Book 14
9
As for the celebrated characteristics of number, and their contraries, and in general the mathematical properties, in the sense that some describe them and make them out to be causes of the natural world, it would seem that if we examine them along these lines, they disappear; for not one of them is a cause in any of the senses which we distinguished with until respect to the first Principles.Cf. Aristot. Met. 1.3.1, Aristot. Met. 5.1, 2.
10
There is a sense, however, in which these thinkers make it clear that goodness is predicable of numbers, and that the odd, the straight, the equal-by-equal,i.e., square. and the powersProbably their power of being represented as regular figures; e.g. the triangularity of 3 or 6. of certain numbers, belong to the series of the Beautiful.Cf. Aristot. Met. 1.5.6. For the seasons are connected with a certain kind of numberi.e., 4.; and the other examples which they adduce from mathematical theorems all have the same force.
11
Hence they would seem to be mere coincidences, for they are accidental; but all the examples are appropriate to each other, and they are one by analogy. For there is analogy between all the categories of Being—as straight is in length, so is level in breadth, perhaps odd in number, and white in color.
