Again, if there are indeed infinite principles, either the things which proceed from them are infinite, and there will thus be the infinite twice, or they are finite, and thus all the principles will not be principles. For things finite in number, will entirely proceed from finite principles. The principles therefore are in vain infinite. To which may be added, that infinity makes both the principles to be unknown, and the things which proceed from them. For the principles being unknown, it is necessary that the things which proceed from them should be unknown; since we then think that we know any thing when we know the causes and the first principles of it. But if the principles are finite, it is evident that there will be a certain number of them: for we say that number is a definite multitude. If however, there is a number of the principles, it is necessary that there should be a cause of the whole number of them. For every number is from one; and this, viz. _the one_ is the principle of numbers. This therefore will be the principle of principles, and the cause of finite multitude, since number itself is one, and the end in the many is one, and it bounds the many by that which is one. But the principle being one, and this being essence, it is necessary if this is admitted to be either corporeal or incorporeal, that it must be acknowledged to be the principle of other things. If therefore, body is the cause of the generation of beings, it is necessary indeed, that it should be divisible and have parts. For every body is in its own nature divisible; since every magnitude is a certain whole and that which is a whole consists of parts. These parts therefore, (but I mean each of them) must either severally participate a certain one, or not participate it. If therefore they do not participate it, they will be many alone, and by no means one. Hence, neither will that which consists from them be a whole. For there being no one, that which consists of all of them will not be one. But if each of the parts participates of something of this kind, and there is something which is the same in all of them, a thing of this kind must necessarily be incorporeal, and impartible according to its own nature. For if this also is itself corporeal, it is either wholly in each of the parts, or not wholly. If therefore, it is indeed wholly in each, it will itself be separated from itself. For the parts in which it is are separate from each other. But if it is not wholly in each of the parts, this also will be divisible, and will have parts after the same manner as the above mentioned parts; and there will again be the same inquiry concerning these, viz. whether in these also there is something common, or nothing; since if there is nothing common, we shall place _the many_ separate from _the one_.