The Pythagoreans thought those who teach for the sake of reward show themselves worse than sculptors, or artists who perform the work sitting. For these, when someone orders wood to make a statue of Hermes, search for wood suited to receive the proper form; while those pretend that they can readily produce the works of virtue from every nature.

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The dyad gets its name from passing through or asunder; for the dyad is the first to have separated itself from the monad, whence also it is called "daring." For when the monad manifests unification, the dyad steals in and manifests separation.

After his father's death, though he was still but a youth, his aspect was so venerable, and his habits so temperate that he was honored and even reverenced by elderly men, attracting the attention of all who saw and heard him speak, creating the most profound impression. That is the reason that many plausibly asserted that he was a child of the divinity. Enjoying the privilege of such a renown, of an education so thorough from infancy, and of so impressive a natural appearance he showed that he deserved all these advantages by deserving them, by the adornment of piety and discipline, by exquisite habits, by firmness of soul, and by a body duly subjected to the mandates of reason. An inimitable quiet and serenity marked all his words and actions, soaring above all laughter, emulation, contention, or any other irregularity or eccentricity; his influence at Samos was that of some beneficent divinity. His great renown, while yet a youth, reached not only men as illustrious for their wisdom as Thales at Miletus, and Bias at Prione, but also extended to the neighboring cities. He was celebrated everywhere as the "long-haired Samian," and by the multitude was given credit for being under divine inspiration.

The Pythagoreans called the monad "intellect" because they thought that intellect was akin to the One; for among the virtues, they likened the monad to moral wisdom; for what is correct is one. And they called it "being," "cause of truth," "simple," "paradigm," "order," "concord," "what is equal among the greater and the lesser," "the mean between intensity and slackness," "moderation in plurality," "the instant now in time," and moreover they call it "ship," "chariot," "friend," "life," "happiness."

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Likewise, they call it "Chaos," which is Hesiod's first generator, because Chaos gives rise to everything else, as the monad does. It is also thought to be both "mixture" and "blending," "obscurity" and "darkness" thanks to the lack of articulation and distinction of everything which ensues from it. Anatolius says that it is called "matrix" and "matter," on the grounds that without it there is no number. The mark which signifies the monad is the source of all things.

Hence the Pythagoreans in their theology called it sometimes "universe," sometimes "heaven," sometimes "all," sometimes "Fate" and "eternity," "power" and "trust" and "Necessity," "Atlas" and "unwearying," and simply "God" and "Phanes" and "sun."
They called it "universe," because all things are arranged by it both in general and in particular, and because it is the most perfect boundary of number, in the sense that "decad" is, as it were, "receptacle," just as heaven is the receptacle of all things, they called it "heaven" and, among the Muses, "Ourania."

Just as without the monad there is in general no composition of anything, so also without it there is no knowledge of anything whatsoever, since it is a pure light, most authoritative over everything in general, and it is sun-like and ruling, so that in each of these respects it resembles God, and especially because it has the power of making things cohere and combine, even when they are composed of many ingredients and are very different from one another, just as he made this universe harmonious and unified out of things which are likewise opposed.

What appears to us to be an accurate definition of justice does not also appear to be so to the Gods. For we, looking to that which is most brief, direct our attention to things present, and to this momentary life, and the manner in which it subsists. But the Powers that are superior to us know the whole life of the Soul, and all its former lives.

Since wise people are in the habit of invoking the divinities at the beginning of any philosophic consideration, this is all the more necessary on studying that one which is justly named after the divine Pythagoras. Inasmuch as it emanated from the divinities it could not be apprehended without their inspiration and assistance. Besides, its beauty and majesty so surpasses human capacity, that it cannot be comprehended in one glance. Gradually only can some details of it be mastered when, under divine guidance we approach the subject with a quiet mind. Having therefore invoked the divine guidance, and adapted ourselves and our style to the divine circumstances, we shall acquiesce in all the suggestions that come to us. Therefore we shall not begin with any excuses for the long neglect of this sect, nor by any explanations about its having been concealed by foreign disciplines, or mystic symbols, nor insist that it has been obscured by false and spurious writings, nor make apologies for any special hindrances to its progress. For us it is sufficient that this is the will of the Gods, which all enable us to undertake tasks even more arduous than these. Having thus acknowledged our primary submission to the divinities, our secondary devotion shall be to the prince and father of this philosophy as a leader.