is that of which the contrary is of necessity true, e.g. that the diagonal of a square is commensurate with the side is impossible, because such a statement is a falsity such that not only is the contrary true but it is necessary that the diagonal should be incommensurate; that it is commensurate, then, is not only false but of necessity false. The contrary of this, the possible, is found when it is not necessary that the contrary is false, e.g. that a man should be seated is possible; for that he is not seated is not of necessity false. — The possible, then, in one sense, as has been said, means that which is not of necessity false; in one, that which is true; in one, that which is capable of being true. — A 'potency' or 'power'[1] in geometry is so called by a change of meaning. — These senses of 'capable' or 'possible' involve no reference to potency. But the senses which involve a reference to potency all refer to the one primary kind of potency; and this is a source of change in another thing or in the same thing qua other. For other things are called 'capable', some because something else has such a potency over them, some because it has not, some because it has it in a particular way. The same is true of the things that are incapable. Therefore the proper definition of the primary kind of potency will be 'a source of change in another thing or in the same thing qua other'.
Chapter 13
'Quantity' means that which is divisible into two or more constituent parts of which each is by nature a 'one' and a 'this'. A quantity is a plurality if it is numerable, a magnitude if it is measurable. 'Plurality' means that which is divisible potentially into non-continuous parts, 'magnitude' that which is divisible into continuous parts; in magnitude, that which is continuous in one dimension is length, in two breadth, in three depth. Of these, limited plurality is number, limited length is a line, breadth a surface, depth a solid.
Again, some things are called quantities in virtue of their own nature, others incidentally, e.g. the line is a quantity by its own nature, the musical is one incidentally. Of the things
- ↑ The reference is to squares and cubes.
