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.
[35b]
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.^{1} 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;
[35c]
the sixth eight times as much as the first; and the seventh twenty-seven times as much as the first.^{2}

1 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 γένηof 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.”

2 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.

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