Tim. For whenever the middle term of any three numbers, cubic or square, Dealing first with square numbers, the proportion here indicated is—a2 : ab :: ab :: b2; conversely, b2 : ab :: ab :: a2; alternately, ab : a2 :: b2 : ab. 

 is such that as the first term is to it, so is it to the last term, and again, conversely, as the last term is to the middle, so is the middle to the first,—then the middle term becomes in turn the first and the last, while the first and last become in turn middle terms, and the necessary consequence will be that all the terms are interchangeable, and being interchangeable they all form a unity. Now if the body of the All had had to come into existence as a plane surface, having no depth, one middle term would have sufficed to bind together both itself and its fellow-terms; but now it is otherwise: for it behoved it to be solid of shape, and what brings solids into unison is never one middle term alone but always two. Two mean terms are required for a continuous proportion of solid (or cubic) numbers, e.g. a3 :a2b :: a2b : ab2 :: ab2 : b3. Thus it was that in the midst between fire and earth God set water and air, and having bestowed upon them so far as possible a like ratio one towards another—air being to water as fire to air, and water being to earth as air to water, —he joined together and constructed a Heaven visible and tangible. For these reasons and out of these materials, such in kind and four in number, the body of the Cosmos was harmonized by proportion and brought into existence. These conditions secured for it Amity, so that being united in identity with itself it became indissoluble by any agent other than Him who had bound it together.

 Now of the four elements the construction of the Cosmos had taken up the whole of every one. For its Constructor had constructed it of all the fire and water and air and earth that existed, leaving over, outside it, no single particle or potency of any one of these elements. And these were his intentions: first, that it might be, so far as possible, a Living Creature, perfect and whole, with all its parts perfect; Tim. and next, that it might be One, inasmuch as there was nothing left over out of which another like Creature might come into existence; and further, that it might be secure from age and ailment, since He perceived that when heat and cold, and all things which have violent potencies, surround a composite body from without and collide with it they dissolve it unduly and make it to waste away by bringing upon it ailments and age. Wherefore, because of this reasoning, He fashioned it to be One single Whole, compounded of all wholes, perfect and ageless and unailing. And he bestowed on it the shape which was befitting and akin. Now for that Living Creature which is designed to embrace within itself all living creatures the fitting shape will be that which comprises within itself all the shapes there are; wherefore He wrought it into a round, in the shape of a sphere, equidistant in all directions from the center to the extremities, which of all shapes is the most perfect and the most self-similar, since He deemed that the similar is infinitely fairer than the dissimilar. And on the outside round about, it was all made smooth with great exactness, and that for many reasons. For of eyes it had no need, since outside of it there was nothing visible left over; nor yet of hearing, since neither was there anything audible; nor was there any air surrounding it which called for respiration; nor, again, did it need any organ whereby it might receive the food that entered and evacuate what remained undigested. For nothing went out from it or came into it from any side, since nothing existed; for it was so designed as to supply its own wastage as food for itself, and to experience by its own agency and within itself all actions and passions, since He that had constructed it deemed that it would be better if it were self-sufficing rather than in need of other things. Hands, too, He thought He ought not to attach unto it uselessly, seeing they were not required either for grasping or for repelling anyone; nor yet feet, nor any instruments of locomotion whatsoever. Tim. For movement He assigned unto it that which is proper to its body, namely, that one of the seven motions For the seven motions see 43 B; and for the (rotary) motion of reason Cf. Laws 898 A. Cf. also 37 A ff., 42 C, 47 D, 77 B. which specially belongs to reason and intelligence; wherefore He spun it round uniformly in the same spot and within itself and made it move revolving in a circle; and all the other six motions He took away and fashioned it free from their aberrations. And seeing that for this revolving motion it had no need of feet, He begat it legless and footless.

 Such, then, was the sum of the reasoning of the ever-existing God concerning the god which was one day to be existent, whereby He made it smooth and even and equal on all sides from the center, a whole and perfect body compounded of perfect bodies, And in the midst thereof He set Soul, which He stretched throughout the whole of it, and therewith He enveloped also the exterior of its body; and as a Circle revolving in a circle He established one sole and solitary Heaven, able of itself because of its excellence to company with itself and needing none other beside, sufficing unto itself as acquaintance and friend. And because of all this He generated it to be a blessed God.

 Now as regards the Soul, although we are essaying to describe it after the body, God did not likewise plan it to be younger than the body For the priority of Soul Cf. Laws 892 A, B, 896 C ff.; and for the right of the elder to rule Cf. Laws 714 E. ; for, when uniting them, He would not have permitted the elder to be ruled by the younger; but as for us men, even as we ourselves partake largely of the accidental and casual, so also do our words. God, however, constructed Soul to be older than Body and prior in birth and excellence, since she was to be the mistress and ruler and it the ruled; and, He made her of the materials and in the fashion which I shall now describe. Tim. Midway between the Being which is indivisible
 and remains always the same and the Being which is transient and divisible in
 bodies, He blended a third form of Being compounded out of the twain, that is
 to say, out of the Same and the Other; and in like manner He compounded it
 midway between that one of them which is indivisible and that one which is
 divisible in bodies. And He took the three of them, and blent them all together
 into one form, by forcing the Other into union with the Same, in spite of its
 being naturally difficult to mix. And when with the aid of Being He had mixed them, and had made of
 them one out of three, straightway He began to distribute the whole thereof
 into so many portions as was meet; and each portion was a mixture of the Same,
 of the Other, and of Being. The choice of these three as constituents of the Soul is
 explained by the use of the same terms in the Sophist 
 (244-245) to denote certain Greatest Kinds or main
 categories. As Professor Paul Shorey has aptly observed ( Amer . Journ. Philol. 
 ix. p. 298), It is necessary that the Soul should recognize
 everywhere . . . the same, the other and essence, those three μέγιστα γένη of the . .
 . Sophist . Hence on the Greek principle that like is
 known by like, Plato makes real substances out of these three
 abstractions and puts them as plastic material into the hands of the
 Demiurgus for the formation of the Soul. And He began
 making the division thus: First He took one portion from the whole; then He
 took a portion double of this; then a third portion, half as much again as the
 second portion, that is, three times as much as the first; he fourth portion He
 took was twice as much as the second; the fifth three times as much as the
 third; the sixth eight
 times as much as the first; and the seventh twenty-seven times as much as the
 first. These seven numbers may be arranged in two branches,
 in order to show the two series of which Timaeus immediately goes on the
 speak: 1 (the 1st), 2 (the 2nd), 4 (the 4th), 8
 (the 6th); 3 (the 3rd), 9 (the 5th), 27 (the 7th). The former branch
 contains the double intervals, i.e., the powers of 2; the
 latter one the triple intervals, i.e., the powers of
 3. Tim. 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 Lit. the double intervals and the triple intervals. See the preceding note. : 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 harmonic Mean. ; 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. 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; 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 He now tilts the inner band, so that it makes an oblique angle with the outer, which is set at the horizontal; from which we see that the Revolution of the Same represents the celestial Equator, moving horizontally to the right (from East to West), and the Revolution of the Other represents the Ecliptic, which moves in a contrary direction to the Equator (from West to East), and at an angle to it. The Ecliptic He divides into seven, to represent the seven planets ; and He gave the sovranty 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, Viz. 2, 3, 4, 8, 9, 27. three double and three triple Viz. 2, 4, 8 double; 3, 9, 27 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 The three are Sun, Venus, Mercury; the four Moon, Mars, Jupiter, Saturn. 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, 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.