that are quantities by their own nature some are so as substances, e.g. the line is a quantity (for 'a certain kind of quantity' is present[1] in the formula which states what it is), and others are modifications and states of this kind of substance, e.g. much and little, long and short, broad and narrow, deep and shallow, heavy and light, and the other terms of the sort. And also great and small, and greater and smaller, both in themselves and when taken relatively to each other, are by their own nature attributes of quantity; but these names are transferred to other things also. Of things that are quantities incidentally, some are so called in the sense in which it was said that 'musical' and 'white' were quantities, viz. because that to which they belong is a quantity, and some are quantities in the way in which movement and time are so; for these are called quantities and continuous because the things of which these are attributes are divisible. I mean not that which is moved, but the space through which it is moved; for because that is a quantity movement also is a quantity, and because this is a quantity time is so.
Chapter 14
'Quality' means (1) the differentia of the essence, e.g. man is an animal of a certain quality because he is two-footed, and the horse is so because it is four-footed; and a circle is a figure of particular quality because it is without angles, — which shows that the essential differentia is a quality. — This, then, is one meaning of quality — essential differentia, but (2) there is another sense in which it applies to the unmovable objects of mathematics; i.e. the numbers have a certain quality, e.g. the composite numbers which are not in one dimension only, but of which the plane and the solid are copies (these are those which have two or three factors); and in general that which exists in the essence of numbers besides quantity is quality; for the essence of each is what it is once, e.g. that of 6 is not what it is twice or thrice, but what it is once; for 6 is once 6.
(3) All the attributes of substances in motion (e.g. heat and cold, whiteness and blackness, heaviness and lightness, and the
- ↑ 1020b 19 read ποσόν τι ὑπάρχει.
