It happens, therefore, in this diagram, that there is a quadruple diapason, that the diapente occurs once, and that tin* tone is redundant. I’or three s'*sfpii;dters, make one diapason and tone. The diagram, however, does not end in atom*, hut in the leinima. Hut this was the tiling proposed to he effected. .Severus, there¬ fore, does not take aw ay the tone, luit does not end in it. So that the w hole diagram according to all the terms, consists of a quadruple diapason, and the diapentes, and one tone. If also we wish in monadic numbers to assume these intervals, we must survey tin* progression extended as far as to twenty-seven. For *2 is double ot unity, 4 is the double of 2, 8 of 4, and It; of 8. And as far a- to this the qua¬ druple diapason extends. Hut of Hi, *21 i> the sesquialter, and this is the diapente, and to this *27 has a sesquioctave ratio. So that the before mentioned symphonies are |w?riect« d horn one part, as far as to twenty-seven. This, therefore, as I have said, is common to all the diagrams. Hut they difibr from each other in this, that some are in tin* form of the fitter x, but others are in a right line. For of the ancients, Adrastus employs figures in the form of X, but Severus ri^ht lines, which in my opinion is Ijetter. For in the figures which are in the form of the letter x, the same numbers are found twice in differt nt places. Hut this is discor¬ dant with the things themselves. For there are not two parts of the soul which are the same. Hut all these numbers are parts of the soul. Tlicv differ also in this, that some of the diagrams end in a tone, but others in the leimma. Some al*>o are more perspicuous, though the same numbers are assumed twice, as is the case w ith those diagrams w Inch distribute the duple and triple 1 ratios in the sid< s of triangles. Hut others place each numlier once mall the intervals, though this causes a more ditlienll ilivision of the duple terms, into super-particular and super-partienl ratios. We have tbefore premised such things as may contribute to tin* theory of the psychogonic diagram, to those who survey it mathematicallv.
As we are enterin': however on the more important explanation of the words of Plato, we think it requisite to speak in the first place, concerning the division itself according to which the soul is divided in these ratios, and to take avvavhy argu¬ ments such things as arc* an impediment to our apprehending the truth respecting it. Let no one, therefore, think that this division is corporeal. For it has l>een before demonstrated, that the middle nature of the soul is exempt from bodies, and at the
Itoth the sense of what is here said, and the version of Thonia:us, require the insertion in tins place of sai rfttrXarrwvt.
Tim. Plat.
\ OL. II.
fBOOK III.
same lime from every partible essence which is distributed about them. Nor must it be supposed that the soul is Ik tier indeed than bodies, but that it is divided after the same manner as the terms or boundaries, and intervals by which bodies 1 are measured. For things that have interval, are not wholly and through the whole present with themselves, ami when divided, are not able to preserve an unconfused union. Hut the soul participating of an impartible allotment, is united to it-elf, and exhibits all the same eh ments subsisting the same in all its parts Nor again must this section of the soul, be considered as a division of numlier. For tin* soul is imb ed number, vet not that which is according to quantity, but that which is essential, self h goften, having the form of unity, and converted to it-elf. Nor h t the prest nee ot tin >e ratios in all tin parts be com¬ pared to spermatic reasons. For fh.se are imperfect, coipon al-forined, and miU-nal, and entirely fall sliort of the immaterial and pure essence of the p-j du¬ cal reasons. Nor let any one assimilate the before-mentioned parts to the theorems of si ielice, because each theorem possesses the vv hole [science of wine i it is a tin mem]. For we do not now ( misiib r the knowledge, but the es-< m e ot
M , u p Nor is it propi r to think that tin- dilh-rem • > of i s-etu e>, are similar to the distinctions of habits. For the killer are entirely varied in tin natures that po—I — 111 . Ill, but the lull ill i are i slablisln d with invariable sann ness in d< liniir- gic boundaries. Il. nee if is necessary to suspend the primordial principle of the psychogenic division from the demiurgic cau-e, and from perfect measures, which eternally pre exist in real beings ; to wbicb also the l)i iiiiurgus looking, divides the soul. For as be divided this universe by intelligible paradigms, thus also hr separates the essence of the soul by tin* most beautiful boundaries, assimilating it to the more ancient and primordial ( auses. I he mode therefore of division, is im- i uih nut, inttilt ctuuf, nndt filed, pn/, t (ire of the t ssem c of lhe soul, gt m rain e of the multitude in it, co lit, live through hurmuni/ into one order, and connect ire of divided parts, at one and the same time being the cause of the umningled purity of the multitude in the soul, and producing a communion of reasons conn rging to the same essence.
\ m l tlir Demiurgiis, indeed, appears to consume the whole by ibvulmg it into parts. J’or thus also in a certain rc>j»ect Timieiis says, that he consumed the iJwlc from which he cut off these parts." I hi-, however, is not the case, but it is necessary to preserve both impartible, and that the wholeness remaining imparli-
* For airtjy lien*, u i*> necessary l<» re.nl uurn
1 For aXXu hafitptoTcv lu re, it is necessary to rca»l a\\' aprpioTo*.
l>lo, tin? division into multitude should he effected. For if we assume one of these only, I mean the sec tion into jiarts, we shall make the soul to he partible alone. The u hole there/ore is distributed into parts, and at the same tunc the n hole remains. Airain, the impartible of the soul equally participates of the impartible and the partible. For it is well said, as we have before observed, by the ihcmoniaral Aristotle, that there is something impartible in partible natures, which is connec¬ tive of them ; so that it is much more necessary, that something impartible should remain, in things which have not only a partible, but also an impartible nature. F’or if this did not remain, that which consists of both would lie alone partible. It is evident however, that it is necessary the whole should remain in the pene- i at ion of the parts, it the Demiurgus is an eternally producing cause, lint he constituted the soul one w hole, prior to the division of it. For he did not obli¬ terate it in producing something else. lint he always produces every thing, and eternally, and causes that which is produced to remain what it is. Hence the wholeness is not destroyed, when the parts are constituted, but it remains, and precedes the parts. For he did not produce the parts prior to the whole, and afterwards generate the whole from these, but vice versa. The essence therefore of the soul is at one and the salt*® time a whole, and lias parts, and is one and multitude. And such is the division of the soul which Tiuucus assumes.
The mode, however, of unfolding it, should accord with the essence ( ,f the soul being liberated from visible, lint elevating itself to essential and immaterial har¬ mony, and transferring from images to paradigms. For the symphony which flows into die ears, and which consists in sounds and pulsations, is very different from that which is vital and intellectual. IVo one, therefore, should stop at the mathematical theory, but should e\< ite himself to a mode * of survey adapted to the essence of the soul ; nor should he think that we ought to direct our attention to interval, or the differences of motions. For these are assumed n mutely, and are by no means adapted to the proposed subjects of investigation. But he should survey the assertions by themselves, and consider how they afford an indication of the psychical middle, and look to the demiurgic providence as their end. In the first place therefore, if you are willing thus to survey, since wholeness is triple, one l*eing prior 1 to parts, another consisting of parts, and another lieing in each of the parts, as we have frequently elsewhere demonstrated ;—this being the case, Plato has already delivered the wholeness of the soul which is prior to parts. For
1 For mroi' lierc, read rpowov.
* Instead of wpet rwr ptpm* in this place, it is accessary to read rpo r w ,
[DOOK. lit.
he made it to he oih? whole prior* to all division into parts, and which as we have said, remains what it is, without In-in- consumed in the production of the parts. For to Ik 1 willin- to dissolve that which is well harmonized is the province of an e\d nature. But the dissolution is ell', clod l.y c onsuming the whole into the parts. In what is now delivered however, he constitutes it a whole from parts, consum¬ ing the whole mixture into the division of its essence, and through the harmony oHI.e parts, remlei.n- it a whole de novo, and . aium- it to he complete from all appropriate parts. Hut lie shortly after teaches us the whoh u. - which is in each of the parts, div ulin- the w hole smil into certain circles, and in oat h of the cm les ins. rtin- .,|| I!,,- irasons, wlm h lie had air. ady mad. manifest to us m what he had 1*. fore said. For lie had said, that in . a. I. of the parts there are three [i. e. same, dill, rent, and essence| in the same manner as in the whole. h\« ry part then lore, as well as the whole, is in a certain n sp. et a triadic whole. lienee it is necessary that the soul should have three wholenesses, because it animates the universe, which is a whole of wholes, each of which is a whole aecordin- to the wholeness which is in apart. So that the soul animating the universe in a twofold respect, hotli as it is a whole, and is consisting ot total parts, it requires two wind, in -M S, and tran-e. ml- the tiling that are animated, havm- snmi thin- external in them, so as circularly to cover the universe, as Tiuia-us says, as with „ veil, Jlv the wholeness, therefore, which is prior to parts, the soul entirely runs above the universe, hut by the r. maiiiin- two connects the universe and the parts it contains, these also In in- vvholi s.
In the next place, it must he observed, that I’lato proceedin'.; from the be-m- njnjr to the end, preserves the monadic and at the same time dyadic nature ol the soul. For he reduces the hyparxis of it to essence, same, and dillereiit, and distributes the number of it aernidm- to a twofold division, h. -liniiii- from mu oart. into duple and tuple numbers. He also surveys the media or middles, in one of them comprehends the other two, 1 and acoordiri- to each ot these unfolds twofold se-ipiialt. r and sesi|iiitertian ratio-, and a^ain cut- these into sesijuioc laves and Icimuias. In what follows lihev ise, he divides the one leli”th into two, and the one li-ure of the soul into two periods. \ml, in short, lie no- where omits the monadic and at the same time dyadic, and this with the trr. ..test
' Amt lur iri * a»*H pf/HOfM/v here, also, read rrpo k. \.
1 i. e. I» the •■e.inielrie luiilille I.r |o.>j><>rlion, n lm ii n.ui|m lr. uds arnliinHical and harinoiiual |>l..p>>r(:o(i I 11 to an\ three iliimhers ill arilhun lieal |»r..|.orli*ni, a fourth uuaili. r is a.ldul, so a> i.. |ir.i<luie i;e..u.etiii.il |ir..|nirli.ui, then this 11n41url11.11 will i«.iu|ireheud hulh that whiili is arith- uiftKnl, ami lh.il which Is hurilionieal Thus ll tu the terms 1 . 2 . J a luurlli Urm is added »il. <>, M> ilul U Iiiav he 1 ; 2 : : 3 : <>, llicn 1 , 2 and 3 aie ui arillmu lital, and 3 and 0 111 harmonic,
proportion.
Dook Iii.]
TIMEX'S OF PLATO.