The Commentaries on the Timaeus of Plato — trans. Thomas Taylor

For 6 ex* eeds 3 bv (he half of 6, and 3 exceed* 2 bv the half of 2.

BOOK III.]

TIM /El'S OF PLATO.

p. 73

Arxl again the sesqniterlian, afterwards the sescjuialfor, and then three sesquialter* in a following order, as is evident from tin* above description.

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

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.

K

p. 74

PROCLUS ON TIIK

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< liniirgic 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 imi 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*.

BOOK 111.]

TIM.EUS OF PLATO.

p. 75

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 penei 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.