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
* Tlic word iiatrrtj/jan is omitted »n the text of Proclus.
* In the text of Proclua also the following word* are wanting, njr i' /icr car* aptBpor vr »pex*»rar,
ifly k mrr^«pn)r.
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
* lilt tie original vi/Vircrqt, which dciuilri relalne, just as wooorijt denotes absolute, quantity.
1 Tor S to 1^, wbuli is dia]>ente, or sesquialter, is coui|M>unded of S to)), which is a tone - and 0 to 8, which is sesquitertian, or diafessaron
TftLEUS OF PLATO.
triple consist of sesquitertiau and sesquialter ratios. But how will these things accord with what has I icon lx fore said ? We reply they must he assumed con¬ sequently to them. For as the two middles divide the universe into two parts, so the sesquitertiau and sesquialter ratios constitute a more partial order of tilings. For these ratios adorn things which exist as wholes, and yet are parts of parts. Each of tin m therefore is a w hole according to the prolngos, hut a part according to the hvpologos, and a part of a jiart, according to the transcen¬ dency of the one with reference to the other. And since in each of the spheres there arc divine and da-moniacal, and also partial genera of souls, such as the genera of ours, and the secondary divine genera wholly participate of the whole of those prior to them ; hut the d.emoniacal genera, though they participate of the whole of divine natures, yet it is according to one certain thing, on which account they are said to he more partial, not being aide to receive all the peculiarities of them; hut the more partial of daunoniacal natures, at diil'erent times participate of a dill'erent peculiarity, and not always of the same characteristics;—hence, the soul partihly contains the ratios of these. And it contains the multiple indeed according to the participation ol the whole ; hut the superparlicular, accordin ,r to one part only, and that the most principal ; and the sup* rpartient according to a communion which is both multitudinous and partible of the participants with the things participated. lienee, through these, the elements and the ci h slid spin res are adorned; participating indeed of the third wholeness, hut at the same time being parts of the two sections ot the universe ; since every wholeness has also parts m conjunction with itself. Different peculiarities therefore pertain to a different sphere, ’ and a dillercnt number proceeds w ith a different element. The sesquioctave ratio also giving completion to the sesquitertiau and sesquialter ratios, generates these plenitudes of the total parts, and coharmoni/es them with their proper wholenesses. ^ on see therefore, that as in the mathematics, the geome¬ tric middle comprehends the remaining two middles, lmt they comprehend the sesquitertiau and sesquialter ratios, and these the sesquioctaves,—after the same manner also, the soul according to the w holeness of itself constitutes the whole world; but according toils essential duad, divides the universe into two parts, and produces the first parts of the universe, which are secondarily wholes. Ac¬ cording likewise to the causes of the third wholeness, it disposes in an orderly manner, and adorns the spheres ; hut according to numbers adapted to these parts, it fills them with appropriate forms and parts.
We may also sjieah as follows : This universe has indeed whole spheres; ami
1 For aXAip *^a» pa here, it i« Decenary to read oXAm
[book tu¬
bas likewise divine, damoniacal and psychical animals in each sphere. For there are distributions of partial souls about each of the spheres. But the har¬ monic ratios of the whole soul, harmonize the essences which are divisible about bodies, and bodies themselves, l'or by its tcry essence [it contains all these, anti the ratios which comprehend them ;*] just as tire, lieing calefactive by its very ex¬ istence, is primarily hot. It contains therefore, the diatessaron harmony, through which it harmonizes the essences divisible about bodies ot each of the spheres, and of the divine, damoniacal, and psychical animals in each, and also bodies to each other. Nor is one thing casually comprehensive of another, nor do somethings casually follow others; lmt damoniacal follow divine animals, and psychical, such as are damoniacal; and conformably to nature, secondary are always co¬ adapted to primary essences. Hence the diatessaron harmony is in each of the spheres. And the ratios imb ed of each sphere to the divine animals contained in it, and of these to damoniacal animals, will be truly sesquioctaves, possessing a p» rfect interval; b< ing at one and the same linn: primarily harmonious, and adapted to bodies. For the ogdoad having a triple interval is corporeal formed, just as the ennead is a plane. But each is allied Inequality. And always se¬ condary corporeal essences are suspended from such as arc primary, paiticipatmg of them, and of the corporeal reason which they contain.* But this the part manifests which is said to he the eighth of the thing participated. 1 hat however vhich remains, is the ratio of psychical to da.-momacal animals, which has the relation of the leimma, is superpartient, and is adapted to thirteen parts. I*or these have not one life, since they ascend and descend, and partibly and anoma¬ lously enjov the natures prior to them. And since the number twelve is ascribed to the [mundane] (bids, and to the natures stijw rior to us, thirteen is adapted to those that do not rank in the number of the (iods. If also of psychical animals themselves, some pertain to undijilcd souls', which Plato is accustomed to call the souls of heroes; but others to gregarious souls, such as ours : if this be the case, the diapente 1 likewise will l>e in each of the spheres. And heroic souls indeed will preserve* towards the diemoniacal, tin: sosqmoctave ratio, through the undefiled form of life; but the souls of the multitude will have towards them the ratio of the leimma. .So that in each of the spheres, there will be sesquiterlian, sesquialter, uni sesquioctave ratios.
1 The words within the bracket* are wanting in the original, but arc supplied from the version of '1 honiauv
* Instead of Toy <y avrjj in tins place, it is obviously necessary to read, rov ty avrott.
1 bur ill cadi of the spheres there will be divine, dauuoiiiacal, beroical, and gregarious souls, and appropriate bodies.
hook ill ]
TiM/r;rs or pi.ato
Or r itlier, it may ho said, (lint tin? universe is divided quadruply, according to tin' four ideas of i(s paradigm, but that in racli of the four parts, time are all animals, the divine, the da-mnniueal, the heroiral, and those of human souls, all which are harmonically co arranged with each other, and with nferenre to their proper wholeness, whether it be tin* heavens, the air, the water, or the earth, the wholeness producing the diapente ; but w ithout this it may be said there is the diatessaron, in the four species of animals, a; Plato himself divides—viz. into the universe, and (he all-various forms of animals. Hence, through these things Plato delivers to us ratios comprehensive of ratios, and perfect according to one harmony ; with which ratios being reph te, the soul tills this visible world, render¬ ing all tilings eflahle and familiar with each other.
“ Leaving a part of each of them. And then again, the interval of this part being assumed, a comparison is from thcncc obtained of number to number, viz. of 23b to 213.”