AVhat ihis leimma is, what ratio it possesses, and how, bring adapted to con¬ cord, it becomes harmonious when eo-arranged with the other ratios, is evident through the mathematics. Hut there is a thing of this hind in the universe, as in a whole ; the ratio of the leimma being in the last of the animals comprehended in it, independently of the before-mentioned demonstration, according to the quadruple section of the whole. I’or from each of the spheres certain eilhixions, and mingled dregs of the elements proci ed into the subterranean regions; pos¬ sessing indeed, much of the tumultuous, dark and material, but at the same time contributing to the whole constitution and harmony of the world. Plato, therefore, placing the cause of these in the whole soul, calls it a leimma, which is significant of ultimate diminution, por since tlieologists arrange the powers of the highest Gods about that place, Jupiter adorning those parts, so as to render them adapted to the participation of such mighty divinities, what ought we to think about the soul of the universe? Is it not that it must in a much greater degree adorn every tiling which appears to he disordered, and that it must possess the cause of the hypostasis of an inordinate nature, and arrange it in a becoming man¬ ner, according to this cause? How, likewise, could it govern the universe, or conduct all things conformably to intelhct, unices it arranges that which is dis¬ orderly, aiul co-harmonizes the last of tilings, with the one life of the world? But if also in the Demiurgus, the causes of these pre-exist, as Orpheus says,
’I tic distant realms of Tartarus obscure,
Earlk’i utmost ends, lus holy feet secure.
VoL. II.
Ttm. Plat .
PROCI US ON Tin:
[book in
m!iv should it be wonderful, that tbe whole soul jvosses^ing all sivch things appropriately in itself, as a divine intellect possesses demiurgically, should antc- cedently contain the cause of the last parts of the world, and of that which is as it were, the sediment of wholes? l'ur the soul comprehends the invisible prior to the visible and .sensible world. AN hat the leimma is therefore, is through these things evident. Hence also the leimina, is both rjuadruple and single. And it is necessary that the soul should comprehend the reason of both, according to which the leiinma subsists rjuadriiply, and singly ; since it is requisite that tins should contribute to the unite r»e, and to each of its parts.
If al»o you direct vour attention to the numbers ot the terms, you will perceive that these preserve a certain admirable analogy. 1 he progression, therefore, into a hundred binaries, manifests an all perfect diminution and separation from cause. For in the soul, it comprehends that which is most partial, and in tin* universe, that which is last, and most material. Hut the four and the live in 1 lie tens, suspend that which is last, and most material, from first natures, and co-arrange them with their principles, l'or the tetrad is allotted a demiurgic, and world-producing quality, lt.it the pentad recals every thing which has pro¬ ceeded, to powers who h have more of the nature of the cue. Again the triad and hexad in the units, impart perfection to these*, through conversion. Hut if also the ratio of-1."I to l'l is superpartieut,* neither will this number lx- dissonant to the* universe. For after the all perfect progression of seiisibles, and a diminution ns far as to the earth, which is said to lx* the twelfth part of tlx* world, all that is under it, will lx* tin* thirteenth part of tlx* whole. And the representations of tlx* elements, which proceed into the subterranean place, will he adapted to this number. That which is most material in tlx* universe therefore, proceeds to the utmost e*\W-nt, is adorned as it proceeds, and returns when adorned. In each part likewise, of the* uuive*r>e, there are tlx* last diminished genera of perpetual natures, to which the number twelve is ascribed; and with gie*at propriety, the-v have habitude, and communion with each other, according to tlx* thirteenth ratio, since the nunilx-r twelve was dedicated by the ancients to the [mundane] Cods, and to the genera that an* always si.sjx nele*el from them. All tlx-se* therefore, the soul unieally comprehends in the ratio of the leiinma. In addition to these tilings likewise*, the* ennead of the units, which three and six procure for us, indicates tlx* end of the psyoltii'al ratii»s. hor lxgm.img from the uionael, thev proceed to the cnriend, and from monads to de rails [i. e>. free.n units to tens], anel from these to hundreds. I or all the progression of the soul is
* l'<>r -13 contains 13, nglitccii linns, silh a riniaintliT ol £).
nooK in.]
TIM.El'S OF PLATO.
triadic, and likewise, its evolution into light from the demiurgic canse, Iwth according to essence, and according to harmony, as we have before observed. And thus we liave shown what it is which the Icimma manifests in the soul.
The whole psychogonic diagram however, has 3 t, or 30 terms. And on this account, the uuiiiIht 3d is adapted to the soul, as being generated from the hexad proceeding into itself; the hexad being ascrilied by the ancients to the soul, because it is the first evenly-odd numlier, just as the soul in the medium between impartible and partible natures,' to the former of which the odd numlier is allied, but to the latter, the even; and aho, because it is circular, in the same manner us the pentad.* The pirtod however, is the image of the intellectual circle, c% bang masculine , but the hexad of the psychical circle, at being feminine. If also yon direct your attention to 34, this numlier too, will be adapted to the soul; since intellect is a monad, as being impartible, but the world is a decad, and the soul a tetrad. Hence, all number is said to proceed from the penetralia of the monad, as far as to the divine tetrad, which brought forth the mother of all things, immutable and unwearied, and which is called* the sacred decad. But the tetrad has for its side the dead, and the double of the square of it added to 2, produces the above-mentioned number;* being an imitation of the soul, which is multiplied by itself, and together with its own prolific power. If likewise 34 is composed from the second sesrjuinctave, viz. from 1G and 13, it will happen, that as the sesquioctave is especially adapted to the soul, so also is this second sesqui- octave. For being a medium between consonant and dissonant intervals, it is adapted to the middle nature of the soul. And in short, the sesquioctave charac¬ terizes the diatonic genii*., according to which the whole soul is harmonized. But lieing assumed as the second, it will accord with the order of the soul, in which the genera of !>eing, have entirely a secondary subsistence.
Farther still, in addition to these things, since the whole diagram contains a quadruple diapason, which is the most full of all symphonies, but the diajrente once, and ends in one tone, it w ill possess the quadruple cause of the division of the world into four parts, proceeding as we have said supei nally, from animal itself, and the four ideas in it, through soul into the universe, and of the i>erfect har¬ mony in each of the parts of the world ; through w hich also, heaven is one world, concordant with itself celestially, and the earth has all things terrestrially, and
1 For the evenly odd nunilier is a medium bctwwn thr odd and the even number.
* For orrai here, it is obviously necessary to read wtrrat.
1 Instead of <Xvovn here, it is necessary to read aXcies^i.
4 i. e. 2X 4* + 2 = 34.
PROCLUS ON TilE
[book in.
10 if
in 3 similar manner each of the tlcmnits between these. Since, houovcr, (lit* world is not only quadripartite, but lias five figures, possessing a tilth idea together with the four, the soul very projK-rly contains in itselt, alter the quadruple diapason, the symphony diapente ; the remaining section being that of the hea¬ vens into eitdit spheres, and of the whole woild into nine, over the former of which the Syrens preside, mentioned in the Kepnlilic, and over the latter the whole of the Muses, under whom tin - Syrens subsist. Ygnin theretore, a tone consenta¬ neously closes the whole diagram; and it is not possible to devise any other divisions than these which are delivered to us by IMato, I mean, the division into four, into live, into eight, and into nine parts, some ot which are mentioned in this Dialogue, and some in the lb public. Very properly therefore, is the whole psy- * hngomc diagram composed ol all the above mentioned parlieul.iis, I mean, a tone, the dia|M-nte, and the quadruple diapason, in order that you may see these throughout the whole world, a> having the power ol the whole diagram. All likewise are assumed according to all the divisions made by IMato ol mundane natures, which are triple, vi/. according to ideas, according to figures, and according to the spheres.
All the other sesquiallcr and sesquioctavc* ratios therefore, were* the bonds ot more partial orders, comprehended either in the live parts ol the univeise, or in the divisions of it into eight and nine; a-, for instance, in the division of it into bods, da moils, souls, natures, and bodies. And ol boils, into those t .a 4 preside over different parts of the world. For in each part ol it, there are dillcrciit orders of (bids; those of tin? second rank being analogous to those that are prior to them. And m a similar manner with respect to du-itioiis, some are ot this, but ot icrs ot that series. Tin like also takes place, in souls, and natures, and bodies. Hut I lie diapi nte symphony, and the sesquioi lav* ratio, are not in v mi assumed all* r the quadruple diapason, but because tin y are comprehensive and eonneetive|u i-iinimoii, of wholes. I say, for instance, that the ratio of tin* ninth to the eighth sphere, comprehends and connects as one ratio, all the parts at once th.it are arranged according t*» a quintuple div isioii, mid all that are divided into eight oid nine. Ilul the U iinm is of nil the sc-quit* Ilian ratios are cilia r the ultimate, and very partible diminutions, according to each portion of the ipiadiipaitile dis- tr.hiition, or they are the common gills of all these ratios, into the last place of the universe; through which (bids, ila nunis, partial souls and iialm* >, proceed into that r* gitui, and at t old vv ilh each *ilher, * miliii mably to the ultimate and perl« « 11y partible symphony, Mich as vv.- say siqierparUnit rali.is possess. 11* m. IMato descending It* this adds, that the D. niiiiigiis diviiling the mixture, had now con¬ sumed the whole of it. For neither bod, nor nature, docs any thing in vain.
Rook 111.]
TIM.BUS or PLATO.