Kitap 14
1
The question might also be raised as to what the good is which things derive from numbers because their mixture can be expressed by a number, either one which is easily calculable,i.e., a simple ratio. or an odd number.It is hard to see exactly what this means. If the terms of a ratio are rational, one of them must be odd. Alexander says a ratio like 1 : 3 is meant. Oddness was associated with goodness (cf. Aristot. Met. 1.5.6). For in point of fact honey-water is no more wholesome if it is mixed in the proportion three times threeApparently the Pythagoreans meant by this three parts of water to three of honey. Aristotle goes on to criticize this way of expressing ratios.; it would be more beneficial mixed in no particular proportion, provided that it be diluted, than mixed in an arithmetical proportion, but strong.
2
Again, the ratios of mixtures are expressed by the relation of numbers, and not simply by numbers; e.g., it is 3 : 2, not 3 X 2Cf. previous note.; for in products of multiplication the units must belong to the same genus. Thus the product of 1 x 2 x 3 must be measurable by 1, and the product of 4 X 5 x 7 by 4. Therefore all products which contain the same factor must be measurable by that factor. Hence the number of fire cannot be 2 X 5 X 3 X 7 if the number of water is 2 x 3.sc. because if so, a particle of fire would simply equal 35 particles of water.
3
If all things must share in number, it must follow that many things are the same; i.e., that the same number belongs both to this thing and to something else. Is number, then, a cause; i.e., is it because of number that the object exists? Or is this not conclusive? E.g., there is a certain number of the sun’s motions, and again of the moon’s,5 in each case, according to Aristotle; cf. Aristot. Met. 12.7.9, 11. and indeed of the life and maturity of every animate thing. What reason, then, is there why some of these numbers should not be squares and others cubes, some equal and others double?
