(55) Timaeus: when joined together, formed eight solid angles, each composed of three plane right angles; and the shape of the body thus constructed was cubic, having six plane equilateral quadrangular bases. And seeing that there still remained one other compound figure, the fifth, God used it up for the Universe in his decoration thereof. Now in reasoning about all these things, a man might question whether he ought to affirm the existence of an infinite diversity of Universes or a limited number; and if he questioned aright he would conclude that the doctrine of an infinite diversity is that of a man unversed

(9) And, in short, it is said that Pythagoras was emulous of the Orphic mode of writing and [piety of] disposition; and that he honored the Gods in a way similar to that of Orpheus, placing them in images and in brass, not conjoined to our forms, but to divine receptacles; because they comprehend and provide for all things; and have a nature and morphe similar to the universe. He also promulgated purifications, and initiations as they are called, which contain the most accurate knowledge of the Gods. And farther still, it is said, that he was the author of a compound divine philosophy and worship of the Gods; having learnt indeed some things from the followers of Orpheus, but others from the Egyptian priests; some from the Chaldæans and Magi; some from the mysteries performed in Eleusis, in Imbrus, Samothracia, and Delos; and some also from those which are performed by the Celtæ, and in Iberia.

It is also said that the Sacred Discourse of Pythagoras is extant among the Latins, and is read not to all, nor by all of them, but by those who are promptly disposed to learn what is excellent, and apply themselves to nothing base. He likewise ordained that men should make libations thrice, and observed that Apollo delivered oracles from the tripod, because the triad is the first number. That sacrifices also should be made to Venus on the sixth day, because this number is the first that partakes of every number , and, when divided in every possible way, receives the power of the numbers subtracted and of those that remain. But that it is necessary to sacrifice to Hercules on the eighth day of the month from the beginning, looking in so doing to his being born in the seventh month.

He further asserted, that it was necessary that he who entered a temple should be clothed with a pure garment, and in which no one had slept; because sleep in the same manner as the black and the brown, is an indication of sluggishness; but purity is a sign of equality and justice in reasoning. He also ordered, that if blood should be found involuntarily spilt in a temple, a lustration should be made, either in a golden vessel, or with the water of the sea; the former of these [i. e. gold] being the most beautiful of things, and a measure by which the price of all things is regulated; but the latter as he conceived being the progeny of a moist nature, and the nutriment of the first and more common matter.

He likewise said, that it was not proper to bring forth children in a temple; because it is not holy that in a temple the divine part of the soul should be bound to the body. He further ordained, that on a festive day neither the hair should be cut, nor the nails paired; not thinking it fit that we should leave the service of the Gods for the purpose of increasing our good. He also said, that a louse ought not to be killed in a temple; conceiving that a divine power ought not to participate of any thing superfluous and corruptible. But that the Gods should be honored with cedar, laurel, cypress, oak, and myrtle; and that the body should not be purified with these, nor should any of them be divided by the teeth.

He likewise ordained, that what is boiled should not be roasted; signifying by this that mildness is not in want of anger. But he would not suffer the bodies of the dead to be burned; following in this the Magi, being unwilling that any thing divine should communicate with a mortal nature. He likewise thought it was holy for the dead to be carried out in white garments; obscurely signifying by this the simple and first nature, according to number and the principle of all things. But above all things he ordained, that an oath should be taken religiously; since that which is behind is long. And he said, that it is much more holy to be injured than to kill a man: for judgment is deposited in Hades, where the soul and its essence, and the first nature of things are [properly] estimated.

Farther still, he ordered that sepulchral chests [i. e. biers] should not be made of cypress, because the sceptre of Jupiter was made of this wood, or for some other mystic reason. He likewise ordained that libations should be performed before the table of Jupiter the Saviour, and of Hercules and the Dioscuri; in so doing celebrating Jupiter as the presiding cause and leader of this nutriment; Hercules, as the power of nature; and the Dioscuri, as the symphony of all things. But he said, that libations should not be offered with closed eyes. For he did not think it fit, that any thing beautiful should be undertaken with shame and bashfulness. Moreover, when it thundered, he ordained that the earth should be touched, in remembrance of the generation of things.

But he ordered that temples should be entered from places on the right hand, and that they should be departed out of from the left hand. For he asserted that the right hand is the principle of what is called the odd number, and is divine; but that the left hand is a symbol of the even number, and of that which is dissolved. And such is the mode which he is said to have adopted in the cultivation of piety. But other particulars which we have omitted concerning it, may be conjectured from what has been said. So that I shall cease to speak further on this subject.

(1) The mode however of teaching through symbols, was considered by Pythagoras as most necessary. For this form of erudition was cultivated by nearly all the Greeks, as being most ancient. But it was transcendently honored by the Egyptians, and adopted by them in the most diversified manner. Conformably to this, therefore, it will be found, that great attention was paid to it by Pythagoras, if any one clearly unfolds the significations and arcane conceptions of the Pythagoric symbols, and thus developes the great rectitude and truth they contain, and liberates them from their enigmatic form. For they are adapted according to a simple and uniform doctrine, to the great geniuses of these philosophers, and deify in a manner which surpasses human conception.

For those who came from this school, and especially the most ancient Pythagoreans, and also those young men who were the disciples of Pythagoras when he was an old man, viz. Philolaus and Eurytus, Charondas and Zaleucus, and Brysson, the elder Archytas also, and Aristæus, Lysis and Empedocles, Zanolxis and Epimenides, Milo and Leucippus, Alcmæon, Hippasus and Thymaridas, and all of that age, consisting of a multitude of learned men, and who were above measure excellent,—all these adopted this mode of teaching, in their discourses with each other, and in their commentaries and annotations. Their writings also, and all the books which they published, most of which have been preserved even to our time , were not composed by them in a popular and vulgar diction, and in a manner usual with all other writers, so as to be immediately understood, but in such a way as not to be easily apprehended by those that read them.

For they adopted that taciturnity which was instituted by Pythagoras as a law, in concealing after an arcane mode, divine mysteries from the uninitiated, and obscuring their writings and conferences with each other. Hence he who selecting these symbols does not unfold their meaning by an apposite exposition, will cause those who may happen to meet with them to consider them as ridiculous and inane, and as full of nugacity and garrulity. When, however, they are unfolded in a way conformable to these symbols, and become obvious and clear even to the multitude, instead of being obscure and dark, then they will be found to be analogous to prophetic sayings, and to the oracles of the Pythian Apollo. They will then also exhibit an admirable meaning, and will produce a divine afflatus in those who unite intellect with erudition.

Nor will it be improper to mention a few of them, in order that this mode of discipline may become more perspicuous: Enter not into a temple negligently, nor in short adore carelessly, not even though you should stand at the very doors themselves . Sacrifice and adore unshod. Declining from the public ways, walk in unfrequented paths. Speak not about Pythagoric concerns without light. And such are the outlines of the mode adopted by Pythagoras of teaching through symbols.

(55) Timaeus: And the third solid is composed of twice sixty of the elemental triangles conjoined, and of twelve solid angles, each contained by five plane equilateral triangles, and it has, by its production, twenty equilateral triangular bases. Now the first of the elemental triangles ceased acting when it had generated these three solids, the substance of the fourth Kind being generated by the isosceles triangle. Four of these combined, with their right angles drawn together to the center, produced one equilateral quadrangle; and six such quadrangles,

(3) And why should I linger over the barbarians, when I can adduce the Greeks as exceedingly addicted to the use of the method of concealment? Androcydes the Pythagorean says the far-famed so-called Ephesian letters were of the class of symbols. For he said that askion (shadowless) meant darkness, for it has no shadow; and katas kion (shadowy) light, since it casts with its rays the shadow; and lix if is the earth, according to an ancient' appellation; and tetras is the year, in reference to the seasons; and d amnameneus is the sun, which overpowers (damazwn); and ta aisia is the true voice. And then the symbol intimates that divine things have been arranged in harmonious order - darkness to light, the sun to the year, and the earth to nature's processes of production of every sort. Also Dionysius Thrax, the grammarian, in his book, Respecting the Exposition of the Symbolical Signification in Circles, says expressly, "Some signified actions not by words only, but also by symbols: by words, as is the case of what are called the Delphic maxims, 'Nothing in excess,' 'Know thyself,' and the like; and by symbols, as the wheel that is turned in the temples of the gods, derived from the Egyptians, and the branches that are given to the worshippers. For the Thracian Orpheus says: "Whatever works of branches are a care to men on earth, Not one has one fate in the mind, but all things Revolve around; and it is not lawful to stand at one point, But each one keeps an equal part of the race as they began."