Page:Works of Plato his first fifty-five dialogues (Taylor 1804) (Vol 2 of 5) (IA Vol2worksofplato00plat).pdf/454

 444

INTRODUCTION

TO THE TIMiEUS.

monized is dependent on others, by which alſo it is naturally moved.

But

the harmony of the foul fubfifts in the middle of thefe two, imparting har¬ mony to others, and being the firfl participant of it herfelf. In order to underftand the figure of the foul, in the firfl; place, mathema¬ tically,

conceive all the above-mentioned numbers to be defcribed in a

certain firaight rule, according to the whole of its breadth ; and conceive this rule to be afterwards divided according to its length.

Then all thefe ratios

will fubfift in each part of the fedlion. For, if the divifion were made accord¬ ing to breadth, it would be neceffary that fome of the numbers fhould be feparated on this fide, and others on that.

Afterwards let the two lengths

of the rule be mutually applied to each other, viz. in the points which divide thefe lengths in half: but let them not be fo applied as to form right angles, for the intended circles are not of this kind.

Again, let the two lengths be

fo incurvated, that the extremes may touch each other ; then two circles will be produced, one interior and the other exterior, and they will be mutually oblique to each other.

But one of thefe will be the circle of famenefs, and

the other of differences and the one will fubfift according to the equinodtial circle, but the other according to the zodiac : for every circle of difference is rolled about this, as of identity about the equinodtial.

Hence, thefe redti-

linear fedtions ought not to be applied at right angles, but according to the fimilitude of the letter X, agreeably to the mind of Plato, fo that the angles in the fummit only may be equal; for neither does the zodiac cut the equi¬ noctial at right angles.

And thus much for the mathematical explanation

of the fwure of the foul. O But again, fays Proclus, referring the whole of our difcourfe to the effence of the foul, we fhall fay that, according to the mathematical difciplines, continuous and difcrete quantity feem in a certain refpedt to be con¬ trary to each other ; but in foul both concur together, i. e. union and divi¬ fion.

For foul is both unity and multitude, and one reafon and many ; and

fo far as fhe is a whole file is continuous, but fo far as number fhe is divided, according to the reafons which fhe contains.

Hence, according to her con¬

tinuity, fhe is affimilated to the union of intelligibles ; but, according to her multitude, to their diftindtion.

And if you are willing to afcend Fill higher

in fpeculations, foul, according to her union, pofTeffes a veftige and refemblance of the one, but according to her divifion fine exhibits the multitude of