this part is the summit of the soul; hut according to the duple and triple part, it proceeds Imm intellect, and returns to it;’ and according to the double of the double, anti the triple of the triple, it proceeds from itself, and attain returns to itself, and through itself a> a medium, to the principles of itself. For through being tilled from these principles it is prolific * of secondary natures. And as indeed, the progression from itself, is suspended from the natures prior to itself, thus also the conversion or regression to itself’ is suspended from the regression of tli*‘ beings that are prior to it. lhit the last parts, according to which it consti¬ tutes the natures posterior to itself, are referred to the first part; in order that a circle without a beginning may hr; unfolded to the view, the end Im mg conjoined to the beginning, and that the universe may become animated, and at the same time endued with intellect, the solid numbers being co-arranged with the first part. Moreover, he says that from these middles, sesquialler and sesipiitcrtian ra¬ tios, and also sesqWioetaves, become apparent. What else, therefore, does he intend to indicate by these things, than the more partial dillerence of the psychical ratios? And the sesquialter ratios indeed present us wit ii an image of partible communion, hut arrording to the first of the parts. The sesipiiterliau ratios, of partible communion according to the middle terms. And tin* sesquioctaves of this communion, according to the last b rms. Hence also, the middles or pro¬ portions arc conjoined to each other, according to the scsipiioetave ratio. For as being surveyed according to opposite genera, they have the smallest communion; hut they are appropriately conjoined to both extremes.
1 imams also adds, that all the sesrpiitr rt inn ratios are filled by the interval of the sesquioctave, in conjunction with the leimma ; indicating that the terminations of all tin ■se ratios, end in more partial hypostases, in consequence of the soul com¬ prehending the causes of the last and |>erfectly partible essences in the world, and pre-establishing in itself, the principles of the order and harmony of them, according to the demiurgic \vill. Tin* soul therefore, possesses the principles of
harmonious progression and regression, and of the division into things first, middle and last; and is one intellectual reason or ratio, receiving its completion from all ratios. And again, that all the harmony of the soul, consists of a quadruple diapason, diapente and tone, is consonant to these things, l'or since
* According to the version of Thoniaeui, there is an omission here in the original, of the words vara bt rr)V bcw\aruav vat rfuwXairiar, avo rev rev rpoutr i, ioi rpol airror ixierptijHi. Indeed the sente requirei tbit addition.
* For porvpot in this place, it it necessary to read yonpot.
* The words ovrvt rj eii caiTijr ewnrrpo^ij, which are omitted in the original, ought to be inserted, conformably to the version of Thomaais,
PllOCLUS ON Tin:
[BOOK Ilf.
then* is harmony in the world, anil also in intellect ami in soul, on which account Tiina-us says, that the soul participates of harmony, and is harmony,—hence the world participates of harmony decadically, hut the sou! tetradieally, and hannonv pre-exists in intellect monadically. And as the monad is the cause of the tetrad, hut the tetrad of the derail, thus also, the intellectual harmony, is the supplier of the psychical, and the psy< local of sensible harmony. lienee Tiuucus conceived that the quadruple diapason, is adapted to the harmony of the soul. For the soul is the proximate paradigm of the harmony in the sensible world. Since however, live 1 figures and live centres in the universe, give* oomph-lion to the whole, the harmony diapente also, imparts to the world the symphony which is in its parts. Since, likewise, the universe is divided into nine parts, the sesipiioc- tave produces the communion of the soul with the world. And In re von may see that the soul comprehends the world, and makes it to he a whole, according to cause, * as one, as consisting of four, and also of five parts, and as divided into nine parts, harmonizing and causally comprehending the whole of it. For the monad, the tetrad, the pentad, and the ennead, 1 procure for u> the whole numlier, according to which all the parts of the world are divided. Hence the ancients assert that the ."Muses and Apollo .Musageles, preside over the universe; the lat»er supplying the one union ol all its harmony ; hut the former connecting the divided progression of this harmony, and rendering their number concordant with the tight Syrens mentioned in the lb public. I bus therefore, in the middle of the monad and the ennead, the universe is adorned tetradieallv and pentadi- callv ; tetradieally indeed, at < ordmg to the four ideas of animals, which the para¬ digm comprehends; but pentadicallv, according to the live figures, through which the Deiniurgus distributed all tilings, hinis* If, as Tima-iis says, introducing the tilth idea, and arranging this harmonieallv in the universe.
Again therefore from the lieginiiing, we mav sav, that the Demiiirgus having twofold powers, the one being ellective of sameness, as we learn in the Parme¬ nides, hut the other, of diflcrcnce ; he both divides and hinds the soul. He is also the filial cause ol these, m order that the soul mav become the middle of wholes, being similarly united and divided, two tilings existing prior to it, divine natures as unities, and beings as things united ; and two also being posterior to
' tor *in ru In-re ri .nl * or«. 'I tn-M- live li^uri-j arc tin toe regular limlies, viz llir ilmli-c.ilirilron, t lie |i\ r uni I, llir inl.ilntlinn, tin ii ii'.ilitilrmt, .uni llir iiitu- tint I lie loo iililri'i .10 tin- linrtlirrn, smith* 01, 1 .oli 111, nnl hi 'Ii ru r« nlie-i, him I lln «< nfrr nl tin- imivrr>r.
1 rmii lln- n r.inii nl I limn 111 >, it o in.-* i-'>;irv In iii'i-it in tlio tin unriU, ij 4- v \ r J rvr o-oyior
wtfin yn, mi n\i ►- mir inrun worn, v, tin ii are wanting in 1 lie nominal.
* l'nr <1 ru lirrr, rt jit iioui
TOOK lll.J
TIM AX’S OF l’LATO.
it, viz. those which are divided in conjunction with others.' ami those which are m every respect partilile. or it you are w illin'; prior to the former, the one itself, hut posterior to the latter, matter itself, tlint the efficient causes of these divisions and bonds, are .vow and different , which arc the jm niliarith s of the demiurgic order. And the paradigmatic causes are tin* sections and bonds of the father. For he’ first cuts, and binds with ineffable bonds. These things also, arc obscurely indicated hy thco/ngixfs when they speak if the Saturnian sections and bonds with which the niaKer of tin unirtrst is said In surround himself, and which arc mentioned by Socrates hi the ( latylns. Hut the lonual causes of the divisions indeed, are the numbers, for according to these the parts are distinguished. Hut of tin; bonds, the middles, and flu* ratios which give completion to these, are tin* formal causes. I’or it is impossible to survey concanses which have the relation of matter, in souls which are incorporeal.]* r \ hese things lieinjg premised, it is evident that the Pemiurgus energizing with twofold powers, viz. with such as are of a dividing, and such as are o| a binding nature, he divides (he tnformed essence of the soul, and the tore* told mixture, the whole remaining that which it is, by the primordial causes ot all div ision, and makes the vv hole of it to consist of scv< n parts, and seven niembeis, comprehended in intellectual boundaries. For since tjie Pemiurgus constituted the soul as tin* medium between an impartible essence, and that essence which is divisible about bodies; but the impartible essence is triple, abiding, pro¬ ceeding, and returning he pre-established the similitude of this in three parts. And lie adumbrated indeed, tin; permanency 4 of this essence bv the first part; but the progression of it by the second ; on which account, perhaps, it is said to be double ot the first part. l*or every tiling which proceeds, has permanency pre-existent to its progression. And he adumbrated its regression by the third part. Hence this part is triple of the first. For every thing which returns, lias proceeded and been permanent.
Since, however, the soul produces the essence posterior to itself, it contains the total essences ot it in itself; the whole of the incorporeal essence indeed, but which is inseparable trom bodies, according to the fourth ami fifth part; but the
The words fi'r qAAm? are omitted in the original, but ought to be inserted conformably to the version of Thomarus.
For onniv here, read mnoi. The Chaldean Oracles also sav that the Demmrgus glitters with intellectual sections.
All this part within the brackets, is omitted m the version of I'hoiuarus, with whom such omissions arc not unfrnjuent.
# For yon/me here, it is necessary to read ftovtftor.
1 Instead of oAij« here, read oAai.
8ft
PttOCLUS ON THK
[dour III.
mhole of the corporeal essence, Recording to the solid nmnliers, viz. the sixth and seventh part. Or [it may 1m- said] that the soul being self-siihsMrnt, and self- energetic, produces itself and converts itself to its principle, according to the square numbers ; hut all the partible ess,-nee posterior to itself according to the culs-s. These seven parts therefore, being divided as we have said, into three and four, the one ratio of geometric analogy, hinds them essentially ; hut the harmonic middle, hinds them according to sameness; and the arithmetical according to difference. These parts however are inserted between the "enmetrii: middle, and are said to give eonipletiou t.i the double and triple intervals ;* heeaiwc all sameness anti all ditl'erence, arc uniformly compn ln nded by essence, and the harmony which subsists according to it. Hut from these middles, the multitude of sesquialter and sestjuitertian ratios, and seMpuoctaves, becomes apparent, this multitude indeed, being of a binding and connecting nature, in the same manner as the middles, but more partially, l or these indeed, are certain ratios; but each of the middles consists of many ratios, which are either the same or diflerent. As analogy then fore, or proportion, is more comprehensive than ratio, thus also the above-mentioned middh-s, allurd a greater cause to the soul, of cornua t* ) con¬ taining the multitude which is in it, since they ini* lU-ctually pi rvaile* through the whole of it. Hence the sesijuialler, and sesquitertian ratios, » r ' ceitain more partial bonds, and an- comprehended in the middles; not accord ng to d liferent habitudes of them with reference to the extremes; Ibr this is mathematical; but according to causal comprehension, and a more total hypostasis.
Again, these bonds, contain the second and third progressions of the ratios; the sesipiialter indeed, conslringing the harmony ol the ratios, through the live centres; hut the sesipiitertian exhibiting their power, through the four elements ■which are everywhere; and rendering all things intelligible and allied to each other; and tlu- seMpiioctaves co-harmonizing the division into !> and ft. Hence, as the world consists of eight parts, and also of nine, the am ieiils.at one time establish right Syrens, and at another nine Muses, as presiding over the universe. Min e the harmony of the whole of things proceeds from these. I he m-stpiilerliun there¬ fore, and sesqmalter ratios, are more total than the ses.piioctaves, bi-cai se they are the suppliers of a more pei fe.t symphony, and antecedently comprehend in less numbers, the harmonious section ol the world. Here therefore, the divisions are separated from each other in their parti* ipauts; hut in the incorporeal reasons
• Tin- irvrn term* I 3. V «>. 8. J7, are raid t>\ P.oclun to t»e inserted between the geometric Dint- die, became I 2. 4 8. and also J. 0. ?7, are in geometric |>ro|toil«>n.
1 f or bocovva* here, read 7o;»oi-»«e
Uooe Iii.]
TJM.EUS Of i’LATO.