PROPOSITION I

All multitude participates in a certain respect of The One.

For if it in no respects participates of The One, neither will the whole be one whole, nor each of the many of which the multitude consists; but there will also be a certain multitude arising from each of these, and this will be the case to infinity. Each of these infinities, likewise, will again be infinite multitude. For participating in no respect of any one, neither according to the whole of itself, nor according to each of the many which it contains, it will be in every respect, and according to the whole, infinite. For each of the many which you may assume, will either be one, or not one, will either be many or nothing. But if each is nothing, that also which consists of these will be nothing. And if each is many, each will consist of infinites infinitely: [and this not in capacity, but in energy]. These things, however, are impossible. For neither does any being consist of infinites infinitely assumed; since there is not more than the infinite; but that which consists of all is more than each. Nor is it possible for any thing to be composed from nothing. All multitude, therefore, participates in a certain respect of The One.
 
 

PROPOSITION II

Every thing which participates of The One, is both one and not one.

For if it is not The One Itself (since it participates of The One) being something else besides The One, it suffers, or is passive to it according to participation, and sustains to become one. If, therefore, it is nothing besides The One, it is one alone, and does not participate of The One, but will be The One Itself. But if it is something besides The One, which is not The One, but its parti- cipant, it is both not one, and one, not indeed such a one as The One Itself, but one being, as participating of The One. This, therefore, is not one, nor is it that which The One is. But it is one, and at the same time a participant of The One. Hence, being of itself not one, it is both one and not one, being something else besides The One. And so far indeed as it abounds, it is not one, but so far as it is passive [to The One] it is one. Every thing, therefore, which participates of The One, is both one and not one.
 
 

PROPOSITION III

Every thing which becomes one, becomes so through the participation of The One, and is one, so far as it suffers the participation of The One.

For if things which are not one become one, they doubtless become so by a conjunction and communication with each other, and they sustain the presence of The One, not being that which The One Itself is. Hence, they participate of The One so far as they suffer to become one. For, if they are already one they will not become one; since that which is does not become that which it is already. But if they become one from nothing, i.e. from the privation of The One, since a certain one is ingenerated in them, The One Itself is prior to them. [And this ingenerated one must be derived from The One Itself. Every thing, therefore, which becomes one, becomes so through the participation of The One, &c.]
 
 

PROPOSITION IV

Every thing which is united is different from The One Itself.

For if it is united, it will participate in a certain respect of The One, so far as it is said to be united. That, however, which participates of The One, is both one and not one. But The One Itself is not both one and not one. For if this were the case, again the one which is in it would have both these, and this would take place to infinity, there being no One Itself at which it is possible to stop; but every thing being one and not one, there will be something united which is different from The One. For if The One is the same with the united, it will be infinite multitude. And in a similar manner each of the things of which the united consists will be infinite multitude. [Every thing, therefore, which is united is different from The One Itself.]
 
 

PROPOSITION V

All multitude is posterior to The One.

For if multitude is prior to The One, The One indeed will participate of multitude, but multitude which is prior to The One will not participate of The One, since that multitude existed prior to the subsistence of The One. For it will not participate of that which is not; because that which participates of The One, is one and at the same time not one; but The One will not yet subsist, that which is first being multitude. It is, however, impossible that there should be a certain multitude, which in no respect whatever participates of The One. Multitude, therefore, is not prior to The One. But if multitude subsists simultaneously with The One, and they are naturally co-ordinate with each other; for nothing of time will prevent them being so; neither will The One of itself be many, nor will multitude be one, as being at one and the same time oppositely divided by nature, if neither is prior or posterior to the other. Hence, multitude of itself will not be one, and each of the things that are in it will not be one, and this will be the case to infinity, which is impossible. Multitude, therefore, according to its own nature, participates of The One, and it will not be possible to assume any thing of it which is not one. For not being one, it will be an infinite consisting of infinites; as has been demonstrated. Hence, it entirely participates of The One. If, therefore, The One which is of Itself one, in no respect participates of multitude, multitude will be entirely posterior to The One; participating indeed of The One, but not being participated by The One. But if The One also participates of multitude, subsisting indeed as one according to hyparxis, but as not one, according to partici- pation, The One will be multiplied, just as multitude is united on account of The One. The One, therefore, will communicate with multitude, and multitude with The One. But things which coalesce, and communicate in a certain respect with each other, if indeed they are collected together by something else, that something else is prior to them. But if they themselves collect themselves, they are not opposed to each other. For opposites do not hasten to each other. Hence, if The One and multitude are oppositely divided, and multitude so far as multitude is not one, and The One so far as one is not multitude, neither will one of these subsisting in the other be one and at the same time two. If, also, there is something prior to them which collects them, this will either be one or not one. But if it is not one, it will either be many or nothing. It will not, however, be many, lest multitude should be prior to The One, nor yet will it be nothing. For how can nothing congregate? It is, therefore, one alone. For this which is the one cannot be many, lest there should be a progression to infinity. It is, therefore, The One Itself, and all multitude is from The One Itself.
 
 

PROPOSITION VI

Every multitude consists either of things united, or of unities.

For that each of things many will not be itself multitude alone, and again that each part of this will not be multitude alone is evident. But if it is not multitude alone, it is either united, or unities. And if, indeed, it participates of The One it is united; but if it consists of things of which that which is primarily united consists, it will be unities. For if there is The One Itself, there is also that which primarily participates of it, and which is primarily united. But this consists of unities. For if it consists of things united, again things united consist of certain things, and this will be the case to infinity. It is necessary, however, that what is primarily united should consist of unities. And thus we have discovered what we proposed at first, [viz. that every multitude consists either of things united, or of unities].