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

• y a* util as 1 may be said to have the form of the duad, in consequence of being a square number or the trevnd power nooK in.]

TIMiEUS OF PLATO.

powers, ami that through the former, he separates his kingdom from that of his father, 1ml through the latter, misjx mis the whole of his fabrication from the pater¬ nal monad. They likewise call energies of this kind, sections and bonds. According to these powers therefore, the Pemiurgus now' separating the essence of the soul in demiurgic bonds, is said to cut oil parts from its wholeness, and again to bind the parts with certain bonds through the middles, through which also, he makes that w hich is divided, to lie connected, just as through the sections he causes that which is united to be divided. Hence, that these things are conformable to theological principles, the words of Plato manifest. Li t us however see how they are so, by considering more minutely what he says. That the whole soul then, is with reference to itself, of the same essence, and consists of similar parts, and is as it were of the same colour, being wholly intellectual and intellectual reason, Plato manifests, by making both the wholes and the parts in it, from the same mixture. For the parts which are cut off from it, are certain divided essences in it. 'Flint there is also a certain dignity in it of iirsi, middle, and last forms, he evinces by adding the word still. For in those things, in which wo wr the same form more obscure, in these we employ the word still; as we do in the celestial essence, in consequence of perceiving a certain mutation about it, and also a si¬ militude to divine bodies, preserved in it. In order therefore that we may not suppose there is the same dignity of all the reasons in the soul, Plato adds the word still, indicating hy it that which wo have mentioned. For by how much the more inwardly wo proceed, and investigate the media of media, hy so much the more shall we meet with more partial forms. For comprehended are more par¬ tial than comprehending natures; ami the.latter are more divine than the former. The world likewise imitating this, has indeed about generation a divine body, hut about body the whole soul. All these before-mentioned sections therefore of the soul, both the generative (for these are the double intervals), and the perfec¬ tive (for these are the triple intervals), are comprehensive of more partial reasons, through which the parts of the universe .are adorned, us far as to the last of things.

“ So that in each interval' there are two middles, one of which, ex¬ ceeds and is exceeded by the same part of the extremes ; but the other, by an equal number surpasses one extreme, and by an equal number is surpassed by the other ." 1

In these words it must he observed in the first place, that the two middles are 2ifly k mrr^«pn)r.

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[book 111.

said by Plato to be comprehended in the geometric middle; and afterwards, that he places the harmonic prior to the arithmetical middle, as being superior to it. For though the arithmetical middle has the spontaneous, and the simple, and an alliance to sameness; for equality is a certain sameness ; and hence Plato shows that m polities the arithmetical middle is effective of friendship, since it embraces the equal according to number, just as the harmonic is effective of justice, since it regards distribution according to desert; and still farther, because the arithmetical middle is allotted quantity per se, but the harmonic, relative quantity; and the for¬ mer is surveyed about the absolute quantity of the parts, hut the latter, about the relative quantity ; 1 for the third, or the fourth part, is the peculiarity of relative quantity ;—though all this be the rase, yet the harmonic, as being nearer to the geometric, is verv propertv arranged before the arithmetical middle: For it affords sameness in the extremes, and distributes greater ratios to greater, but less to less terms ; and through this, is more adapted to distribution according to desert. It must be said therefore, that the harmonic middle binds together all the psychical sameness, and imparts to celestial natures an indissoluble communion ; distri¬ buting to tin* greater circles indeed, greater powers and motions, but to the less, less powers. For the comprehending are moved sw ifter than the comprehended spheres. For the arithmetical middle connects all the difference in the soul, and imparts to sublunary natures, a communion with each other, according to an equal permutation. For among these, one thing is not at all more acted upon by, than it acts upon, others. And this property of being changed into each „tbi r, is equally inherent in all die r lements in generation, according to arithmeti¬ cal equality ; which also imparts to more attenuated natures, greater and swifter motions, hut slower and less motions to such as consist of larger parts.

“ I5nt as sesquialter, sesquitertian, and sesquioetave intervals were pro¬ duced from those bonds in the former intervals, he filled with the interval of the sesquioetave, all the sesquitertian parts.”

That from the above-mentioned tw o middles, the harmonical and the arithmetical bonds being produced in the intervals of the double and triple terms, the sesquiter¬ tian and sesquialter ratios appearing in those middles, are cut by the interval of the se-quioctave, is evident from w hat lias been said, and w ill also be manifest, if you direct your attention to the terms (3, H, 1*2, and 18.* l or in these, the double ami