Tlio Pemiiirgus therefore did not constitute a mixture of parts either exceeding nr deficient, bill produced it such as was suliicient to the wholeness itself of the soul, l’or tin* whole which is from parts, is neither more nor less than its proper parts, hut entirely derives its completion from appropriate parts. Hence the whole of that which is mingled, consists of harmonic ratios, ami all this harmony is, in short, the essential paradigm of the harmony of the universe, accor¬ ding to all the divisions in the world. Moreover, the whole number of the essen¬ tial monads of the soul is 10oi)l7,' proceeding according to all the orders of miml*ers. Decadieally, indeed, in order that the soul mav become mundane : for the decad is the number of the world, iiut pentadically, in order that it inav be converted to itself: for the pentad is sell comertive. Jhincadicallv, in order that it may not alone m contain the universe monadic-ally, but also as proceeding to the last of things from the monad. But tctradically, as collecting the ipiadri- partite division into one. And hebdoniicallv, as converting all things to the monad, to which tin- hebdomad is alone referred, being motherless and virile. And in the soul of the world indeed, the above number subsists totally; m divine souls, as having their energies directed to that 1 soul, it subsists both totally and partially ; in daunnus, as energizing still mon partially, it exists vice versa, partial¬ ly and totally ; and in human souls, alone partially, and alone gnosticallv. For thus all forms subsist in these souls, such for instance as the form of mail, of daMiion and of Hod ; in order that through these they may know, that all things subsist m more excellent natures productively, and at the same time gnosticallv. This mixture therefore, is alone the mixture of the whole soul, and it subsists after the same manner m each divine soul, ami similarly in du-monincal souls, each of whit li his intellect placed above its proper essence, a peculiar ve¬ hicle, and a life distributed about this. If, however, in partial souls, it be r«*rjuisite to assume the peculiarity of each, it is a medium between the impartible which is above, and the partible which is posterior to them,* or it is partly the one, and partly the other of these. And though we have elsewhere discussed this largely, yet we shall particularly inn stigate it, when we come to explain what is said by- Plato concerning the generation of partial souls.
' InUc.l t Ilf rvarni rnffi rr-rniir i ill till* place, It l» rcrjllidle to read, tryraKovrntu re nrtnpa\<,t -et.
* It iv necessary lirre !■» supply fiornr.
1 For Tftot mnoi' in tins place, read — on*
* It appears to me lliat after rnaarijf ifny tn \n,t horn iu llic original in tlrs place, liie words /jr*rr
arc wanMii"; and tliat immediately afler, instead of ro re vr rp avrat «a< to fttr' avrat
fifptiTor, we should read top Tt vwrp avrat o/irptcrtv, cat rov per avrat fitpttrrcp .
Imiocli’S on the
[ROOK 111.
*• Havin'*, therefore, cut all this cl mil decomposition nccording to length, so as to produce two from one, he adapted middle to middle, each to the other, as it were in the form of the letter X."
In the first place, it is requisite to show mathematically of what kind the figure of the soul is, and thus, afterwards, introduce the theory of the things ; in order that being led in a becoming manner by the phantasy, we may render ourselves adapted to the scientific apprehension of what is said. All the numbers there¬ fore, must 1 m* conceived to be desclibed in one rule, as those who are skilled ill music are accustomed to do. And let the rule have the numbers according to the whole of its depth, and be divided according to its length. All the ratios therefore, will !>c in each of the s« etions. For if the division was made according to breadth, it would he entirely necessary that some of the niunlH*rs should be taken here, but others there. Since however, the section is according to length, but all the iiuiiiImts are in all the length, there will be the same iiiiuiIkts in each ot the parts. For it is evident, that it is not the same thing, to divide the length, and to divide according to the length ; since the latter signifies, that the section proceeds through the whole length, but the former, that the length is divided, ljet the rule, therefore, bo thus divided according to length,* and let the two lengths lx* applied to each other in the points which bisect the lengths, ye! not so as to l>e at right angles: for neither will the circles 1m* at right angles. Ia*t the two lengths likewise be so ineurvated, that they may again lx* conjoined at the extremities. Two circles therefore, will 1m* formed, of which one will In* in¬ terior, but the other exterior, and they will lx* oblique to each other. One of these likewise, is called the circle of the same, but the other, the circle ot the different. And the one indeed, subsists according to the equinoctial circle, but the other, according to the zodiac. For the whole circle of the different revolves about the zodiac, but that of the same about the equinoctial. Hence, we conceive that the right lines ought not to lx* applied to each other at right angles, but like
* In the original of this place there is nothin" more than rouo ynfi .ri ou ravror to fiTjtot. 1 i.e
rest of ihe sentence in the translation is added from the version of Tliouiaus.
* Thus for instance, tel ihe number* be disposed according lo depth as follows :
Ac.
AC.
i . . a .
Ac.
i . g . a .
iV c .
Ac.
Then the line* drawn longitudina'b. will rcpiesvnt the division of the rule according I® length
BOOK lit,]
T1 MAX'S OF PLATO.
th<* letter \ as Plato says, so as to cause the angles to Ik? equal only at the summit, but those on each side, and the successive angles, to he unequal. For the equi¬ noctial circle does not cut the zodiac at right angles. Such therefore, in short, is the mathematical discussion of the figure of the soul.
Again however, surveying the things themselves from the beginning, let us refer what is said by Plato, to the psychical essence. And, in tlie first place, we must obsone, that continued and discrete quantity are divided from each other, accor¬ ding to the mathematical sciences, and are in a certain way opposed to each other, so that it is not possible for the discrete to be continued, or the continued to be dis¬ crete quantity. In the soul however, both these concur, viz. union, and separ¬ ation. For it is a monad and number, one reason, one multitude, anil many things. And as being a whole indeed, it is continued ; but as number, it is di¬ vided, according to the reasons which it contains. Through its continuity like¬ wise, it is assimilated to the union of intelligible^, but through its multitude, to the separation of them. And by ascending still higher than these, wo shall find that according to its union, it possesses an image and representation of the one, but according to its division, of the multitude of the divine numbers. Hence, it nei¬ ther has an arithmetical essence alone ; for it w ould not be continuous ; nor alone a geometrical essence ; font would not 1m* divided, lint it must Ik* said, that it is at one and the same time both the arithmetical, and the geometrical essence. So far however, as it is the arithmetical essence, it has also, at the same time, the harmnnic.nl essentially. For the multitude in it is harmonized, and it comprehends in sameness, both absolute anil relative quantity. Hut so far as it i*> the geome¬ trical, it contains the spherical essence. For the ciicles in it are both immove¬ able and moved ; immoveable indeed essentially, but moved according to a vital energy. Or rather, it possesses both these at once; for they are self-motive. Hut the self-motive, is at one and the same time moved and immoveable. For it moves itself. Hut to move, or be the cause of motion, jiertains to immove¬ able power. The soul therefore, comprehends essentially all sciences ; geometry indeed, according to its wholeness, its figure, and its lines; but the arithmetical science, according to its multitude, and the essential monads in it, as we have before shown. Hut it comprehends the harmonic science, according to the ratios of numliers ; and the spheric science, according to its twofold circulations. In reality also, it is the essential, self-motive, intellectual, and united bond of the mathematics, comprehending all things unaccompanied with figure, and with limit filed purity. Hence it comprehends figures iinfiguredly, things separated, unitedly, and without interval things accompanied with interval. For these pertain to the essence of the soul. And it is necessary to survey all things in it aAcr this manner.
IMtOl'LlIS ox Tim
[hook iii.
Moreover, this likewise ought to be assumed from what hns been said, tliat nil secondary natures, are analogous to those? that are prior to them, and that e\erv where, (he one precedes multitude. For as the theory of the hyparxis of the soul commenced from its essence, and that of its harmony from the e/n part, thus ;dso the doctrine concerning its figure, places the one length prior to the two. And as sameness and dillereiici are from essence, so the triple and duple ratio are from the monad, but from the one h ngth, the circle of the tunic, and the circle of the different. As likewise, tin* antecedents are to the antecedents, so are the consequents to the consequents, and all things are homologous to each other, viz. essence, harmony, and form. Vnd all tilings are indeed everv when-, on account of the ps\chi«‘.d lile, beiii '4 as it were ot one colour, and of similai parts. The tome however, and the triple, subsist m a greater decree in the circle of (he same, but the d/jf event, and tin duple, in the circle ot the different. All the ratios likewise, arc e\ery where, but after a different manner in first and secondary natures; in the former indeed, intellectually, totally, and unitedly; but in the latter, doxastieally, distributively, and partially. And thus much concerning these particulars.
Concerning this section however, and the two lengths and circles, it is worth while to consider, what tin y must be said to be. For the ditine lainblu lms soars on high, and solicitously investigates invisible natures, viz. the one soul, and the two souls that proceed from it. For of every order an imparticipable monad is the leader, prior to the things participated, and there is a number appropriate to and connascent with impartu ipabh-s. 1 he «luail also is from unitv, in the same manner as in the < bids themselves. Tiuneus therefore, he savs, hav inn through the psychogony fabricat< d in words the one and supermundane soul, from which the soul of the universe and other souls are derived, now produces the duad from this. For the section manifests the demiurgic division, which proceeds in sameness and jierfei lion, generating the same things according to second iiuiu- l>crs. Hut the division according to length, exhibits to us the progression super- nallv proceeding from the Ibmiurgus. 1 hrough these however, two souls arc i;eni rated, alii r the one soul, eai h ot w Inch has the s une ratios, are conjoined to, and arc in each otlur, and are divided front each other. And they likewise preserve alt muiiingled purity, together with union with each other. ! or tin y are united to their own centres, and this is the adaptation of middle to middle, llut since aUo, these souls are intellectual, and participate of a divine intellect, the Demiurgus prior to the p m ration of the universe, bent them into a circle, and comprehended them in a motion according to the same, and in the same, making them to be intellectual, imparting to them a divine intellect, and inserting
Suok 111 . J
TIM A'. US or PLATO.
tlx-(liiad of souls, in the intollectnul duad, which transcends them essentially [And thus far the divine lamhliclms.]