But Parmenides begins to speak about it as follows: " Proceed therefore, and still farther consider this. What? We have said that the one participates of essence, so far as it is being. We have said so. And on this account the one being appears to be many." But he completes his discourse about the first monad thus : ** Are not three things odd, and two even ? How should they not ?' And about the second monad, as follows : " Hence there will be the evenly-even, and .the oddly-odd, and the oddly-even, and the evenly-odd." But he .completes his discourse about the third and all the succeeding triad, as follows : " The one being therefore, is not only many, but it is likewise necessary that the one which is distributed by being should be many. Entirely so." The first triad, therefore, of the intelligible, and at the same time, intellectual Gods, is through these things unfolded to us by Plato, and which possesses indeed, according to the first monad the first powers of numbers, I mean the odd and the even, and is completed through these principles which were in intelligibies occultly, viz. monad, duad, triad. But according to the second monad it possesses the second powers of numbers which subsist from these [i. e. from the first powers]. For the section of the forms of the even number, is allotted a second order. And the oddly-odd is subordinate to the first odd numbers. But according to the third monad, it possesses the more partial causes of divine numbers. Hence also, a separation into minute parts, infinity,
Chap. Xxxiv. of Plato. 297
all-perfect division, and unical and essential number are here ; receiving indeed, the unical and the essential from unity and being, but the sepa- ration of number from difference. For every where difference is in the three monads, but it particularly unfolds the multitudes of numbers, according to the third monad, generates more partial Gods, and divides being in conjunction with the Gods. For neither is deity in these imparticipable, because unity is not separate from being, nor is essence destitute of deity, because neither is being deprived of the one.
Since however, all things are in each of the monads, but unically and intelligibly in the first, generative!}', and according to the peculiarity of difference in the second, and intellectually, and according to being in the third ;— this being the case, Plato when unfolding to us the first monad, very properly begins from the monad, and proceeds as far as to the triad; but when teaching about the second, he begins from evenly-even num- bers, and proceeds as far as to those that are evenly-odd, both which belong to the nature of the even number. Aud when he adds the third monad, he begins from being, and recurs through difference to the one* For having shown that being participates of number, he from hence leads us round to unical number, employing the mode of conversion in the conception of this monad.
If, however, it be requisite to survey the unknown peculiarity of divine numbers, and how the first order of intelligibles and intellectuals, and number which subsists according to this order, is the most ancient of all numbers, in the first place, we should consider the infinity mentioned by Parmenides, and see whether he does not say that intelligible multitude is infinite on account of this number, in consequence of its being unknown Proc. Vol. I. 2 P
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and incomprehensible by partial conceptions. For the all-perfect, and all-powerful peculiarity of divine numbers is exempt from the compre- hension of partible natures, [such as ours]. They are therefore unknown, and on this account are said to be inexplicable, and not to be investigated. For number also in the last of things, and multitude, together with the known have likewise the unknown. And we are notable to comprehend the progression of every number iu consequence of being vanquished by infinity. The incomprehensibility therefore, of this power which is un- known according to a discursive energy, is comprehended according to cause, in intelligible numbers and multitudes. For there would not be a thing of this kind in the last of numbers, unless the unknown preexisted in intelligible numbers, and unless the former were ultimate imitations of the exempt incomprehensibility of the latter.
In the second place, after this, we may also add, that unical numbers are likewise of themselves unknown. For they are more ancient than beings, more single than forms, and being generative of, exist prior to the forms which we call intelligible. But the most venerable of divine ope- rations manifest this, since they employ numbers, as possessing an ineffa- ble efficacy, and through these effect the greatest, and most arcane of works. And prior to these nature ineffably, according to sympathy, im- parts different powers to different ' things, to some solar, but to others lunar powers, and renders the productions of these concordant with* numbers. For in these monadic numbers also, the forms of numbers,, such as the triad, the pentad, and the heptad, are one thing, but the unions of the forms another thing. For each of these forms is both one,, and multitude. Hence form is unknown according to the highest union.
If therefore, monadic number participates of a certain unknown power, much more must the first number possess this peculiarity unically exempt from the whole of things. And besides this, we may also assume the anagogic power of numbers, not only because they define the periods of the physical restitutions, circumscribing our indefinite lation by appropriate measures, perfecting us according to these measures, and conjoining us.
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CHAP. XXXIV.
to our first causes, but because likewise, number in a remarkable manner possesses a certain power of attracting to truth, as Socrates says in the Republic, leading us to intelligibles from a sensible nature. ' As there* fore, the last number is allotted this peculiarity, what ought we to say about the first number? Is it not this, that it unfolds intelligible light, especially persuades to an establishment in intelligibles, and through its own order announces to us the uniform power of principles? If there- fore, we rightly assert these things, we shall in a greater degree admire Timaeus, who having placed time over the perfections of souls, and the whole world, through which it would become move similar to animal itself says, that time proceeds according to number, and by number mea- sures the existence of total souls. And as in intellectuals, number is established above the celestial circulation, collecting and causing it to be one, thus also in sensibles Timaeus says, that time being number measures the celestial periods, and comprehends in itself the first causes of the per- fection of the periods. If also, Socrates in the Republic, in the speech of the Muses, speaks about the one and entire period of the universe, which he says a perfect number comprehends, does it not through these things appear that divine number is perfective of wholes, and restores them to their pristine state, and that it measures all periods? The power likewise of collecting things imperfect to the perfect, accedes to all things from number, which elevates souls from things apparent to those that are un* apparent, illuminates the whole world with the perfection of motion, and defines to all things measures, and the order of periods. But if not only a perfect number contains the period of a divine generated 1 nature, but another second number after this is the lord of better and worse genera- tions, as the same Socrates says, number will not only restore things to their pristine state, but will also be of a generative nature. And it is evident that these things subsist in a divided manner, according to the second and third periods of numbers; but at once, and contractedly inthefirstof
' Instead of *w*yw> ^t «T« tuj* v^tw on ri|v *i»*ifti)f fun*, it U necetaary to read ira*/»» rti To)* voijtx* **a ttj; ai«4qn|{ $u<m>i.
" Eyery perpetually circulating body is called by Plato, a divine generated nature.
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30Q ON THE THEOLOGY BOOK IV.
numbers, The first number therefore, is generative, mensurative, and perfective of generated natures.
The first order therefore of mtelligiblcs and intellectuals is thus sur- veyed by Parmenides. But after this the order which possesses the middle place of intelligibles and intellectuals, and which a little before wc called connective, presents itself to the view. It is however denominated in a three-fold respect, viz. one, many, whole, parts, finite, infinite. For since the separation of unities and beings from number, extends to it, the one and being, which we have said difference divides, become wholes. But the thing* proceeding from these, are the parts of these. And wholeness indeed connectedly contains parts, but these are contained by their wholeness, in one way indeed, by the one, but in another by being. For there indeed, I mean in the summit of the intellectual Gods, unity was the cause of multitude, at the same time being exempt from multi- tude, and generative of the many. But here unity is coarranged with multitude. Hence also it is a whole which has reference to many unities as to parts. Since however, the connective order is triple, one division of it being intelligible, another intelligible and intellectual, and anotheF intellectual, the first monad indeed subsists according to the one and the many ; but the second, according to whole and parts ; and the third, ac- cording to the finite and the infinite. For where the first triad ends, there the second has its beginning. Hence, in the triad prior to this> Parmenides infers that the one is many. And in this triad, he concludes the same thing together with what remains. There however, the one was generative of infinites; but here the one is comprehensive of many, the whole of parts, and the finite of infinites. Hence, there indeed, unity is
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CHAP. XXXV.
exempt from the many ; but here it is coarranged with multitude. Hence also, the first coarrangement generates whole together with parts; but the subsistence of whole and parts produces the finite and at the same time infinite. For these are successive to each other, viz. the one, the whole, the finite, and the things which are as it were in an opposite arrangement to these, the many, parts, infinites. And the one itself is indeed the prin- ciple of the rest. But whole has now a habitude Avith respect to parts, and a representation of the duad, and proceeds into a coarrangement with reference to the parts. The finite however, is now multitude, participating of bound and the one, and is as it were a triad. For it is neither bound alone, as the monad, nor infinite alone, as the duad, but it participates of bound, which is primarily a triad. Every thing finite therefore, is a whole, but not every whole is finite. For the infinite is a whole, whether it is multitude, or magnitude. And every whole indeed, is one, but not every one is a whole. For that which is without habitude to multitude is not a whole. The one therefore, is beyond whole ; but whole is beyond the finite.
After the same manner also, infinite parts are said to be the parts of that which is finite. For the infinite of itself has no subsistence; by which also it is evident that the infinite is not in quantity in energy,' but in capacity. All parts however are not infinite. For according to bound they are characterized by one of the parts. And again, parts indeed are many, but the many are not entirely parts. The niauy therefore, arc prior to parts : and parts are prior to infinites. Hence, as the many are to the one, so are parts to whole, and so are infinites to the finite. And these three connectedly-containing monads, give completion to the middle order of inlelligibles and intellectuals. For unity indeed, is the supplier of stable and intelligible connection to all the secondary orders. But wholeness connects the progressions of divine natures, and produces one habitude of the orderly distribution of wholes. And the finite monad imparts by illumination to the conversions of second natures, connection with the natures prior to them. And one of these iudced is analogous*
' iv Tfl mfytix is omitted is the original-