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

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.

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 Dintdie, 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.

V «>. 8. J7, are raid t>\ P.oclun to t»e inserted between the geometric Dintdie, 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.

of the soul, the more'total contain the more partial. Since, however, the srsquiortaves are the muses of the mo-t partial symphony, that uhic.li is posterior to them is not undeservedly said to he imp< lied into the la^t order of the univi rse. j\ot that even this is dissonant to the whole itself, since it compels ihe partial rfliuxinns from each of the elements, into the place under the earth. Tor as the elements exist in many places, in the heavens, and in the sublunary region, this biuinia collects the last dregs of them there, and conjoins them to wholes ; so that Imtli together may give completion to the whole harmony of the universe. In short, theretore, the soul is the cause 1 * * 4 of all the harmony in the centres, and hi the elements of the universe. Ilem e also we say, that the harmony of it is entirely intellectual and essential, causally preceding sensible harmony. And Tinueus wishing to indicate this through images,* employs harmonic ratios, and pre-supposes in the soul some causes more comprehensive than others, and which subsist prior to every form of the soul ami to all its knowledge. lienee I think it is not proper to discuss any thing of this kind, so as to explain [in a merely mathematical wa\] either tin* parts, or the ratios, or the analogies; hut it is requisite to survey all these essentially, according to the first division itself, and harmony of the soul. It is also necessary to refer all things to the demiurgic and intellectual cause; but to comprehend the sesquioelaves and leimmas in the srsquitertian and si squialter ratios ; tin se in the middles ; and these in one of them which is the most principal of all ; and likewise to reduce the more partial to the more total causes, and sur¬ vey them divided from them. And thus much concerning the harmonic ratios, lint again adducing the text from the beginning, let us endeavour to discuss it more clearly.

“ lie first took one part from the whole. In the next place he took away the double of this. And after this, a third part, which was sesquialter indeed of the second, but triple of the first."

We hate before observed, that it is not proper to until rstand what is here said by Plato, lnathematieallv, but phvsicallv, or plul osopbically. For the essence of the soul, does not con.-ist of mathematical numbers ami ratios, but all these numbers and ratios, adumbrate its truly 1 existing essence, ami the demiurgic ami vivific divisions in it. llut of what things the mathematical ratios are images,*

1 The words rj v-i'X’J n,ria e<rn, arc omitted in llic original.

* For rtriruv here, il i>> necessary to read n.i i ui .

1 Instead of cvrwt in this place, it is requisite to read orr*n.