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

And the geometric middle extends the same ratio to all the terms ; imparting by illumination union to first, middle, and last natures, through the presence of essence to all tilings.

The Demiurgus therefore imparts three connective unions to the soul, which Plato denominates middles, as binding together the middle order of wholes.

* It i* litre necessary l« tlie wools t] rwr trrpori |rwr.

* For here, it is necessary lo read rvt

p. 80

PKOCLUS ON THE

[book 111.

And of these, the geometric middle collects the multitude of essences, and causes essential progressions to lie one : for one ratio is the image of union. But the harmonic middle, hinds total samenesses, and the hyparxes of them into one communion. And the arithmetical middle, conjoins first, middle, and last dif¬ ferences. For, in short, diil'erenre is the mother of numbers, as we learn in the Parmenides. These three, however, \i/.. essence, sameness, and dillerenee, are in each part of the soul, and it is requisite to conjoin all of them to each other through a medium and colligative reasons.

In the next place, w e >..) that the soul is a plenitude of reasons, she being more simple than seiisihh-s, hut more composite than intelligihles. Hence imnrus assumes seven ratios m the soul, viz. the ratios of equality, multiplicity, suhumltiplicity, the sup* rparticular and superjiartient ratios, and the opposites of these, the siihsiijHTpartic.ilar, anil subs.qierpartient, hut not the ratios which are eompounded from these. For these are adapted to corpor. a! reasons, since they are composito and partible. The reasons in the soul, however, proceed indeed into multitude and partihility, vet together with multitude, they exhibit simplicity, and the uniform in conjunction w ith a distribution into parts. Hence tin y are not allotted an hypostasis in the monad, and the impartible, in the same manner as intellect. For intellect is alone monadic ami impartible. Nor does the mul¬ titude of them proceed into composite reasons. And multiple ratio indeed is in oneway only partible, viz. according to the proluiitu 1 or greater term : for the hyJ>olo"Os, or less term, is without division, and is not prevented from being unity. But the siiperparticular, is divisible in a twofold respect, viz. according to the prologos and hypologos; hut is impartible according to dillerenee.* And the biqverpartient is partible, both according to the prologos and hypologos, and ac¬ cording to dilh reiice. 1 So that the first of these, is div isihle in one way only, the second hilariously, and the third trifarioiisly. But equality is impartible. Tlie sold therefore constitutes the universe by these ratios ; the cnrporeal-formed nature indeed, by that which is tnl iriously partible; the nature oi superhetes by

But equality is impartible. Tlie sold therefore constitutes the universe by these ratios ; the cnrporeal-formed nature indeed, by that which is tnl iriously partible; the nature oi superhetes by

* Thus for instance, 3 .! to 4 is a multiple ratio, which ill its lowest terms, is that of S to 1 . But J it div isihle, ami 1 accurately speaking is nut. Broclus, therefore, in what he now says, speaks of multiple ratio when reduce*! lo its lowest terms.

1 Thus llie superparlicular ratio of 0 lo 1, o in Hs lowest lerms the rate * f 3 lo , and bolh 3 and J are divisible, dut this latio according to the differ*nee of the terms, is indivisible; for this diflertiKC h 1.

t hus for instance, the su|vrrparlieul ratio 3 to 5, which is superhiparticnl, being in Us lowest terms, for this isthe case with all superpartient ratio*, is evidently partible, both according to the ptologot and hypvlogoi ; and it is al»o partible according to the difference of the terms. For tins dif¬ ference is

BOOK III.]

TIM XUS Ol PLATO.

p. 81

that which is hilariously partible ; every linear nature, hy that which is partible in one way only ; anti hy the impartible the impartihility which comprehends all things. For there is something impartihle in partible natures. These things, therefore, are truly asserted.

p. 81

that which is hilariously partible ; every linear nature, hy that which is partible in one way only ; anti hy the impartible the impartihility which comprehends all things. For there is something impartihle in partible natures. These things, therefore, are truly asserted.

It is necessary however, to survey these after another manner; premising, that mini hers which are more simple, and nearer to the monad, ought to he conceived as more primary than those w hich are more composite. For Plato also. Inn ing arranged one part prior to all the rest, refers all of them to this, and > mis in terms which are especially composite and solid. Having therefore premised this, I say that equality and the ratio of equality, has the relation of a monad to all ratios. And what the monad is in quantity perse, that the equal is in relathe quantity. Hence conformably to this, the soul introduces a common measure to all things which subsist according to the same reasons; which measure likewise, brings with it one idea the image of sameness. But according to the suhmultiple, and multiple ratio, it governs all the whole series of things, connectedly comprehend¬ ing them, and exhibiting each total form of mundane natures frequently produced hy itself m all mundane beings. Thus, for instance, U produces the solar, and also the lunar form, in divine souls, in demoniacal and human souls, in irrational ani¬ mals, in plants, ami in stones themselves, and adorns the most universal genera hy the more partial series. And according to the snperparticular and suhsiiperparticular ratios, it adonis such things as are wholes in their participants, and which are participated according to one certain thing contained in them. But according to the buperpartient and subsuperpartient 1 ratios, it adorns such things as are wholly participated by secondary natures, in conjunction with a division into multitude. For of animal indeed, man participates, and the whole of this form is in him, yet not alone, but the whole is in him according to one thing, t it. the human form; so that it is present to its participant with the whole, and one certain thing w hich is a part of it. But what are called common genera, par¬ ticipate of one genus, yet not of this alone, but together with this of many other genera also, which arc parts, ami not a part of that one genus. Thus, for instance, a mule participates of the species from which it has a co-minglcd generation. Each species, therefore, either participates of one genus according to one, and thus imitates the superparticular ratio w hich contains the w hole, and one part of the whole; or it participates that which is common and many things besides, and thus imitates the superpartient ratio, which together with the whole possesses also many parts of the whole. And besides these there is no other participation of

Tim. Plat. •

1 Xwt-rifitptf as omitted in lb* original.

Von. II.

L

8*2

I'ROCLUS ON THE