(7) Hence, too, the errant spheres, being moved contrarily to the inerrant one, are moved by one another by mutual contrariety, [and also] by the spable one through contrariety itself. And this can otherwise not be. The Bears up there , which neither set nor rise, think'st thou they rest or move? A: They move, Thrice-greatest one. H: And what their motion, my Asclepius? A: Motion that turns for ever round the same. H: But revolution - motion around same - is fixed by rest. For "round-the-same" doth stop "beyond-same". "Beyond-same" then, being stopped, if it be steadied in "round-same" - the contrary stands firm, being rendered ever stable by its contrariety.

(436) rather say that one part of him is in motion while another is at rest. Very true. And suppose the objector to refine still further, and to draw the nice distinction that not only parts of tops, but whole tops, when they spin round with their pegs fixed on the spot, are at rest and in motion at the same time (and he may say the same of anything which revolves in the same spot), his objection would not be admitted by us, because in such cases things are not at rest and in motion in the same parts of themselves; we should rather say that they have both an axis and a circumference, and that the axis stands still, for there is no deviation from the perpendicular; and that the circumference goes round. But if, while revolving, the axis inclines either to the right or left, forwards or backwards, then in no point of view can they be at rest. That is the correct mode of describing them, he replied. Then none of these objections will confuse us, or incline us to believe that the same thing at the same time, in the same part or in relation to the same thing, can act or be acted upon in contrary ways. Certainly not, according to my way of thinking. Yet, I said, that we may not be compelled to examine all such objections, and prove at length that they are untrue, let us assume their absurdity, and go forward on the understanding that hereafter, if this assumption turn out to be untrue, all the consequences which follow shall be withdrawn. Yes, he said, that will be the best way.

(6) If space is, therefore, to be thought, [it should] not, [then, be thought as] God, but space. If God is also to be thought, [He should] not [be conceived] as space, but as energy that can contain [all space]. Further, all that is moved is moved not in the moved but in the stable. And that which moves [another] is of course stationary, for 'tis impossible that it should move with it. A: How is it, then, that things down here, Thrice-greatest one, are moved with those that are [already] moved? For thou hast said the errant spheres were moved by the inerrant one. H: This is not, O Asclepius, a moving with, but one against; they are not moved with one another, but one against the other. It is this contrariety which turneth the resistance of their motion into rest. For that resistance is the rest of motion.

(86) Suppose a WHEEL standing before thee, with seven wheels one so made in the other that it could go on all sides, forward, backward and cross ways, without need of any turning back or stopping. See Ch. 19, par. 81 et seq.

(11) For the Deity is like a wheel, which with its fellies and spokes, and with all the naves, turneth about, and is fellied together, as seven wheels, so that it can go any way, forward, backward, downward, upward and crossways, without turning back.

(7) As the geometrician, who endeavours To square the circle, and discovers not, By taking thought, the principle he wants, Even such was I at that new apparition; I wished to see how the image to the circle Conformed itself, and how it there finds place; But my own wings were not enough for this, Had it not been that then my mind there smote A flash of lightning, wherein came its wish. Here vigour failed the lofty fantasy: But now was turning my desire and will, Even as a wheel that equally is moved, The Love which moves the sun and the other stars.

(3) That which Timaeus argues of the soul Doth not resemble that which here is seen, Because it seems that as he speaks he thinks. He says the soul unto its star returns, Believing it to have been severed thence Whenever nature gave it as a form. Perhaps his doctrine is of other guise Than the words sound, and possibly may be With meaning that is not to be derided. If he doth mean that to these wheels return The honour of their influence and the blame, Perhaps his bow doth hit upon some truth. This principle ill understood once warped The whole world nearly, till it went astray Invoking Jove and Mercury and Mars. The other doubt which doth disquiet thee Less venom has, for its malevolence Could never lead thee otherwhere from me. That as unjust our justice should appear In eyes of mortals, is an argument Of faith, and not of sin heretical. But still, that your perception may be able To thoroughly penetrate this verity, As thou desirest, I will satisfy thee.

(529) nothing of that sort is matter of science; his soul is looking downwards, not upwards, whether his way to knowledge is by water or by land, whether he floats, or only lies on his back. I acknowledge, he said, the justice of your rebuke. Still, I should like to ascertain how astronomy can be learned in any manner more conducive to that knowledge of which we are speaking? I will tell you, I said: The starry heaven which we behold is wrought upon a visible ground, and therefore, although the fairest and most perfect of visible things, must necessarily be deemed inferior far to the true motions of absolute swiftness and absolute slowness, which are relative to each other, and carry with them that which is contained in them, in the true number and in every true figure. Now, these are to be apprehended by reason and intelligence, but not by sight. True, he replied. The spangled heavens should be used as a pattern and with a view to that higher knowledge; their beauty is like the beauty of figures or pictures excellently wrought by the hand of Daedalus, or some other great artist, which we may chance to behold; any geometrician who saw them would appreciate the exquisiteness of their workmanship, but he would never dream of thinking that in them he could find the true equal or the true double, or the truth of any

(4) 'He made each of these tripartite; and how these three beings become each of them tripartite, that learn from me now, my friend!

(2) Thus distant round the point a circle of fire So swiftly whirled, that it would have surpassed Whatever motion soonest girds the world; And this was by another circumcinct, That by a third, the third then by a fourth, By a fifth the fourth, and then by a sixth the fifth; The seventh followed thereupon in width So ample now, that Juno's messenger Entire would be too narrow to contain it. Even so the eighth and ninth; and every one More slowly moved, according as it was In number distant farther from the first. And that one had its flame most crystalline From which less distant was the stainless spark, I think because more with its truth imbued. My Lady, who in my anxiety Beheld me much perplexed, said: "From that point Dependent is the heaven and nature all. Behold that circle most conjoined to it, And know thou, that its motion is so swift Through burning love whereby it is spurred on." And I to her: "If the world were arranged In the order which I see in yonder wheels, What's set before me would have satisfied me;

(55) According to Pythagoras, the position of each body in the universe was determined by the essential dignity of that body. The popular concept of his day was that the earth occupied the center of the solar system; that the planets, including the sun and moon, moved about the earth; and that the earth itself was flat and square. Contrary to this concept, and regardless of criticism, Pythagoras declared that fire was the most important of all the elements; that the center was the most important part of every body; and that, just as Vesta's fire was in the midst of every home, so in the midst of the universe was a flaming sphere of celestial radiance. This central globe he called the Tower of Jupiter, the Globe of Unity, the Grand Monad, and the Altar of Vesta. As the sacred number 10 symbolized the sum of all parts and the completeness of all things, it was only natural for Pythagoras to divide the universe into ten spheres, symbolized by ten concentric circles. These circles began at the center with the globe of Divine Fire; then came the seven planers, the earth, and another mysterious planet, called Antichthon, which was never visible.

(2) All things accord in number:

which he very frequently uttered to all his disciples. Or again, Friendship is equality; equality is friendship . Or in the word cosmos , i. e. the world ; or by Jupiter, in the word philosophy , or in the so much celebrated word tetractys . All these and many other inventions of the like kind, were devised by Pythagoras for the benefit and amendment of his associates; and they were considered by those that understood them to be so venerable, and so much the progeny of divine inspiration, that the following was adopted as an oath by those that dwelt together in the common auditory:

(12) At this point I have just recollected the following. In the end of the Timoeus he says: "You must necessarily assimilate that which perceives to that which is perceived, according to its original nature; and it is by so assimilating it that you attain to the end of the highest life proposed by the gods to men, for the present or the future time." For those have equal power with these. He, who seeks, will not stop till he find; and having found, he will wonder; and wondering, he will reign; and reigning, he will rest. And what? Were not also those expressions of Thales derived from these? The fact that God is glorified for ever, and that He is expressly called by us the Searcher of hearts, he interprets. For Thales being asked, What is the divinity? said, What has neither beginning nor end. And on another asking, "If a man could elude the knowledge of the Divine Being while doing aught?" said, "How could he who cannot do so while thinking?"

(26) If the whole wheel, circumference or sphere of the stars be well considered, then it is soon found that the same is the mother of all things, or the nature out of which all things are come, and wherein all things stand and live, and whereby everything moveth; all things are made of these powers, and therein they all abide eternally.

(11) Then the Formative Mind ([at-oned] with Reason), he who surrounds the spheres and spins them with his whorl, set turning his formations, and let them turn from a beginning boundless unto an endless end. For that the circulation of these [spheres] begins where it doth end, as Mind doth will. And from the downward elements Nature brought forth lives reason-less; for He did not extend the Reason (Logos) [to them]. The Air brought forth things winged; the Water things that swim, and Earth-and-Water one from another parted, as Mind willed. And from her bosom Earth produced what lives she had, four-footed things and reptiles, beasts wild and tame.

(5) Such, then, is the style of the example in arithmetic. And let the testimony of geometry be the tabernacle that was constructed, and the ark that was fashioned, - constructed in most regular proportions, and through divine ideas, by the gift of understanding, which leads us from things of sense to intellectual objects, or rather from these to holy things, and to the holy of holies. For the squares of wood indicate that the square form, producing fight angles, pervades all, and points out security. And the length of the structure was three hundred cubits, and the breadth fifty, and the height thirty; and above, the ark ends in a cubit, narrowing to a cubit from the broad base like a pyramid, the symbol of those who are purified and tested by fire. And this geometrical proportion has a place, for the transport of those holy abodes, whose differences are indicated by the differences of the numbers set down below.

(64) For the being of God is like a wheel, wherein many wheels are made one in another, upwards, downwards, crossways, and yet they continually turn, all of them together.

(12) Whereas yet always the form of all the seven wheels, and the one only nave in the centre of all the wheels, is fully in sight, and so it is not understood how the wheel is made; but the wheel always appears more and more wonderful and marvellous, with its rising up, and yet abideth also in its own place.

(1) From centre unto rim, from rim to centre, In a round vase the water moves itself, As from without 'tis struck or from within. Into my mind upon a sudden dropped What I am saying, at the moment when Silent became the glorious life of Thomas, Because of the resemblance that was born Of his discourse and that of Beatrice, Whom, after him, it pleased thus to begin: "This man has need (and does not tell you so, Nor with the voice, nor even in his thought) Of going to the root of one truth more. Declare unto him if the light wherewith Blossoms your substance shall remain with you Eternally the same that it is now; And if it do remain, say in what manner, After ye are again made visible, It can be that it injure not your sight." As by a greater gladness urged and drawn They who are dancing in a ring sometimes Uplift their voices and their motions quicken; So, at that orison devout and prompt, The holy circles a new joy displayed In their revolving and their wondrous song.

(1) After this we must narrate how, when he had admitted certain persons to be his disciples, he distributed them into different classes according to their respective merits. For it was not fit that all of them should equally participate of the same things, as they were naturally dissimilar; nor was it indeed right that some should participate of all the most honorable auditions, but others of none, or should not at all partake of them. For this would be uncommunicative and unjust. While therefore he imparted a convenient portion of his discourses to each, he benefited as much as possible all of them, and preserved the proportion of justice, by making each a partaker of the auditions according to his desert.

Hence, in conformity to this method, he called some of them Pythagoreans, but others Pythagorists; just as we denominate some men Attics, but others Atticists. Having therefore thus aptly divided their names, some of them he considered to be genuine, but he ordained that others should show themselves to be the emulators of these. He ordered therefore that with the Pythagoreans possessions should be shared in common, and that they should always live together; but that each of the others should possess his own property apart from the rest, and that assembling together in the same place, they should mutually be at leisure for the same pursuits. And thus each of these modes was derived from Pythagoras, and transmitted to his successors.

Again, there were also with the Pythagoreans two forms of philosophy; for there were likewise two genera of those that pursued it, the Acusmatici, and the Mathematici. Of these however the Mathematici are acknowledged to be Pythagoreans by the rest; but the Mathematici do not admit that the Acusmatici are so, or that they derived their instruction from Pythagoras, but from Hippasus. And with respect to Hippasus, some say that he was a Crotonian, but others a Metapontine. But the philosophy of the Acusmatici consists in auditions unaccompanied with demonstrations and a reasoning process; because it merely orders a thing to be done in a certain way, and that they should endeavour to preserve such other things as were said by him, as so many divine dogmas.

They however profess that they will not speak of them, and that they are not to be spoken of; but they conceive those of their sect to be the best furnished with wisdom, who retained what they had heard more than others. But all these auditions are divided into three species. For some of them indeed signify what a thing is; others what it especially is; but others, what ought, or what ought not, to be done. The auditions therefore which signify what a thing is, are such as, What are the islands of the blessed? The sun and moon. What is the oracle at Delphi? The tetractys. What is harmony? That in which the Syrens subsist . But the auditions which signify what a thing especially is, are such as, What is the most just thing?

To sacrifice. What is the wisest thing? Number. But the next to this in wisdom, is that which gives names to things. What is the wisest of the things that are with us, [i. e. which pertain to human concerns]? Medicine. What is the most beautiful? Harmony. What is the most powerful? Mental decision. What is the most excellent? Felicity. What is that which is most truly asserted? That men are depraved. Hence they say that Pythagoras praised the Salaminian poet Hippodomas, because he sings: