Page:Works of Plato his first fifty-five dialogues (Taylor 1804) (Vol 2 of 5) (IA Vol2worksofplato00plat).pdf/452

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INTRODUCTION TO THE TIMJEITS.

be conſidered as reprefenling the foul of the world, abiding in, proceeding from, and returning to, herfelf, viz. abiding according to that firfl part, pro¬ ceeding through the fecond, and this without any paffivity or imbecility, but returning according to the third : for that which is perfe&ive accedes to beings through converfion.. But as the whole of the mundane l'oul is perfedf, united with intelligible^, and eternally abiding in intelledf, hence fire pro¬ videntially prehdes over fecond ary natures; in one refpedf indeed over thofe which are as it were proximately connected with- herfelf, and in another over folid and compared bulks. twofold.

But her providence over each of thefe is

For thofe which are eonnedled' with her effence in a following

order, proceed from her according to the power of the fourth term (4),. which poffeffes generative powers; but return to her according to the fifth (9). which reduces them to one.

Again, folid natures, and all the fpecies

which are difcerned in corporeal maffes, proceed according to the odiuple of the firfh part (i. e. according to 8), which number is produced by two, is folid, and pofTeffes generative powers proceeding to all things ; but they return according to the number 27, which is the regreffion of folids, pro¬ ceeding as it were from the ternary, and exifting of the fame order according to nature : for fuch are all odd numbers. And thus much for the hi-fi feries of numbers, in which duple and triple ratios are comprehended ; but after this follows another feries, in which the duple are filled with fefquitertian and fefquialter ratios, and the fefquitertian fpaces receive a tone.

And here, in the firfl place, in the duple progreffion-

between 6 and 12, we may perceive two mediums, 8 and 9..

And 8 indeed:

fubfifrs between 6 and 12 in an harmonic ratio; for it exceeds 6 by a third part of 6, and it is in like manner exceeded by 12 by a third part of 12. Like wife 8 is in a fefquitertian ratio to 6, but 12 is fefquialter to 8. Befides, the difference between 12 and 8 is 4, but the difference between 8 and 6 is 2. And hence, 4 to 2, as well as 12 to 6, contains a duple ratio : and thefe are the ratios in which the artifice of harmony is continually employed.

We

may likewife compare 9 to 6 which is fefquialter, 12 to 9 which is fefqui¬ tertian, and 9 to 8 which is fefquiodtave, and forms a tone; and from this companion we (hall perceive that two fefquitertian ratios are bound together by this lefquiodtave, viz. 8 to 6 and 9 to 12. Nor is an arithmetical medium wanting in thefe numbers ; for 9 exceeds 6 by 3, and is by the fame number exceeded