Timaeus (Hackett Classics) by Plato

Author:Plato [Plato]
Language: eng
Format: epub
Tags: ebook, book
Publisher: Hackett Publishing Company, Inc.
Published: 2000-03-15T04:00:00+00:00

Combining the two series in ascending order and omitting duplication we get:

In this series the value of each term but the first is either 4/3 or 3/2 or 9/8 the value of its predecessor. Finally, the intervals of 4/3 (e.g., between 1 and 4/3, or between 3/2 and 2, or 3 and 4) are now themselves “filled” by intervals of 9/8. In the interval between 1 and 4/3, for example, we can insert new intervals, each of which multiplies its predecessor by 9/8, but we can do so no more than twice (1—9/8—81/64 …. 4/3), since a third attempt (729/512) would exceed 4/3. The interval between 81/64 can only be filled up with a “leftover,” a number by which 81/64 can be multiplied to equal 4/3. This number turns out to be 256/243.

4. The creation of the circles of the Same and the Different: The stuff thus arranged is cut lengthwise into two strips that are fastened center to center, and the ends of each connected together. The outer strip is the circle of the Same, and the inner one that of the Different. For the positions and movements of these circles, see the next note.

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