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

Hence, we conceive that the right lines ought not to lx* applied to each other at right angles, but like rest of ihe sentence in the translation is added from the version of Tliouiaus.

* In the original of this place there is nothin" more than rouo ynfi .ri ou ravror to fiTjtot. 1 i.e

* Thus for instance, tel ihe number* be disposed according lo depth as follows :

1 . 2 . 3 .

p. 4

• •

8 .

‘-’7

Ac.

1 . 1 . .1

p. 4

• V

S

J7

AC.

i . . a .

p. 4

. >1 .

s .

■-*7

Ac.

i . g . a .

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• !•

. S .

•7 iV c .

1 . J . 3 .

. 4

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Then the line* drawn longitudina'b. will rcpiesvnt the division of the rule according I® length

BOOK lit,]

T1 MAX'S OF PLATO.

Ill

th<* letter \ as Plato says, so as to cause the angles to Ik? equal only at the summit, but those on each side, and the successive angles, to he unequal. For the equi¬ noctial circle does not cut the zodiac at right angles. Such therefore, in short, is the mathematical discussion of the figure of the soul.

equal only at the summit, but those on each side, and the successive angles, to he unequal. For the equi¬ noctial circle does not cut the zodiac at right angles. Such therefore, in short, is the mathematical discussion of the figure of the soul.

Again however, surveying the things themselves from the beginning, let us refer what is said by Plato, to the psychical essence. And, in tlie first place, we must obsone, that continued and discrete quantity are divided from each other, accor¬ ding to the mathematical sciences, and are in a certain way opposed to each other, so that it is not possible for the discrete to be continued, or the continued to be dis¬ crete quantity. In the soul however, both these concur, viz. union, and separ¬ ation. For it is a monad and number, one reason, one multitude, anil many things. And as being a whole indeed, it is continued ; but as number, it is di¬ vided, according to the reasons which it contains. Through its continuity like¬ wise, it is assimilated to the union of intelligible^, but through its multitude, to the separation of them. And by ascending still higher than these, wo shall find that according to its union, it possesses an image and representation of the one, but according to its division, of the multitude of the divine numbers. Hence, it nei¬ ther has an arithmetical essence alone ; for it w ould not be continuous ; nor alone a geometrical essence ; font would not 1m* divided, lint it must Ik* said, that it is at one and the same time both the arithmetical, and the geometrical essence. So far however, as it is the arithmetical essence, it has also, at the same time, the harmnnic.nl essentially. For the multitude in it is harmonized, and it comprehends in sameness, both absolute anil relative quantity. Hut so far as it i*> the geome¬ trical, it contains the spherical essence. For the ciicles in it are both immove¬ able and moved ; immoveable indeed essentially, but moved according to a vital energy. Or rather, it possesses both these at once; for they are self-motive. Hut the self-motive, is at one and the same time moved and immoveable. For it moves itself. Hut to move, or be the cause of motion, jiertains to immove¬ able power. The soul therefore, comprehends essentially all sciences ; geometry indeed, according to its wholeness, its figure, and its lines; but the arithmetical science, according to its multitude, and the essential monads in it, as we have before shown. Hut it comprehends the harmonic science, according to the ratios of numliers ; and the spheric science, according to its twofold circulations. In reality also, it is the essential, self-motive, intellectual, and united bond of the mathematics, comprehending all things unaccompanied with figure, and with limit filed purity. Hence it comprehends figures iinfiguredly, things separated, unitedly, and without interval things accompanied with interval. For these pertain to the essence of the soul. And it is necessary to survey all things in it aAcr this manner.

Hence it comprehends figures iinfiguredly, things separated, unitedly, and without interval things accompanied with interval. For these pertain to the essence of the soul. And it is necessary to survey all things in it aAcr this manner.

p. 112

IMtOl'LlIS ox Tim

[hook iii.

Moreover, this likewise ought to be assumed from what hns been said, tliat nil secondary natures, are analogous to those? that are prior to them, and that e\erv where, (he one precedes multitude. For as the theory of the hyparxis of the soul commenced from its essence, and that of its harmony from the e/n part, thus ;dso the doctrine concerning its figure, places the one length prior to the two. And as sameness and dillereiici are from essence, so the triple and duple ratio are from the monad, but from the one h ngth, the circle of the tunic, and the circle of the different. As likewise, tin* antecedents are to the antecedents, so are the consequents to the consequents, and all things are homologous to each other, viz. essence, harmony, and form. Vnd all tilings are indeed everv when-, on account of the ps\chi«‘.d lile, beiii '4 as it were ot one colour, and of similai parts. The tome however, and the triple, subsist m a greater decree in the circle of (he same, but the d/jf event, and tin duple, in the circle ot the different. All the ratios likewise, arc e\ery where, but after a different manner in first and secondary natures; in the former indeed, intellectually, totally, and unitedly; but in the latter, doxastieally, distributively, and partially. And thus much concerning these particulars.