Περὶ τῆς ἐν Τιμαίῳ ψυχογονίας

Sections

1 – 1 1 – 1 1 – 1 2 – 2 2 – 3 3 – 3 4 – 4 5 – 5 6 – 6 7 – 7 7 – 7 8 – 8 9 – 9 9 – 9 10 – 10 11 – 11 12 – 12 12 – 12 13 – 13 14 – 14 15 – 15 16 – 16 16 – 16 17 – 17 18 – 18 19 – 19 20 – 20 21 – 21 22 – 22 23 – 23 23 – 23 24 – 24 25 – 25 26 – 26 26 – 26 27 – 27 27 – 27 28 – 28 29 – 29 29 – 30 30 – 30 31 – 31 31 – 31 32 – 32 32 – 32 33 – 33 33 – 33

İngilizce Yunanca

29 Here the question will be first concerning the quantity, next concerning the order, and in the third place concerning the force and virtue of the numbers. As to the quantity, we are to consider which he takes in the double and triple intervals. As to the order, whether they are to be placed in one row, according to the direction of Theodorus, or (as Crantor will have them) in the form of a Λ, placing the unit at the top, and the duples and triples apart by themselves in two several files. Lastly, we are to examine of what use and virtue they are in the structure and composition of the soul.

30 As to the first, we shall relinquish the opinion of those who affirm that it is enough, in proportions, to consider the nature of the intervals, and of the medieties which fill up their vacancies; and that the demonstration can be made out for any numbers whatsoever that have spaces sufficient to receive the aforesaid proportions. For this being granted, it makes the demonstration obscure, without the help of schemes, and drives us from another theory, which carries with it a delight not unbecoming philosophy.