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The excerpt represents the core issue or deciding factor on which you must meditate, and is drawn from Timaeus by Plato: mean which exceeds and is exceeded by an equal number (e.g.
- over 1, 4/3, 3/2, - over 2, 8/3, 3, - over 4, 16/3, 6, - over 8: and
- over 1, 3/2, 2, - over 3, 9/2, 6, - over 9, 27/2, 18, - over 27.).
Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the
connecting terms in the former intervals, he filled up all the intervals of
4/3 with the interval of 9/8, leaving a fraction over; and the interval
which this fraction expressed was in the ratio of 256 to 243 (e.g.
243:256::81/64:4/3::243/128:2::81/32:8/3::243/64:4::81/16:16/3::242/32:8.).
And thus the whole mixture out of which he cut these portions was all
exhausted by him. This entire compound he divided lengthways into two
parts, which he joined to one another at the centre like the letter X, and
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