then it is composed of those parts and is not a simple unity. When a body perishes, it breaks down into these parts; when it is formed, it is formed from them.

This error arose from the resemblance between discrete and continuous quantity: they supposed that what holds for discrete quantity also holds for continuous quantity. Yet this is true only of number. I mean that we say one number is more than another because it contains more parts—that is, units.

This does not hold for continuous quantity. Thus, of continuous quantity we say that it is greater or larger, not that it is more; whereas of number we say that it is more, not that it is larger. On their account, all things would be numbers, and there would be no continuous magnitude at all. Geometry would therefore be identical to arithmetic.

It is self-evident that every magnitude can be divided into two halves. I mean the three magnitudes: line, surface, and body. Moreover, continuous quantity is that within which a boundary can be posited where the ends of both portions meet; this is not possible with number.

Yet a counterargument to this, too, is that a body and the other parts of continuous quantity admit of