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,' 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' 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. For voefwv, it is necessary to read vontav. 1 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' 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 • For υπουρανια, it seems to be necessary that we should read ουρανια, time intellectual number possesses, and of what it is the cause to the Gods. In the next place, we must likewise assert that the first number is of a feminine nature. For in this, difference first shines forth, separating the one from being, and dividing the one into many unities, and being into many beings. What therefore is the difference which is the cause of these things to the Gods? For if we should call it a genus of being, in the first place indeed, how is it prior to being? For separating being and the one, it is arranged between both of them. But existing as a middle, it calls forth indeed the one into generations, but it fills being with generative cause. If therefore, it is prior to being, how will it be one certain genus of being? And in the second place, after this, the different which is a genus of being, is every where essential, and is by no means inherent in superessential natures. But difference itself is primarily present with the unities themselves, and separates and produces many unities from one. How therefore, can superessential difference ever come to be the same with the difference which gives completion to essences? In the third place, that different [which is a genus of being,] presents itself to the view in intellectuals, according to the demiurgic order. But 'difference itself is the intelligible summit of intellectuals. And the former indeed, subsists together with sameness; but the latter has by itself a subsistence in the intelligibles of intellectuals. To which also may be added, that in what follows, Plato as he proceeds makes mention of difference, and generates it in conjunction with sameness. How therefore, does he effect the same conclusion twice? For he does not employ such Proc. In the original agiuos is omitted. 20 a repetition as this in any one of the other conclusions. For whole, which he seems to assume twice, is not the same whole, viz. the intellectual is not the same with the intelligible; but these, as we have said, differ from each other. For how could he unfold to us the different progressions of divine natures, if he collected the same conclusions? According to all these conceptions, therefore, we must separate the difference which is generative of numbers from the genus of beings. But if difference itself is not the nature of the different, but a power generative of beings, it will be collective of being and the one. For every where power is allotted an hyparxis of this kind. For through power the one participates of being, and being of the one. Power therefore was the cause, not of division, but of communion, of contact without separation, and of the habitude of the one to being, and of being to the one. Hence it is necessary that it should neither be arranged according to intelligible power, nor according to the intellectual difference of beings; but that being the middle of both, it should subsist analogous to intelligible power, but should generate in the extremities of intellectuals the portion of the different. What else therefore is it than the feminine nature of the Gods? Hence also it imitates intelligible power, and is prolific of many unities, and of many beings. And how could it otherwise separate number from itself, and the forms and powers of number, unless it was the cause of the divine progressions in a feminine manner. Multitude therefore is paternally in intelligibles, but maternally in intellectuals. Hence, in the former indeed, it subsists monadically, but in the latter according to number. Very properly therefore, in the second genera of the Gods also, union is derived from the male, but separation from the female divinities. And bound indeed proceeds from the males, but infinity from the females. For the male is analogous to bound, but the female to infinity. The female, however, differs from infinite power, so far as power indeed, is united to the father, and is in him; but the female is divided from the paternal cause. For power is not only in the female divinities, but is also prior to them, since the intelligible powers are in the male divinities, according to Timæus, who says that the power of the demiurgus is the cause of the generation |