiarity.

A particular number is the boundary of this plant, and again, another number of this animal; just as of a triangle 6 is the boundary, of a square 9, and of a cube 8.

The musician harmonizes his lyre through mathematical numbers. Likewise, nature harmonizes hers through her own natural numbers, orderly arranges, and modulates her productions.

Numbers are participated by the heavens. Even to the blind, there is:

• a solar number
• a lunar number

For the restitutions of the heavenly bodies to their pristine state (αποκαταστασεις) would not always be effected through the same things, and in the same manner, unless one and the same number bad dominion in each.

Yet all these contribute to the procession of the celestial spheres, and are contained by their perfect number. But there is also a certain natural number belonging to every animal. For things of the same species would not be distinguished by organs after the same manner, nor would they arrive at puberty and old age about the same time, or generate, nor would the fœtus be nourished or increase, according to regular periods, unless they were detained by the same measure of nature.

According to the best of the Pythagoreans also, Plato himself, number is the cause of better and worse generations.

Hence though the Pythagoreans sometimes speak of the squares and cubes of natural numbers, they do not make them to be monadic, such as the number 9, and the number 27.

But they signify through these names, from similitude, the progression of natural numbers into, and dominion about, generations.

Similarly, though they call them equal or double, they exhibit the dominion and symphony of ideas in these numbers. Hence different things do not use the same number, so far as they are different, nor do the same things use a different number, so far as they are the same.

In short, physical numbers are material forms divided about the subject which receives them. But material powers are the sources of connexion and modification to bodies.

For form is one thing, and the power proceeding from it another. For form itself is indeed impartible and essential; but being extended, and becoming bulky, it emits from itself, as if it were a blast, material powers which are certain qualities.

Thus, for instance, in fire, the form and essence of it is impartible, and is truly the image of the cause of fire= for in partible natures, the impartible has a subsistence. But from form which is impartible in fire, and which subsists in it as number, an extension of it accompanied with interval takes place about matter, from which the powers of fire are emitted, such as heat, or refrigeration, or moisture, or something else of the like kind. And these qualities are indeed essential, but are by no means the essence of fire.

For essences do not proceed from qualities, nor are essence and power the same thing. But the essential every where precedes power. And from this being one the multitude of powers proceeds, and the distributed from that which is undistributed; just as many energies are the progeny of one power.”

P. 107. For Pythagoras always proclaimed, that nothing admirable pertaining to the Gods or divine dogmas, should be disbelieved.

Fourth Symbol

Iamblichus explains in the Protreptics the fourth symbol:

“This dogma venerates and unfolds the transcendency of the Gods, affording us a viaticum, and recalling to our memory that we ought not to estimate divine power from our judgment.

But it is likely that some things should appear difficult and impossible to us, in consequence of our corporeal subsistence, and from our being conversant with generation and corruption; from our having a momentary existence; from being subject to a variety of diseases; from the smallness of our habitation; from our gravitating tendency to the middle; from our somnolency, indigence and repletion; from our want of counsel and our imbecility; from the impediments of our soul, and a variety of other circumstances, although our nature possesses many illustrious prerogatives.

At the same time however we perfectly fall short of the Gods, and neither possess the same power with them, nor equal virtue.

This symbol therefore in a particular manner introduces the knowledge of the Gods, as beings who are able to effect all things. On this account it exhorts us to disbelieve nothing concerning the Gods. It also adds, nor about divine dogmas; viz. those belonging to the Pythagoric philosophy.

For these being secured by disciplines and scientific theory, are alone true and free from falsehood, being corroborated by all-various demonstration, accompanied with necessity. The same symbol, also, is capable of exhorting us to the science concerning the Gods= for it urges us to acquire a science of that kind, through which we shall be in no respect deficient in things asserted about the Gods.

It is also able to exhort the same things concerning divine dogmas, and a disciplinative progression. For disciplines alone give eyes to, and produce light about, all 320 things, in him who intends to consider and survey them. For from the participation of disciplines, one thing before all others is effected, viz. a belief in the nature, essence, and power of the Gods, and also in those Pythagoric dogmas, which appear to be prodigious to such as have not been introduced to, and are uninitiated in, disciplines; So that the precept disbelieve not is equivalent to participate and acquire those things through which you will not disbelieve; that is to say, acquire disciplines and scientific demonstrations.”