Stephanus 36

36a the double and the triple intervals, cutting off yet further portions from what remained and setting them in between, so that within each interval there were two means: one exceeding and exceeded by the same fraction of the extremes, the other exceeding by an equal number and exceeded by an equal number. And when intervals of half again, of a third again, and of an eighth again had arisen out of these bonds within the earlier intervals, 36b he went on to fill every third-again interval with the eighth-again kind, leaving over a portion of each—the portion left over of each being an interval whose terms stood, number against number, as 256 to 243. And by now the mingled stuff from which he had been cutting these portions was entirely used up. Then he split this whole fabric down its length in two, brought the halves together middle to middle, like a man's two hands clasped, and bent them 36c into a single circle, joining them to themselves and to one another at the point directly opposite the clasp, and he carried them around in the motion that keeps them always in the same way within the same place; and he made one of them the outer circle and the other the inner. The outer motion he decreed to be that of the nature of the same, the inner that of the other. The circle of the same he caused to move round to the right along its side, the circle of the other to the left along the diagonal, and he gave the mastery to the 36d revolution of the same and like: this one he left single and undivided, but the inner one he split six times, into seven unequal circles, each keeping the ratio of the double and of the triple—three of each sort—and he appointed the circles to go in opposite directions to one another; in speed, three went at one pace, and the other four at paces unequal both to one another and to the three, yet borne along in due measure.

And when the whole fabric of the soul had come to be according to the mind of its maker, he then went on to weave all the bodily frame within 36e it, and bringing center to center he fitted them together; and the soul, woven through from the center out to the farthest reach of heaven, wrapping the heaven round about on the outside, and turning within herself, began a divine beginning of unceasing and intelligent life for all time to come.

Timaeus: And so the body of the heaven came to be visible; the soul herself is invisible, partaking of reasoning and

36a the double and the triple intervals. He was still cutting portions off from it and setting them between these intervals, so that in each interval there were two means. One of the two exceeded the outer terms by the same fraction of each, and was exceeded by them by the same fraction. The other exceeded by an equal number and was exceeded by an equal number. When the bonds had formed in the earlier intervals—distances of one and a half, of one and a third, and of one and an eighth—36b he filled every interval of one and a third with the interval of one and an eighth, leaving a small part of each one over. When that leftover fraction was set as a number against a number, its terms were 256 to 243. And at that point the mixture, from which he had cut all these pieces, was completely used up. So he split this whole structure lengthwise into two halves. Then he bent each one, middle onto middle, like a cross, and made them into one circle. He fastened them to themselves and to each other at the point directly opposite the crossing, and he kept them turning around by the motion that carries them in a circle, always in the same place. 36c He made one circle outer and the other inner. The outer motion he marked out as that of the nature of the same; the inner motion, that of the other. He turned the circle of the same around the side, toward the right, and the circle of the other along the diameter, toward the left. And he gave the mastery to the 36d rotation of the same and the like; for he left that one circle undivided. The inner circle he cut six times into seven unequal circles, each keeping the ratio of double and triple—three of each kind. He ordered those inner circles to move in opposite directions to one another. Three of them moved at the same speed, and four at speeds unlike one another and unlike the three, though each still moved in a fixed ratio.

And when the whole structure of the soul had come out as its builder intended, he then built all the body-like stuff inside 36e it, and joined middle to middle. The soul spread out from the middle to the far edge of heaven all around, wrapped heaven on the outside, and turned within itself. So it began a divine start of unceasing and intelligent life, for all time to come.

Timaeus: So the body of heaven came to be visible, while the soul itself is invisible, though it shares in reasoning and

36a Timaeus: After that He went on to fill up the intervals in the series of the powers of 2 and the intervals in the series of powers of 3 in the following manner: He cut off yet further portions from the original mixture, and set them in between the portions above rehearsed, so as to place two Means in each interval, —one a Mean which exceeded its Extremes and was by them exceeded by the same proportional part or fraction of each of the Extremes respectively; the other a Mean which exceeded one Extreme by the same number or integer as it was exceeded by its other Extreme. And whereas the insertion of these links formed fresh intervals in the former intervals, that is to say, intervals of 3:2 and 4:3 and 9:8, He went on to fill up the 4:3 intervals with 9:8 intervals. 36b This still left over in each case a fraction, which is represented by the terms of the numerical ratio 256:243. And thus the mixture, from which He had been cutting these portions off, was now all spent.

Next, He split all this that He had put together into two parts lengthwise; and then He laid the twain one against the other, the middle of one to the middle of the other, like a great cross; 36c and bent either of them into a circle, and join them, each to itself and also to the other, at a point opposite to where they had first been laid together. And He compassed them about with the motion that revolves in the same spot continually, and He made the one circle outer and the other inner. And the outer motion He ordained to be the Motion of the Same, and the inner motion the Motion of the Other. And He made the Motion of the Same to be toward the right along the side, and the Motion of the Other to be toward the left along the diagonal; and He gave the sovranty 36d to the Revolution of the Same and of the Uniform. For this alone He suffered to remain uncloven, whereas He split the inner Revolution in six places into seven unequal circles, according to each of the intervals of the double and triple intervals, three double and three triple. These two circles then He appointed to go in contrary directions; and of the seven circles into which He split the inner circle, He appointed three to revolve at an equal speed, the other four to go at speeds equal neither with each other nor with the speed of the aforesaid three, yet moving at speeds the ratios of which one to another are those of natural integers.

And when the construction of the Soul had all been completed to the satisfaction of its Constructor, then He fabricated within it all the Corporeal, 36e and uniting them center to center He made them fit together. And the Soul, being woven throughout the Heaven every way from the center to the extremity, and enveloping it in a circle from without, and herself revolving within herself, began a divine beginning of unceasing and intelligent life lasting throughout all time.

And whereas the body of the Heaven is visible, the Soul is herself invisible but partakes in reasoning and in harmony,