The intelligible number therefore of the intellectual genera, proceeds from these, and through these. And it possesses indeed properties incomprehensible by human reasonings, but which are divided into two first effective powers, viz. the power generative of wholes, and the power which collects into union all progressions. For according to the monad indeed, it collects intellectual multitude, and conjoins it to intelligibles; but according to the duad it produces multitude, and separates it according to difference. And according to the odd number indeed, it collects the many orders into indivisible union; but according to the even number, it prolifically produces into light all the genera of the Gods. For being established as the middle of the intelligible and intellectual Gods, and giving completion to the one bond of them, it is carried in its summit indeed, in intellectuals as in a vehicle, but being united to intelligibles, it evolves intelligible multitude, and calls forth its occult and unical nature into separation, and prolific generation. It also collects that which is intellectual into union and impartible communion. And not this only, but generating all things as far as to the last of things, according to the incomprehensible cause of the duad and the nature of the even number, it again unites the proceeding natures and convolves them according to the monad, and the sameness of the odd number. Through unity indeed, and the duad, it produces,[238] collects and binds all things intelligibly, occultly, and in an unknown manner to the intelligible, and effects this even in the last matter and the vestigies of forms which it contains. But through the even and odd number it constitutes the two coordinations, viz. the vivific and the immutable, the prolific and the effective, all the impartible genera of fabricating and animal-producing powers, those powers that preside over a partible life, or partible production, the more intellectual and singular mundane natures, and which belong to the better coordination, and those natures that are more irrational and multiplied, and which give completion to the subordinate series. And again, through this divided generation we may see that each of the proceeding natures, is united and at the same time multiplied, is indivisible and divided in its causes, and through diminution is separated from them. And we attribute indeed things that are more excellent and more simple to the nature of the odd number, but things that are less excellent and more various, to the nature of the even number. For every where indeed, the odd number is the leader of impartible, simple, and unical goods; but the even number is the cause of divided, various, and generative progressions. And thus we may see all the orders of beings woven together according to divine number which is most ancient, intellectual, and exempt from all the dinumerated genera. For it is necessary that number should exist prior to the things that are numbered, and that prior to things which are separated there should be the cause of all separation, according to which the genera of the Gods are divided, and are distinguished in an orderly manner by appropriate numbers.

If therefore in intellectuals there are divisions, contacts, and separations of the proceeding natures, and likewise communications of coordinate natures, it is necessary that number should be prior to intellectuals, which divides and collects all things intelligibly by the powers of itself. And if all things subsist occultly, intelligibly, in an unknown manner and exemptly in this summit,[239] there is a number of them, and a peculiarity unical and without separation. Number therefore subsists according to the middle bond of intelligibles and intellectuals, being indeed expanded above intellectuals through intelligible goods, but subordinate to intelligibles through intellectual separations. And it is assimilated indeed to intelligibles according to the power which is collective of many things into union, but to intellectuals according to the power which is generative of the many from the one. But from this highest place of survey of the intellectual Gods, it constitutes the first intellectual numbers themselves which have the nature of forms, are universal, and preside over the whole of generation and production. It likewise constitutes the second numbers, which are supermundane, and vivific, and measure the Gods that are in the world. But it constitutes as the third numbers, these celestial governors of the perpetual circulations, and who convolve all the orbs according to the intellectual causes of them. And it constitutes as the last numbers those powers that in the sublunary region connect and bound the infinity and unstable nature of matter by forms, and numbers and reasons, through which both the wholes and parts of all mortal natures are variegated with proper numbers. But it every where connects the precedaneous and more perfect genera of the Gods by the odd number, but the subordinate and secondary genera, by the even number. Thus for instance, in the intellectual orders, it produces the female and the prolific according to the even number, but the male and the paternal according to the odd number. But in the supermundane orders, it characterizes similitude and the immutable according to the odd number, but dissimilitude and a progression into secondary natures, according to the even number. For thus the Athenian guest also, orders that in sacred worship odd things should be distributed to the celestial, but even to the terrestrial powers. And according to each of these genera that which is of a more ruling nature must be referred to the odd number, but that which is subordinate, to the even number.

The nature of number, therefore, pervades from on high, as far as to the last of things, adorning all things, and connecting them by appropriate forms. For how could a perfect number comprehend the period of the whole world, as the Muses in Plato assert that it does? Or how could numbers, some of which are productive of fertility, and others of sterility, comprehend the descents of souls? Or how could some of them define the ascents of souls in less, but others in greater periods, as Socrates says in the Phædrus, where he delivers to us restitutions consisting of three thousand and ten thousand years? Or how could time itself which is unically comprehensive of the psychical measures, proceed according to number, as Timæus says it does, unless divine number exists prior to all these, which imparts to all things a principal cause of order according to numbers? Since all things therefore subsist through numbers and forms, numbers are allotted a progression from the intellectual summit. But forms have their generation from intelligible[240] forms. For forms subsist primarily in the third triad of intelligibles. But numbers are primarily in the first triad of intellectuals; since also in the effects of these, every number indeed is form, but not every form is number.

If, however, it be requisite clearly to unfold the truth, numbers are also prior to forms. For there are indeed superessential numbers, but there are not superessential forms. And according to this reasoning every form is number, as also the Pythagoreans said. For Timæus being a Pythagorean, not only asserts that there are intelligible forms, but also intelligible numbers; for he says that the intelligible forms are four. There however, number is intelligibly, and monadically according to cause. For intelligible animal is a monad, occultly containing the whole of number. But in the summit of intellectuals, number subsists separately, evolving the number which preexists in the monad according to cause and uniformly. For there is a difference, I think, between saying multitude in its cause, and multitude from its cause, and between saying united, and saying separated multitude. And the one indeed is prior to number, but the other is number. So that according to Timæus there are intelligible numbers together with forms, and prior to forms. And according to Parmenides, number is after multitude. For Timæus calls uniform and occult multitude the number of forms. But since number is primarily in the Gods, but forms participate of the divine unities, he denominates the first ideas four. For monad and triad, were primarily indeed in the Gods themselves, but secondarily in intellectuals; and superessentially indeed in the former, but formally in the latter. In intelligibles therefore, multitude was unically; but in intellectuals it subsists separately. But where there is separation there also there is number, as we have frequently observed. Hence likewise all the genera of the Gods are from hence generated. And they are divided, the paternal indeed and generative, among intelligibles and intellectuals; but the demiurgic and vivific, among intellectuals. And the genera indeed, that bind through similitude, are divided among supermundane natures; but those that are both exempt and distributed, are divided among the liberated Gods. And the celestial[241] and sublunary genera, are divided among the mundane Gods. And in short, all the coordinations of beings receive their distinction and separation from this order. From these things therefore, it is evident what the peculiarities are which intelligible and at the same time intellectual number possesses, and of what it is the cause to the Gods.