Commentary on the Timaeus of Plato

It is also necessary to refer all things to the demiurgic and intellectual cause; but to comprehend the sesquioctaves and leimmas in the sesquitertian and sesquialter ratios ; these in the middles ; and these in one of them which is the most principal of all ; and likewise to reduce the more partial to the more total causes, and sur vey them divided from them. And thus much concerning the harmonic ratios. But again adducing the text from the beginning, let us endeavour to discuss it more clearly.

" He first took one part from the whole. In the next place he took away the double of this. And after this, a third part, which was sesqui alter indeed of the second, but triple of the first." W e have before observed, that it is not proper to understand what is here said by Plato, mathematically, but physically, or philosophically. For the essence of the soul, does not consist of mathematical numbers and ratios, but all these numbers and ratios, adumbrate its truly' existing essence, and the demiurgic and vivific divisions in it. But of what things the mathematical ratios are images,* ' The words rj \,v^rj nina tart, arc omitted in the original. 1 For fieo-wc here, it is necessary to read ru-nrwr. 1 Instead of ovrwi in this place, it is requisite to read orrwt. * For eurorwi here, it it neoessary to read «««ort«. Tim. Plat. VOL. II. M yU 1'KOCLUS ON TIlli [BOOK HI. and how they develope the essence of the HOid of the universe, it is not easy for those to assign, who do not look, to the conceptions of Plato. Hut this is munif.-st from the discord of the interpreter* ; and the opposition of the modem to the more ancient expositor*, evinces the dillicully of this theory. For some of them think lit to refer 1o the woven spheres, the first seven terms, to whirh we have as sumed as analogous the numbers that exhibit the whole diagram.

1ml others refer them to the distances of tl.e spheres from the centre of the eat ill, ill which place they arrange the monad. Others again, refer them to (he motions of the spheres. [Others, to the magnitudes of the stars. And others adapt them to the velocities of the celestial orbs.]' Hut others, refer them to other such like expla nations. Their interpretations however, are attended with many difficulties, and among the rest with this, that they are discordant with the observations of recent astronomers, and to the demonstrations given by them. To which also may be. added, that Plato no where defines, either the magnitude, or the distance, or the swiftness, or the motion of the stars; but admitting that one star is greater than another, lie does not add how much, and aftt-r what manner, it is greater. And that the thing proposed by him to be discussed in this part, is psychogony, and not cosmogony. For though it is requisite to effect the same things, in a certain respect, in the soul, and in the world ; yet it is proper first l to survey the powers in the soul itself, and the reasons of the things which are effected external to it. Hut their explanation of the terms or numbers given by Plato, is especially contrary to them. For in the terms, that which has the fifth order, is greater than the sixth, as for instance, !) than ».' In what they say, however, the fifth magnitude, or interval, or whatever they wish to call it, is entirely less than the sixth. Their expositions, therefore, do not accord with the Platonic terms.

Afterthc.se, there is another triU- of interpreters, who give a more important explanation of these particulars. For Amelins not adopting the opinion, — which he says was that of Plotinus, was delivered by him, in his unwritten or oral con ferences, and has Ix-en siilliciently confuted by those posterior to him,*— endea vours to explain these terms after another manner. For sine*' the soul is compre hensive of all mundane natures, as for instance of Cods, da-mons, and men; he savs, that in one way it comprehends according to the monad, every mundane 1 The words within the brackets are wauling in the original, and are inserted from the version of Lennicus Thomacui. * For wi.-rrpov here, read *f*jTtpov. 1 For ««.TII£G» here, it is necessary to read otrnfof. * The beginning of this sentence a wanting in the original, but is supplied from the version of Tliomxus. u'.ouiii.] TIM /BUS OF PLATO. 01 genus of Gods; nor must we \vonder, if the soul should I>o said to be compre hensive of Gods. This opinion, therefore, some one of those posterior to Amelius refer to him. For God is multifariously predicated, since not only tin; superessential and intellect are called Gods, hut likewise divine souls, and di\ine bodies. He is therefore of opinion, that the soul of the universe comprehends according to its unity the divine number; but according to its duad and triad, the (la'iiioniacal ^enus. For since daemons are suspended from the Gods, and preside over us, this soul, according to the duad, excites the providence of them ;

but perfects, according to the triad, the conversion of them to the Gods. For, as we have said, the habitude of them is twofold, because they are between the Gods and us. But according to the tetrad and ennead, it providentially attends to all human life. For this also is twofold, being divided into the Ix-tter and the worse. And by the ennead indeed, it adorns the more excellent, but by the tetrad arranges the subordinate life. Justly, by the octad and the number twenty-seven, it proceeds to every thin^, and as far as to the last of things, and perfects tame animals by the odd, but savage animals by the even numlMT. For it adorns each thing by appropriate powers ; subordinate natures, every where by even numbers, but more venerable and powerful natures, and which in a greater degree are allied to the Gods, by odd numlnTs.

Porphyry, however, after a certain admirable manner, (though these things have been before related) evinces by many arguments, that the soul is harmonized, and that it (ills the whole world with harmony. But he infers this from the soul being a multitude. Bring however a multitude, it is either without arrangement, or is harmonized. But it is true to assert the latter of it, and not the former. For being the fabrication of intellect, how can it be inordinate, and nnharmonized ? lie also infers it from this, that the soul conducts every thing in the world by harmonic reasons, and refers the generation of animals, and the one co-ordination of them, to the universe, \\hat, however, these reasons an-, which are sc< n to subsist in the very hypostasis of the soul, he neither teaches, nor thinks them deserving of attention ; but says that the essence of the soul possesses in itself harmonic reasons, not as the images of some things, and the principles of others, but as binding together the multitude of powers it contains. For it it is in reality not only impartible, but also partible, it is not only necessary that its essence should !«• one, but likewise that it should !>c multitudinous. But if multitudinous it must either be innumerable, or numerable. It is impossible, however, that it ' should be innumerable. For an innumerable multitude is inordinate. It is therefore numerable. Uut if numerable, it either consists of nnharmoni/ed or of harmonized parts. It is however impossible that it should consist of unhar-

04 IMIOCLL'S ON THE [BOOK m. monized parts : for it has not any thing of this kind naturally. It therefore entire ly consists of harmonized parts; but if of harmonized parts it must necessarily subsist according to the most excellent harmony, since it is the first of things harmonized. The most excellent harmony however, is that which is according to the diatonic genus : for this is venerable, abundant, and grand. Hence, the soul is entirely harmonized conformably to this ; so that its essence will consist of parts harmonized according to the diatonic genus. These things, however, being true, nothing prevents the harmonic ratios from being at the same time images of certain divine things; just as the body of this soul is indeed spherical,' yet through its sphericity, is said to be an imitation of intellect, and these things accord with each other. And thus far 1'orpliNry, who, in what he here says, affords us an occasion of collecting something true concerning the soul. But the divine lamblichus celebrates these numbers with all his power, as ex hibiting certain admirable peculiarities. And he calls indeed the monad, the caii-e of sameness and union ; theduad, the supplier of progression and separation ; and the triad, the leader of the iv^n -ssion of the thin-s that have proceeded. lie also savs, that the tetrad is truly all-harmonic, containing all ratios in itself, and unfolding in itself the second orderly distribution of things;

and that the ennead is effective of true perfection and similitude, being perfect from perfect numbers, and participating of the nature of sameness. But he calls the o^doad, the rinse of universal progression, and of pervading through all things. Lastly, he says, that the number twenty-seven is ef fective of the regression of the last of things to the first, in order that on each .vide of the tetrad, there may be permanency, progression, and regression, there primarily, but here secondarily. For the ennead has an alliance to the monad, being rt lira' one (;v nt,v c^a-a); but the ogdoad to the duad, being the cube of it; and the number twenty-seven, to the triad, through a similar cause. Through the former numbers therefore, the soul imparts to more simple natures, permanencies', progressions, and regressions, but through the latter it imparts these to more com posite natures. But the tetrad being the middle, because indeed, it is a square, has jM-rmanency ; but because it is evenly-even, has progression ; and because it is filled with all ratios from the monad, has regression. These, however, are symbols of divine and arcane, things.

After this explanation, which is thus admirable, the philosopher Theodora*, proceeding in a certain path peculiar to himself, says, that the soul is the third principle after the one principle of all things, one soid being fontal, another uni versal, and another the soul of this universe. He also says, that the lir>t of these is indivisible, the second divisible, and that the third possesses all-various divi sions. Since therefore, there is a triple difference of soul, that which is soul itself and is fontal, subsists between tlie impartible and partible essence ; of which the former is universal intellect, but the latter is divisible into atoms. Hence the first soul is the medium between these, as subsisting from both which are prior to it, and becoming one whole from the three middle genera. But the second, and which is universal soul, is divided into parts, and is harmonized. For the first soul, abiding wholly in itself, a division is produced, which is a progression from the soul that is a whole prior to parts, into the soul that consists of parts. And the third stud is that which is fabricated through right lines and circles. For in this the division manifests a diminution from that soul which is a whole prior to parts. Hence he divides the whole of this discussion concerning the psychogony into three parts, conformably to the three souls that have been mentioned; one subsisting according to the mingling, another according to the harmonizing, and another according to the forming energy of intellect.

Having therefore, made this division of the psychogony and souls, he considers the distribution into parts, and the seven terms, as alone pertaining to the uni\ersal soul. Re ferring likewise these terms to the division of the unhersal soul, he thinks it necessary that celestial natures should be produced by this soul from the duple, but sublunary natures from the triple order. For he distributes appropriate num bers to each of the elements, to earth indeed 7, to lire 11, to water i), and to air 1.3. For the geometrical. proportion, which is 1, 2, 4 [and the sum of the termsof which is 7] pertain* to cartli ; perhaps indeed on account of the name ; and j>erhaps also, because as earth contains the remaining elements, so the geometric comprehends the oilier middles. But the arithmetical proportion which pertains to water, is -2. 3. 4; through 2 communicating with earth, and because likewise, it is especially friendly to multitude, and consists of an element which is the most multitudinous of all others, vi/.. the icosaedron. And the harmonical proportion, which pertains to air, is 3. 4. (» ; because this communicates with the arithmetical, according to two of its terms 3 and 4, which are the greater in the former, but the less terms in the latter, proportion. Since, however, the harmonic middle is two fold, consisting either in the duple ratio of the extremes, or in the triple ratio;

for Plato assumes it as the middle of either duple or triple terms; — hence, making the extremes to be 3 and (}, according to the double of the extremes, [i. e. accord ing to a duple ratio] he obtains the peculiar element of the air, viz. the octaedron, which has G according to the angles, but 4 according to the base of the two pyra mids, and 3 according to the superficies of the octaedron, which is trigonic. But according to the other harmonic middle, which is '2. 3. (5, he obtains the ele ment of tire; liccause these according to the two terms 3 and (» communicate with the terms prior to them [3. 4. 6], which are there the extremes, but are here the

94 PROCLUS ON THE [BOOK in. greater terms ; and moreover, because the element of fire has 0 sides, but twice the tetrad, in its angles and sujR'rficies, and a triangular base. Very properly, therefore, does 7 pertain to earth, 9 to water, 13 to air, but 11 to fire; the ratios being assumed in the above-mentioned numbers, from which they are pro duced. For 7 consists of 1. 2. and 4 ; 9, of 2. 3. and 4 ; 13, of 3. 4. and 0; and 11, of 2. 3. and 6; each having two terms in common with the number next to it, just as the elements have two sides in common. From the composition how ever of these, a triple order is effected. And of the middle terms of the propor tions proximate to each other, the one is greater than the other, which is also the case with the extremes, as is evident in earth and water, and in fire and air,1 as is evident in the given terms. Again, he attributes the number 15 to celestial natures; the monad indeed, to the circle of same, but the double hebdomad to the circle of difli rent, on account of the twofold circulation of each, viz. of the spheres themselves, and the stars contained in them, which are seven, the spheres being also seven. These things, however, which are mathematically asserted, bring with them a certain not inelegant theory.

Uut how they are assimilated to the things which are now discussed, and how they may l>e 1'jthagorically interpreted, is not at all noticed by Theodorus, in such a way as to be able to satisfy him who does not negligently attend to what Plato says. All the>e particulars are indeed ele gantly invented, but he refers the analysis of the Platonic diagram to monadic numl>ers, not looking to the ratios resulting from them, so as to assume every thing, viz. the middles, the oesquialter and sesquitertian ratios, the sesquioctaves and leiminas ; it being by no means possible to discover these in the first num bers, which he employs in the above-mentioned di.strihutions, into the elements and the heavens.

After these, therefore, let us survey another mode of discussion, which is adopted by our preceptor, is generative not of one only, but of many and admir able conceptions, and which we also made use of In-fore. He says then, that each of these things may be considered in a twofold respeet, in the whole soul of the universe as one, according to union, and in the many ratios, and in the multitude contained in it, according to division. For the soul is both one and multitude, one reason, and the numl>er of all-various forms, and imitatesthe demiurgic whole ness, and the separation of the powers of the father. In the first place, therefore, we must understand what it is according to the whole of itself, abiding, and pro- • Thu»inthe number* 1. '2.4, which pertain to earth, and in 2. 3. 4, wh'uh pertain to v»*l« r, (lie mid dle terra 3 i» greater than the middle term v>, and llu> is also the case ioth«- mini her* 3. 4. <>, and 2. 3. (i, the former of which pertain U air, and the latter to fire. In the extreme* *l»o, the extreme C it greater than 1, and the extreme 3, than •«,'.

ceeding in itself, and returning; to itself, and also providentially attending in one way to the immaterial and pure forms of mundane natures, hut in another to all bodies, and the partihle essence. Understanding this likewise, we must say, that it abides according to the one or first part; but proceeds according; to the second, the progression being conceived to l>e divine, and not according to passion or imbecility; and that it returns according to the third part. For the jierfective accedi-s to beings from this. But being all-jierfect, and established* in intelligibles, and abiding eternally in intellect, it also providentially attends to secondary natures. And in one way indeed, it providentially inspects the natures that are proximately suspended from it, but in another, solid masses themselves. It like wise attends to each of these in a two-fold respect. For the natures which proxi mately participate of it proceed from, and return to it; proceeding indeed, ac cording to the prolific power of the fourth part, hut returning to their one cause, according to the re-elevating power of the fifth part. We may also survey these solid numbers in corporeal masses ; which proceed indeed, according to the octu ple of the first part, this numlier Ix-ing dyadic and solid, and at one and the same time prolific, and capable of proceeding to all things; but they return according to the nnmlier twenty-seven, this being a solid conversion, as triadic, and as per taining to the nature of sameness.

For such is the odd number. Hence, there are three progressions, and three regressions, about the one and united perma nency of the soul. Hence too, there are three even and three odd numbers, proceeding from the monad, and complicated with each other; localise the soul itself also proceeds, and returns. And proceeding indeed, it produces the first receptacles of itself, and that which is primarily invested with figure. Producing it also, it imparts interval to it and bulk. But in its regression to itself, it causes it to be spherical, and on this account causing it to be a thing of this kind, it produces the world in it; effecting the progression of it according to the even » number, but the regression according to the odd number, and both these cubically, lie-cause it is the generation and regression of solids. The progression therefore, and regression are triple ; the first being unfigured, the second accom panied with figure primarily, and the ' third secondarily ; hut ail these as in numbers.

In the next place, we must pursue the theory, conformably to the multitude which is in the soul, and Hay that the ratios in it are comprehensive of ratios. 1 For cfi/fpfj^iryifK litre, rrad cn^pv/urrijr. * For aftruut in this place, read nnnarwi. * It i* Mcctsary here to supply the words wpvrw, «r 4e. 90 PROCLUS ON THE [BOOK in. And some of them indeed, are divided in it, after the manner of wholes, but others after the manner of parts. ' And some are total, others generic-, others specific, and others partial. The total indeed, are such as the ratios of the middles ; hut the generic, are those which are found in the duple, or triple terms ; and the nj>ecific, are tho>e which are under these.* Tor each of them has a multifarious subsistence. .But the partial ratios are those of the sesquioctaves and leimmas, into which, as parts, all the sesquialter and sesquitertian ratios are di vided. We must also say, that the soul contains tht one union of the ratios, through the essential monad ; but the division of the ratios, through the progression of the. duad ; and the comprehension of them, ' through the multiple terms. For these are comprehensive of the .super-particular ratios, and have ;ui essence more total than these ratios; just as tin- super-particulars comprehend the sesquioctaves and leimmas ; the former having the relation of species, but the latter being arranged in the order of parts.

For to make the geometrical proportion alone comprehensive of the other two middles, in the first place, causes the whole essence of the soul to be as it were demiurgic geometry. For elsewhere, Plato calls this analogy the judgment of Jupiter. In the next place.it shows that these two mid dles, when surveyed with the geometric middle, and comprehended in it, dispose wholes in an orderly manner according to justice; but that when separated from it, they ure the causes of confusion and injustice. For a distribution of the equal to things unequal, is entirely unjust ; as is aKo, the conjunction of contraries to each other, without a certain geometrical equality. Hence the harmonic middle is in want of the geometric analogy, in order that it may bring together contraries elegantly, just as Plato did, in harmoni/ing lire and earth, through the two

O * * nt elements [of air and water]. The arithmetical middle likewise, eiier^i/ing together with this, possesses rectitude in its operations. For thus the unequal in unequal things is equal.4 Distributing therefore equals to unequal*, it preserves the peculiarity of itself, and exhibits distribution according to desert, which is the prerogative of the geometric middle. Farther still, we must say, that the soul imitates the first principles of things. 1 For f*tpi here, it is obviously necessary to read ^rpvt-. * i. e. They are the lupologi, which have been before explained. 1 IWtweeu (''m and roVVairXdaiuc In rr in (lie original, it is neccssarv to insert, conformably to the version of Thomarus, the words rr/» ^><i?ot rpooiou, ij Ir ruv Xuyun- rrpio^t) ria, t. \. * Thus in the terms 1. '2. 3. 0, which are in geometric proportion, the terms 1. 2. 3 also being in arithmetic proportion, the difference is uruquid between the terms 2 and 3, and the teniu 3 and <>, and also between the terms 1 and ?, and 3 and (i, but the ratio It equal ; and therefore, by the union of the arithmetic with the geometric middle, the unequal in unequal number* is equalized.

BOOK in.] TIM/EUS OF PLATO. 97 Through the first part indeed, the one cause of wholes ; through the duple pro gression, the bi formed principles after the one ; through the even and odd num bers, the male and female of the Gods; through the triadic division of each, the intelligible triads; and through the hebdomad of terms, the unical and intellec tual hebdomad. Through the first part also the soul makes ' the world to be a self-perfect God ; through the dyadic it exhibits the multitude and variety in it; through the division of even and odd numbers, it divides the whole of the male and female, from the Gods themselves as far as to plants ; according to the duad and triad indeed, the male and female in tho Gods, but according to the tetrad and ennead, those which are in the genera superior to us; and according to the two cubes, [0 and 27] the male and female which proceed as far as to the terres trial and ultimate1 species of life. But through the heptad of terms, it connects and guards all things, provides for them intellectually, and orderly disposes wholes in a becoming manner, stably and invariably. It likewise through this, adorns the parts of these, and the parts of the parts, and whatever there may bo among the last of things, which is of itself irrational, and as it were the leimma of the fabrication of the world. Hence conformably to these conceptions, we may be able to interpret the several words of Plato, and looking to these we may dissolve many doubts. 1st us therefore from the beginning refer the words of Plato severally to these, according to the explications of our preceptor.

In the first place therefore, not to say that the Demiurgus inserted the parts in the soul, but that he took them away from it as being already* in it, and that having taken them away, he again gave completion to the essence of tin; soul from them, indicates to us, that this mixture is not as it were the subject of the soul, nor as the matter of it, or that it is similar to that which is invested with figure, and receives this figure from the artist; but that being a form, it is the plenitude of forms ; so that the indefmiteness and the matter, which are said by the more recent interpreters to be in intelligibles, have no place in the present theory. Secondly, to co-arrange all the other parts, viz. the terms, 2, 3, 4, 9, 8 and 27 with reference to the first part, ascribes the principal dignity to the monad, and does not permit us to conceive it to be such a thing, as the multitude fancy the monad to be, viz. that which is the least in quantity, and having the relation of matter to number, but leads us to consider it as the ruling principle of all the essence of the soul, as the root of the powers contained in it, and the Vesta of the

1 For aa\rt here, it it necessary to read wwu. * Instead of ^Ooj-iwr in this place, as \tpaai*r i%j»sl before it, I conceive it to be obviously necessary ' Instead of >)?« here, it is neces>urv to read i^tj. Tim. Plat. VOL. II. N 99 PROCLUS ON THE [BOOK in. numl*r which gives completion to it. In the next place, does not the expression the double of the first part, accord with what has been said by us? For the double is entirely formed by the duad, and is inferior to the hyparxia which is charac terized by unity. It also proceeds into multitude, being increased in quantity, but diminished in power. Such also is the mode of the psychical progression. For the soul abiding according to the most divine part of itself, and as Orpheus says, establishing its head in intellect, it proceeds from thence, according to the duad in itself, proceeding into itself, and generating the multitude of reasons, and all-various forms which it contains. Having proceeded however, it again returns to its principle, thus producing a certain essential circle. Through this regression likewise, it is conjoined to the prolific power in itself, according to which it pro duced itself, and to the monad which establishes it, and causes it to be one. For the perfective and convertive power, is conjoined to both, vi/. to the prolific and to the one-making cause. And if it be requisite to speak concisely, as life pro ceeds from being, but intellect is conjoined to life, and to being, thus also the progression of the soul, is from the prolific cause, but its regression is to both causes;

in a sesquialter manner indeed to the cause which is [immediately] above it; but triply to the cause which is beyond this. For it is lit that the convertive or regressive form .should pursue the whole [of that to which it returns] and diminish division, which the sesquialter imparts. For the double being vanquished through the whole of itself by the duad, the sesquialter is indeed analogous to it, but diminishes the ratio of subjection.1

Farther still, it is evident that the triple exhibits the third interval in that which returns from the abiding principle. To which may lie added, that the triad being the first number, and primarily a whole, having a beginning, middle and end, is assimilated to the monad, which comprehends all multitude unically. Through this therefore, Plato shows, that the .subject of the soul consisting of three wholes, is again triple. For he divides it into the abiding, proceeding, and returning, according to the division of the divine genera. For in them also there is a triple genera, one of which abides, another proceeds, and another is converted, or returns to its principle. And one indeed is the cause of sameness, stable power, and essence; another, is the primary leader of generations, progressions, and multiplications; and another, is perfective, and the cause of the elevation of secondary to primary natures. But through the words that follow, he shows how 1 Thus 2 to 1 is a «1u|>le. and 3 lo 2 is a s^quialter ralio. But the latter is analogous to the former : for 2 : 1 : : 3 : "- The sesqublter Lowever diminishes tb« ratio of subjection. For '2 contains 1 twice, but 3 contains C only once and one Lalf of '2 besides.

the soul adorns secondary natures, according to the very essence of itself. For prior to the soul imparting powers or energies, he demonstrates that it contains these ratios in itself, from which, and through which it governs, the first partici pants of itself, and such things as are adorned by it, according to a second sepa ration from it ; itself indeed, having wholly the relation1 of a monad, but they imitating its* progressions and regressions. For the soul prior to them, proceeds indeed dyadically, but is converted triadically. And the whole of it indeed that proceeds, is separated from that which abides: for it is separated doubly. But that which is converted, or returns, is separated by half.1 For separation is the peculiarity of progression, but sameness and similitude of conversion. For that which returns, is made as it were that which abides, becoming all instead of one, and instead of a whole prior to parts, a whole consisting of parts. And it appears indeed to be the triple of that which abides ; but is less than it in power, and comprehensive of the parts contained in it. " Then u fourth part, double of the second, a fifth, triple of the third, a sixth, octuple of the first, and a seventh twenty-seven times the first."

The all-perfect essence itself of the soul, is comprehended through the abovementioned numbers ; of which one abides in the soul, another, proceeds from, and another, is converted to it. Since, however, it is necessary to survey the parts of it, and the causes of those things that are in it, these also Plato copiously explains, delivering to us, the comprehending and comprehended ideas in it of all things. Through the fourth therefore, and the fifth parts, the soul comprehends the reasons of all its first participants. And it contains indeed, the progression of them through the fourth part, but their regression through the fifth.4 [Hence Plato refers the fourth part to the second, but the fifth to the third, because parts imitate wholes, and subsist analogously to them.'] But through the sixth and seventh parts, it constitutes, as we have before observed, solid masses themselves; gene- ' It is necessary here, to supply the word Xoyoi/. 1 For HITCH in this place, it is requisite to read nvriji. 1 That which proceeds is separated doubly from that which abides : for the duple ratio 2 to 1, or ' is doubly separated from J. Hut that which is converted, or returns, is separated from the abiding principle by half. For ] differs from 1 by I. So that what proceeds, anduNoih.il which returns, are here to be considered according to habitude, i. c. according to their proximity and alliance, the former to unity immediately, but the latter to unity through 2 as a medium. The words, Tt)v frr tx-ivrfMtfifr 6ia rij< »-fji»rri/t, are omitted in the original.

1 The. words -within the brackets are supplied from the version of Thomatus. PROCLUS ON THE [BOOK in. rating them indeed, according to the sixth part, but converting them according to the seventh part. For the total form of it, is terminated by the progression of these. And you may see how the numbers, and the order of the progression, are adapted to the soul. For the beginning from the monad, gives to the ROU! a progression from intellect ; but the termination in these cubes, evinces the harmony of all the celestial orbs,' for they produce by their composition the celestial harmony. Each of them likewise is a harmony. For the Pythagoreans are accustomed to call a cube harmony, because it is the only figure that has equal* angles, analo gous to the sides and the superficies.' And the second* of the terms indeed, have a progression from, and a regression to the monad. l?nt again, these remaining as wholes, the third' of the terms are divided into that which proceeds, and that which returns, and are referred to the terms proximately placed above them.6 And again, the fourth7 of the terms, are referred to the monad; because of the seven terms, the monad imitates that which abides; but the middle terms having the form of the duad," imitate that which proceeds ; and the last terms, that which returns. For both the last terms are triadic. For the octuple itself, is in a certain respect triadic, as proceeding into the third order. We have therefore the one wholeness of the soul in the mixture, the triple9 of it in the third, and the qua druple of it in the fourth terras; conformably to which also it fabricates wholes according to each form of prondnice. And in the wholeness indeed, we shall find it comprehending the triple form, but in the triple the tetradic form, and always collecting parts into union through wholes.

" But after these things, lie; tilled the double and triple intervals, still cutting oil' parts from thence [i. e. from the whole1, and placed them between the intervals." Theologivts say, that in the Demiurgus there are dividing and connecting " 1 For ao/ionut here, it is necessary to read ovpat/iuv. 1 Instead of fttaat in this place, it is requisite to read taat. > The Pythagoreans calkd a cube harmony, b<-cau»« it has 8 angles, 12 §ide», or bounding lines, and () superficies; aucl 6, 8, 1-2 are in harmonic proportion. * i. e. '2 aud 3. * i. e. 4 and y. * For KToi.fi/jfKtivt here, read vr€f>*ttfAtvovi. 7 i. e. S and '27, and these being cubes, are images of stability. * <) as well as 4 may be said to have the form of the duad, in consequence of being a square numbtr or the itcond power. B For cirirXtivy here, it is necessary to read rpiw\ovv. 10 Instead of rvtracruus in this place, it is ncccsiary to read OVXKTUCM. powers, and that through tlio former, lie separates his kingdom from that of hi* fatlier, but through the latter, suspends the whole of his fabrication from the pater nal monad. They likewise eall energies of this kind, sections and bonds. According to these powers therefore, the Demiurgns now separating the essence of the soul in demiurgic bonds, is said to cut off parts from its wholeness, and again to bind the parts with certain bonds through the middles, through which also, he makes that which is divided, to l>c 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. Let 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. That there is also a certain dignity in it of first, middle, and last forms, he evinces by adding the word still. For in those things, in which we see the same form more obscure, in these we employ the word,?////; 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 by it that which we have mentioned. For by how much the more inwardly we proceed, and investigate the media of media, by so much the more shall we meet with more partial forms. For comprehended are more par tial than comprehending natures; and the. latter are more divine than the former.

The world likewise imitating this, has indeed about generation a divine body, but 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, as 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 be observed in the first place, that the two middles are * The word £ia<rri)pcm is omitted in the teitof Proclus. * lu the text of Proclus also the following word* are wanting, njr i' t»j» fttv car* api0/j«r rrtptx****'t iff ie «nrrr«Mn|r. ,0? PROCLUS ON THE [»OOK in. said by Plato to 1* comprehended in the geometric middle; and afterwards, that lie places the harmonic prior to the arithmetical middle, as being superior to it. For though !he arithmetical middle has tiie spontaneous, and the simple, and an alliance to sameness ; for equality is a certain sameness ; and hence I'lato shows that in 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 re« -Tinls 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, but the latter, about the relative quantity ; ' for the third, or the fourth part, is the peculiarity of relative quantity ;

— though all this be the case, yet the harmonic, as being nearer to the geometric, is very properly 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 the greater circles indeed, greater powers and motions, but to the less, less powers. For the comprehending are moved swifter 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 other, is equally inherent in all the elements in generation, according to arithmeti cal equality ; which also imparts to more attenuated natures, greater and swifter motions, but slower and less motions to such as consist of larger parts.

" But as sesquialtcr, sesquitcrtian, and scsquioctave intervals were pro duced from those bonds in the former intervals, he filled with the interval of the sesquioctave, all the scsquitertian parts." That from the above-mentioned two middles, the harmonica! and the arithmetical bonds beim; produced in the intervals of the double and triple terms, the sesquitertian and sesquialter ratios appearing in those middles, are cut by the interval of the •sesquioctave, is evident from what has been said, and will also be manifest, if you direet your attention to the terms 0, «, 1'J, and 18.1 For in these, the double and 1 In the original »r/Wor»jt, which denotes relalive, just as wooorqt denotes aluolute, quantity. * For 8 to lv», which is diapente, or sesquialler, is compounded of 8 to {>, which is a tone; and 6 to 8, winch is fesquitrrtiaii, or tliafessaroo. triple consist of sesquiterlian and sesquialter ratios. But how will those things accord with what has been before said ? Wo reply they must l>c assumed con sequently to them. For as the two middles divide the universe into two parts, so the sesquitertian and sesquialter ratios constitute a more partial order of things. For these ratios adorn things which exist as wholes, and yet are parts of parts. Each of them therefore is a whole according to the prolo^os, but a part according to the hypologos, and a part of a part, according to the transcen dency of the one with reference to the other.

And since in each of the spheres there are divine and demoniacal, 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 ; but the demoniacal 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 mon» partial, not Ix'ing able to receive all the peculiarities of them; hut the more partial of da>moniacal natures, at different times participate of a different peculiarity, and not always of the same characteristics; — hence, the soid partibly contains the ratios of these. And it contains the multiple indeed according to the participation of the whole; but the superparticular, uccordin" to one part only, and that the most principal ; and the superpartient accordin" to a communion which is both multitudinous and partible of the participants with the things participated. Hence, through these, the elements and the celestial spheres are adorned ; participating indeed of the third wholeness, but at the same time being parts of the two sections of the universe; since every wholeness has also parts in conjunction with itself. DiU'erent peculiarities therefore pertain to a different sphere, ' and a different number proceeds with a different element. The sesquioctave ratio also giving completion to the sesquitertian and sesquialter ratios, generates these plenitudes of the total parts, and coharmoni/.es them with their proper wholenesses.

You see therefore, that as in the mathematics, the geome tric middle comprehends the remaining two middles, but they comprehend the sesquitertian and sesquialter ratios, and these the sosquioctaves, — after the same manner also, the soul according to the wholeness 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 ; but according to numbers adapted to these parts, it fills them with appropriate forms and parts.

We may also speak as follows : This universe has indeed whole spheres; and 1 For oXXi) ffatpa here, it i* DCCCJWJ to read oXXiji J04 PROCLUS ON THE [BOOK in. has likewise divine, daemoniacal 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. For by its very essence [it contains all these, and the ratios which comprehend them ;'] just as lire, being calefactive by its very ex istence, is primarily hot. It contains therefore, the diatessaron harmony, through which it harmonizes the essences divisible about bodies of each of the spheres, and of the divine, demoniacal, 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; but da-moniacal follow di\ine animals, and psychical, such as are da'inoniacal ; and conformably to nature, secondary are always coadapted to primary essences. Hence the diatessaron harmony is in each of the spheres. And the ratios indeed of each sphere to the divine animals contained in it, and of these to da-moniacal animals, will be truly sesquioctaves, possessing a perfect interval ; being at one and the same time 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 to equality. And always se condary corporeal essences are su>peiided from such as are primary, participating of them, and of the corporeal reason which they contain.1 But this the part manifests which is said to be the eighth of the thing participated. That however which remains, is the ratio of psychical to demoniacal animals, which has the relation of the leimma, is superpartient, and is adapted to thirteen parts. For tlieaehave not one life, since they ascend and descend, and partibly and anoma lously enjoy the natures prior to them. And since the number twelve is ascribed to the [mundane] (Jods, and to the natures sujwrior to us, thirteen is adapted to those that do not rank in the number of the Cods. If also of psychical animals themselves, sonic pertain to undcjilcd 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 diapente1 likewise will be in each of the spheres. And heroic souls indeed will preserve towards the.- demoniacal, the sesquioctave ratio, through the undefiled form of life; but the souls of the multitude will have towards them the ratio of the leimma. 80 that in each of the spheres, there will be sesquitertian, sesquialter, and sesquioctave ratios.

1 The words within the brackets are wanting in the original, but are supplied from the version of * Instead of row iv avry iii this place, it is obviously necessary fo read, row tv avrots. 1 Tor in each of the spheres there will be divine, demoniacal, beroical, and gregarioiu souli, tnd appropriate bodies. OOOK in.] TIM.ECS OF PLATO. I,).", Or r.ithcr, it may he said, that tin? universe is divided quadniply, according to the four ideas of its paradigm, but that in each of the four parts, there are all animals, the di\ine, the demoniacal, the hcroical, and those of human souls, all which are harmonically co-arranged with each other, and with reference to their proper wholeness, \vliether it be the heavens, the air, the water, or the earth, the wholeness producing the diapente ; hut without this it may be said there is the diatessaron, in the four species of animals, n.; Plato himself divides— \u. into the universe, and the 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 replete, the soul fills this visible v.orld, render ing all things eflablc and familiar with each other.

" Leaving a part of each of them. And then "gain, the interval of this part being assumed, a comparison is from thence obtained of number to number, vix. of 2o(> to 213." What this leimma is, what ratio it possesses, and how, being adapted to con cord, it becomes harmonious when co-arranged with the other ratios, is evident through the mathematics. lint there is a thing of this kind in the universe, as iu a whole ; the ratio of the leimma being in the last of the animals comprehended in it, independently of (he before-mentioned demonstration, according to the quadruple section of the whole. For from each of the spheres certain elllnxions, and mingled dregs of the elements proceed into the subterranean regions; pos sessing indeed, much of the tumultuous, dark and material, but at the same time contributing to the whole constitution and harmony of the world. Plato, therefore, placing the cause of these in the whole soul, calls it a leimma, which is significant of ultimate diminution. For since theologists arrange the powers of the highest Gods about that place, Jupiter adorning those parts, so as to render them adapted to the participation of such mighty divinities, what ought we to think about the soul of the universe? Is it not that it must in a much greater degree adorn every thing which appears to be disordered, and that it must possess the cause of the hypostasis of an inordinate nature, and arrange it in a becoming man ner, according to this cause? I low, likewise, could it govern the universe, or conduct all things conformably to intellect, unless it arranges that which is dis orderly, and co-harmonizes the last of things, with the one life of the world ? But if also in the Demiurgns, the causes of these pre-exist, as Orpheus says,

The distant realms of Tartarus obscure, Earth's utmost ends, Ins holy feet secure. Tim. Plat. VOL. II. O why should it be wonderful, that the whole soul jwssessing all such things appropriately in itself, as a divine intellect possesses demiurgically, should ante cedently contain the cause of the last parts of the world, and of that which is as it were, the sediment of wholes ? For the soul comprehends the invisible prior to the visible and sensible world. What the leimma is therefore, is through these things evident. Hence also the leimma, is both quadruple and single. And it is necessary that the soul should comprehend the reason of both, according to which the leimma subsists rjuadruply, and singly ; since it is requisite that thus should contribute to the universe, and to each of its parts. If also you direct your attention to the numbers of the terms, you will perceive that these preserve a certain admirable analogy. The progression, therefore, into a hundred binaries, manifests an all-perfect diminution and separation from cause, rorintliesoul.it comprehends that which is most partial, and in the universe, that which is last, and most material. JJut the four and the five in the tens, suspend that which is last, and most material, from first natures, and co-arrange them with their principles. For the tetrad is allotted a demiurgic, and world-producing quality. B.it the pentad recals every thing which has pro ceeded, to powers which have more of the nature of iht one.

Again the triad and hexad in the units, impart perfection to these, through convcr^on. But if also the ratio of '2411 to I.'J is snperpartient,1 neither will this number be dissonant to the universe. For after the all-perfect progression of seiisibles, and a diminution as far as to the earth, which is said to In- the twelfth part of the world, all that is under it, will be the thirteenth part of the whole. And the representations of the elements, which proceed into the subterranean place, will be adapted to this number. That which is most material in the universe therefore, proceeds to the utmost extent, is adorned as it proceeds, and returns when adorned. In each part likewise, of the unherse, there are the last diminished genera of perjM-tual natures, to which the number twelve is ascribed; and with great propriety, they have habitude, and communion with each oilier, according to the thirteenth ratio, since the numl>er twelve was dedicated by the ancients to the [mundane] Cods, and to the genera that are always su>]>ended from them. All these therefore, the soul unically comprehends in the ratio of the leimma. In addition to these tilings likewise, the ennead of the units, which three and six procure for us, indicates the end of tho psychical ratios. For l>egin,iing from the monad, they proceed to the enriead, and from monads to decads [i. e. from units to tens], and from these to hundreds. For all the progression of the soul is

1 For M3 contains 13,rigli|ccn «iiiu», with a rcniaimltT off). triadic, and likewise, its evolution into light from the demiurgic canse, l>otli according to essence, and according to harmony, as we have before observed. And thus we have shown what it is which the leimma manifests in the soul. The whole psychogonic diagram however, has 31, or 3(j terms. And on this account, the nuinlxT 36 is adapted to the soul, as being generated from the hexad proceeding into itself; the hexad being ascril>ed by the ancients to the soul, because it is the first evenly-odd niunlxT, just as the soul i* the medium between impartible and partible natures,1 to the former of which the odd number is allied, but to the latter, the even ; and also, because it is circular, in the same manner us the pentad.' The pentad however, is the image of the intellectual circle, as being masculine, but the hwad of the psychical circle, at being feminine. If al>o you direct your attention to 34, this numlxT too, will be adapted to the soul ; fcince intellect is a monad, as being impartible, but the world is a decad, and the soul a tetrad. Hence, all number is said to proceed from the penetralia of the monad, as far as to the divine tetrad, which brought forth the mother of all things, immutable and unwearied, and which is called1 the sacred decad. But the tetrad has for its side the duad, and the double of the square of it added to 2, produces the above-mentioned number ;* being an imitation of the soul, which is multiplied by itself, and together with its own prolific power.

If likewise 34 is composed from the second sesquioctave, viz. from 10 and 18, it will happen, that as the sesquioctave is especially adapted to the soul, so also is this second sesquioctave. For being a medium between consonant and dissonant intervals, it is adapted to the middle nature of the soul. And in short, the sesquioctave charac terizes the diatonic genus, according to which the whole soul is harmonized. But l>eing a.ssumed as the second, it will accord with the order of the soul, in which the genera of being, have entirely a secondary subsistence.

Farther still, in addition to these things, since the whole diagram contains a quadruple diapason, which is the most full of all symphonies, but the diapcnte once, and ends in one tone, it will possess the quadruple cause of the division of the world into four parts, proceeding as we have said supei nally, from animal itself, and the four ideas in it, through soul into the universe, and of the i>erfect har mony in each of the parts of the world ; through which also, heaven is one world, concordant with itself celestially, and the earth has all things terrestrially, and ' For the e»r nly-odd number is a medium between the odd and the. even number. * For rwrcii here, it is obviously necessary to read wivrai. 1 Instead of cXuovvi here, it ia necessary to re*d 4 i. e. 2 x 4* + 2 = 34. wtf PKOCLUS ON THE in a similar manner each of the elements between these. Since, however, the world is not only quadripartite, but has five figures, possessing ;i fifth idea together with the four, the soul very pro|>erly contains in itself, after the quadruple diapason, the symphony diapente ; the remaining section being that of tlie hea vens into t-iijht spheres, and of the whole woild into nine, over the former of which the Syrens preside, mentioned in the Republic, and over the latter the whole of the Muses, under whom the Syrens subset. Again therefore, a tone consentanroush closes the whole diagram; and it is not possible to devise any other divisions than these which are delivered to us by Plato, I mean, the division into four, into live, into eight, and into nine parts, some of w Inch are mentioned in this Dialogue, and some in the Republic. Very properly therefore, is the whole psy- ( ho'Mmie diagram composed of all the above-mentioned particulars, I mean, a

tone, the dia|H.-ntc, and the quadruple diapason, in order that you may see these throughout the whole world, as having the power of the whole diagram. All likewise an- assumed according to all the divisions made by Plato of mundane natures, which are triple, vi/. acconling to ideas, according to figures, and according to the spheres. All the other sesquialter and sesquioctave ratios therefore, were the bonds of more partial orders, comprehended either in the live parts of the universe, or in the divisions of it into right and nine; as, lor instance, in the division of it into (iods damous, souls, natures, and bodies. And of (iods, into those that preside over different parts of the world. For in each part of it, there are different orders ofCuxU; those of the second rank being analogous to those that are prior to them. And in a similar manner \vilh respect to da-mons, some are of this, but others of that series. The like also takes place, in souls and natures "'ul bodies. Hut (he diapente symphony, and the sesqiiioctave ratio, are not in vain assumed after the quadruple diapason, but hecau>e they are comprehensive and connective in common, of wholes. I hay, for instance, that the ratio of the ninth to the eighth sphere, comprehends and connects as one ratio, all the parts at once that are arranged according to a quintuple di\ MOII, and all that are divided into eight and nine.

Hut the Icimmas of all the seM|in!. i liaii ratios are either the ultimate, and very partible diminutions, according to each portion of tin- quadripartite ihsirilmtion, or they are the common gifls of all the.se ratio*, into the last place of the universe; through which < iod>, daemons, partial souls and natures, proceed into that region, and accord vvilh each other, confoimabU to the •illiniale and perfectly partible sNiuphony, Mich as we say siiperpaitient ratios possess. Hence Plain descending to this adds, that the Deinmrgiis dividing the mixture, had now con sumed the whole of it. For neither Cod, nor nature, docs any thing in vain.

ROOK in.] TIM.EUS OF PLATO. 10<> Tin* Demiurgus therefore did not constitute a mixture of parts either exceeding or deficient, but produced it such as was sullicicnt to the wholeness itself of the soul. For the whole which is from parts, is neither metre nor less than its proper parts, but entirely derives its completion from appropriate parts. Hence the whole of that which is mingled, consists of harmonic ratios, and all this harmony is, in short, the essential paradigm of the harmony of the nnherse, accor ding to all the divisions in the world. Moreover, the whole numUer of the essen tial monads of the soul is 10 }1M7,' proceeding according to all the orders of numlwrs. Decadically, indeed, in order thai the soul may become mundane : for the derad is the numl>er of the world. Jiut pentadically, in order that it may be converted to itself: for the pentad is self-convertive. Enncadically, in order that it may not alone * contain the universe monadically, but also as proceeding to the last of things from the monad. But tetradically, as collecting the quadri partite division into one. And hebdomieally, as converting all things to the monad, to which the hebdomad is alone referred, being motherless and virile. And in the soul of the world indeed, the above number subsists totally ; in divine souls, as having their energies directed to that ' soul, it subsists both totally and partially ;

in daemons, as energizing still more partially, it exists vice versa, partial ly and totally ; and in human souls, alone partially, and alone jjnosticallv. For thus all forms subsist in these souls, such for instance as the form of man, of daMiion and of CJod ; in order that through these they may know, that all things subsist in more excellent natures productively, and at the same time gnostieallv. This mixture therefore, is alone the mixture of the whole soul, and it subsists after the same manner in each divine soul, and similarly in da-moniacal souls, each of which has intellect placed above ils proper essence, a peculiar ve hicle, and a life distributed about this. If, however, in partial souls, it In.' requisite to assume the peculiarity of each, it is a medium between the impartible which i.s above, and the partible which is posterior to them,* or it is partly the one, and partly the other of these. And though we have elsewhere discussed this largely, yet we shall particularly investigate it, when we come to explain what is said by Plato concerning the generation of partial souls.

1 InslC.I'l of n-nrniTaffi Trtt<i,trt in tin-, |)lacc, it li rojui-ite to read, tvvfanc.vrnttt rrnnafXH^irtt. 1 It ii necessary lirro to siijiplv fivrnr. 1 For tpftt ctfiinr in (hi* place, read rpnj ft-nirjr. * It appears to me llut after rvnirrift ifi-^ fr« Xa/jflartic in llic original in tliia place, the words fir<rrr »«ri are wanting ; and that immediately after, instead of ro rt vxtp avrai a/^uirror, «ai TO fitr' avrni firptvror, we »kould read rnv re vwrp uvrcu afirpivrov, cat rov fitr' avrai 1MIOCLUS ON THE [BOOK in. " Having, therefore, cut all this doublecomposition according to length, so as to produce two from one, he adapted middle to middle, each to the other, IIH it were in the form of the letter X." In tins firnt place, it in requisite to show mathematically of whnt kind thw figure of the soul is, and thus, afterwards, introduce the theory of the tilings; in order that being led in a becoming manner by the phantasy, we may render ourselves adapted to the scientific apprehension of what is Maid. All the numbers there fore, must !*• conceived to be dcsciibed in one rule, as those who are skilled in music are accustomed to do. And l<-t the rule have the numlwrs according to the whole of its depth, and be divided according to its length. All the ratios therefore, will l>e in each of the sections. Tor if the division was made according tobreadth.it would be entirely necessary that some of the numbers should be taken here, hut others there.

Since however, the section is according to length, but all the numljers are in all the length, there will be the same iiumlx-rs in each ot the parts. For it is evident, that it is not the same thin-;, to divide the length, and to divide according to the length ; since the latter sig.iili«-s, that the section proceeds through the whole length, but the former, that the length is divided.' Let the rule, therefore, be thus di\ided according to length,' and let the two lengths Ix- applied to each other in the points vthich bisect the lengths, yet not so as to he at right angles: for neither will the circles IK- at right angles, ly-t the two lengths likewise he so incunated, that they may again be conjoined at the extremities. Two circles then-fore, will be formed, of which one will l>e in terior, but the other exterior, and they will l>e oblique to each other. One of these likewise, is called the circle of the same, but the other, the circle of the different. And the one indeed, subsists according to the equinoctial circle, but the other, according to the zodiac. For the whole circle of the different revolves about the zodiac, but that of the same about the equinoctial. Hence, we conceive that the right lines ought not to l>e applied to each other at right angles, but like

1 In tli* original of tlm place there i> notliin; more llian n* no ynp c^W, »n ov ravrov TO (tiftot. 1 he. rest of the sentence in the translation is added from the version of Ttioinaeus. • Thin for imtance, let the numbers be disposed according to depth as follow* : . y . 8 Then the line* drawn longitudinals will rqnestnt the division of the rule according l« length. BOOK in.] Tl.NLEUS OF PLATO. HI the letter X as Plato says, so as to cause the angles to l>e equal only at the summit, but those on each side, and the successive angles, to be unequal. For the equi noctial rirrle 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, 1^-t us refer what is said by Plato, to the psychical essence. And, in the first place, we must observe, 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 discn te quantity. In the soul however, both these concur, viz. union, and separ ation. For it is a monad and number, one reason, one multitude, and 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. Arid by ascending still higher than these, we 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 would not be continuous ; nor alone a geometrical essence ; for it would not 1x3 divided. IJut it must Ix' 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, tlie harmonica! essentially. For the multitude in it is harmonized, and it comprehends in sameness, both absolute and relative quantity. But so far as it is the geomotrical, it contains the spherical essence. For the circles in it are both immovoable 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. But the self-motive, is at one and the same time moved and immoveable. For it moves itself. But to move, or be the cause of motion, pertains 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, ami the essential monads in it, as we have before shown. IJut it comprehends the harmonic science, according to the ration of numlicrs ; and the spheric science, according to its twofold circulations. la reality ulso, it is the essential, self-motive, intellectual, and united bond of the mathematics, comprehending all things unaccompanied with figure, and with nndffiled purity. Hence it comprehends figures uufiguredly, things separated, unitedly, and without interval things accompanied with interval. For thetto pertain to the essence of lire soul. And it is necessary to Hiirvey all things in it after this manner.

Moreover, this likewise ought to be assumed from what 1ms been said, that nil secondary natures, are analogous to those that are prior to them, and that every Mhere, the une precedes multitude. For as the theory of the hyparxis of the soul commenced from its essence, and that of its harmony from the one part, thus idso the doctrine concerning its figure, places the one length prior to the t\\o. And as sameness and difference are from essence, so the triple and duple ratio are from the monad, but from the one length, the circle of (In- same, and the circle of the ui/fcrent. As likewise, the 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. And all things are indeed every where, on account of the psychical life, being as it were of one colour, and of similar parts. The same however, and the triple, Mib>ist in a greater degree in the circle of the same, but the different, and the duple, iu the circle of the different. All the ratios likewise, are e\ery where, but alter a different manner in first and secondary natures; in the former indeed, intellectually, totally, and unitedly; but in the latter, doxastically, distributive!), and partially. And thus much concerning these particulars.

Concerning this section however, and the two lengths and circles, it is worth while to consider, what they nm.st be said to be. For the divine lamblichus soars on high, and solicitously investigates invisible natures, vi/. the one soul, and the two souls that proceed from it. For of every order an imparticipable monad is the leader, prior to the thing*, participated, and there is a number appropriate to and connascent with imparticipahles. The duad also is from unity, in the same manner as in the Clods themselves. Tiuueus therefore, he says, ha\ ing through the psychogony fabricated in words the one and supermundane soul, from which the soul of the universe and other souls are derived, now produces the duad from this. For the section manifests tin: demiurgic division, which proceeds in samene>s and |x-rfectioii, generating the same things according to second numl>ers. But the. division according to length, exhibits to us the progression supernally proceeding from the Demiurgus. Through tin se how ever, two souls are generated, alter the one soul, each of which has the same ratios, are conjoined to, and arc in each other, and are divided from each other. And they likewise preserve an unmingled purity, together with union with each other. For they are united to their own centres, and this is the adaptation of middle to middle. But since also, these souls are intellectual, and participate of a divine intellect, the Demiurgus prior to the generation of the uni\er>e, bent them into a circle, and comprehended them in a motion according to the same, and in the same, making them to be intellectual, imparting to them a divine intellect, and inserting

HOOK in .j TIM/EUS OF PLATO, m the duad of souls, in the intellectual duad, which transcends them essentially. [And thus far tho divine lumblichus.j We therefore admit, that all this is well said so far as pertains to the theory of things: for these particulars are prior to the world. Hence also in mundane natures, then- is (lie monad, afterwards the duad, and afterwards the heptad. For in the universe then? is one soul, which is that of the universe. But after this. I here are two souls which divide the heaven into the circulation of the same' and the circulation of the different. And after these, there are. seven souls, which distribute in an orderly manner the planetary sphere*. We conceive it how ever, to he more concordant with the words of Plato neither to understand what is now said, as pertaining to those super-mundane souls, nor to the multitude of mundane souls, hut as asserted of the soul itself of the universe. Plato therefore himself shortly after, having spoken concerning all the divisions of the soul, says, " Hut iclien all the composition of the soul icas produced conformably to the intention of its composing artificer, after this he fashioned within it the \iholc of a corporeal- formed nature." In which words he denominates the scud one, and this as no other than the soul of the universe. For it is this soul which comprehends the whole of a corporeal-formed nature.

Hence the demiurgic divisions, and the two-fold lines and circle.*, must he assumed in this * soul ; for in so doing we shall not l»e in want of arguments. Since therefore, it is the collector of all immoveahle and iiller-molivo natures, of imparlihlcs and parlihles, of paradigms and tljc last imam's, and of tnily-e\i>tin^ beings, and such as are not truly beings, the nature /if it i> very properly two-told, partly pertaining to more excellent, and partly to subordinate beings. Because however, these are entirely separated from each other, tlie\ require after a certain manner two1 media. And in corporeal natures indeed, the two conjoining media are separated from each oilier; but in incorpo real natures it is one Informed essence, which binds together the extremes ; one part of which being conjoined to intelligible*, is intellectual, scientific, shilling with divine wisdom, anagocjic, and comprehending the causes of things; but the, other part hem;; proximate to partible natures, is elleetive of difference, comes into contact with sensible.**, recurs to the providential inspection of secondary natures, i> artificial, and comprehends such other things as are allied to those. All the ratios however, are in each of these. For in this, the essence of the soul diliers from the intellectual essence. For the latter indeed, is uniform, and antecc-

1 For cjvrci' licrr, it is necessary to read rni/r&i'. * Instead ol rir' niroi'f in lliis J)lacr, it 19 rojuiiitc In read r T' tivrtjt, ' IV r ^r»i»' lirrr, read tout*. Tint. rial. VOL. II. T TIM/EUS OF PLATO. [BOOK in. Hently comprehends all forms monadically ; but the former is dyadic, and con tains the same reasons, dianoctically and doxastically ; in one way indeed, in the circle of the same, but in another in the circle of the different. [And thus the soul imitates its cause.] ' For she is both a monad and a duad, as with reference to the monad [Saturn], the father of the intellectual Gods. And the soul is a monad as with reference to the universe, but a duad, with reference to intellect. For in short division itself and multiplication derive, their subsistence from this Goddess [Hliea]. The vivific principle therefore, is the cause of progression, multitude, and multiplication. Hence some philosophers, assimilating to the Gods things which are deri\ed from them, think tit to arrange intellects accordin^- to the masculine, hut souls according to the feminine genus of the Gods. For intellect is indivisible, and of the form of the odd number; but soul is divisible and biformed. And the former is analogous to paternal, but the latter to prolific causes. And the one is allied to bound, but the other to infinity. If likewise, I should IK- asked ho\v the soul is one, and how it is biformed, I should say, that it is one indeed, as self-motive;

for this is common to all psychical life, and to the parts it contains; but that it is biformed according to two-fold lives, viz. the life which is eomeited to tir>t natures, and the life which providentially attends to secondary natures. 1 should also say, that according to the essen tial it has <.ne life : for self-motion is the essence of the soul, Jlut according to same and different, I should distinguish its two-fold lives.

Why however, did the Deminrgu* first constitute the soul rectilinearly, but afterwards circularly, and after what manner is a right line adapted to the esseiu e. of the soid ! To this we reply, that it is requisite to conceive the soul as analo gous to a right line. For as a ri-^ht line proceeds without cu.-.ature, and defi nitely from this to that point ; for there is only one right line between two points ; and as it is infinite in its own nature, so likewise the soul is generated an infinite power. Intellect also, like an indivisible point, is the leader of the soul, compre hending it indivisibly, and antecedently containing in an impartible manner the whole of its essence. For the impartible is allied to intellect ; but that which is primarily partible to soul. Hut a point and a line are things of this kind. Hence, a right line is very properly ascribed to the soul, and afterwards a circle, which we say, art- simple lines. But a point is ascribed to intellect. For from thence 1 The words within llie hrarkels die wanting in llie original; hut it ii|>pear> to me lli.it th«y ought to l* m-.rtol, though they were likewise wanting in the MS. of Thoma-us. In llic original therefore after the words o.VXui N «i ry Ourrpnv, I couceite there is an omission of ».ui OITU-J »> vf^l pipiiTai rt]f tai/riji airiuv. But the fontal cause of the soul ii Rhea.

i KIII.] TIMJEUS OF PLATO. 115 ,is from a certain adytum, the reason of the soul presents itself to the view, unfold ing the impartihility of intellect, and announcing its occult and ineffable union. Intellect itself however, is lirmlv established in itself, understandin"- all I infrs with a traiujuil energy ; l>eiii£ a point and a centre as with reference to the soul. For if the soul is a circle, intellect is the centre, or1 the power of the cir cle. Hut if the soul is a rijjlit line, intellect is a point, comprehending without interval that which has interval, imparlibly that which is partible, and rentrically * the circular form. Intellect itself however, is a circle, as with reference to the nature of Mr istmi/, alioul \\hich ' it on all sides converges, through a de-sin* of the diic, and of contact with it. Farther still, after another manner also we may say, that a line is adapted to the soul. For intellect indeed, though some one should ^ive to it motion, yet it has this energy intransitive. For it surveys at once the. whole of the intelligible, having an eternal life, and cnersizinj; about the same things, in the same nature, and according to the same. But soul possesses a transitive energy. For at diffe rent times, it applies itself to dillerent forms. And this j«» true even of the soul of the universe. For, as I'lato savs in the IMia-drus, it is the peculiarity of soul to eneru,i/e through time, lint every transitive!

motion is -,i line. For it has -c/icinr and :,//////(/•, and the rectilinear, and one tiling for the be^innin^, and another for the end. So that in this re<peel we refer a line to the psychical lift'. .N'^aiii. tin- imuiovt able cause is motive of self-motive natures; for these pro\iinaieK participate- of it ; but the self-moving cause is motive of alter-motive natures. Since therefore, the soul provides for aller-motive natures, beiui; essentially prior to tin in, and as living from itself, transcends all things that have an adventi tious hi'.-, conformably to tbis, it also has the linear form in its providential ener gies ; bein^ motive, and constitutive of niter-motive natures ; ju*» as a line is the <listance of one tiling from another, and an egression or departure from itself. In Miiat is said therefore, about the mixture of the soul, and also in what is said con cern in i; numbers and middl'-s I'iato unfolds the bein^ itself of the soul, and shows liow it is one and many, what progressions il has, and \vhat regressions both to superior natures, and to itself; how it produces and converts things pos terior to itself; and how it fills with ratio*, and binds together the whole world, iiut in what he says concerning the riyht line- and circles, he delivers to us the vital and intellectual peculiarity of the soul, and indicates how it participates of

1 Fur i'/ licrr, il i< urci ssary to r«.itl i). * lur.te.td of ir»Xrn.)i iii lliis pl.icr.it i> obviously necessary to rc;i(l lorpirwi. ' () \oyni licrc appear* lo l>c s(i|«crl1ii<ni5, as is alsor^t rv<> r'ini in the next line. For the original i«, •wrpi r/r o Xoyoi Tra>rn\"0(r oirrtvti roflj» rev trot, tai r>7» rov (voi, »~ai rij« irpoi ro er ff»ra^i;i. lltf PROCLUS ON TI1K [BOOK nt the life in intellect, and how it is converted to itself, so fur as it in self-vital and self-moved. For the right line manifests the progression oftlie psychical life from more excellent natures ; l>ut the inflexion into a circle indicates intellectual cir culation. For the soul is allotted this power, and also that which is productive of the life in itself, from its father. Since however, the psychical life is twofold, the one being dianoetic, hut the oilier doxastic, two lines present themselves, and are l>ent into two circles. In short therefore, the essence of the soul, being a whole and consisting of parts, is harmonized number. Hut its lite is rectilinear, and is uniform and In formed. .And Ms intellect is dianoetic and doxastic. For there are in it Iwin^, life, and intellect. Or rather prior to tin- gnostic, perceiving that the vital powers are in themselves at one and the same time transitive, and self-motive, we must, say, that the right line adumbrates the transitive, hut the circle, the self-motive nature of these powers.

For they aiv moved from themselves to themselves. Hence Tima-ns delivering to us in \v hat is hen- said, the vital motion by itself alone, assumes the rectilinear, and the circular motion, but in what follows unfolds the gnostic motions of the circles; the soul now becoming self-motive, inconsequence ofthe whole of it moving itself. If therefore, we now admit that the right lines are lives, and these essential; on \\hich account also, the Deminrgns made the composition oftlie soul itself to be rectilinear, as possessing life by its very exist ence; — if we admit this, then we mu - t say, that the circle manifests what the qua lity is of the form of this life, \i/. that it is self-moved, beginning from, and rcturnin<r to itself: and that it is not like the life, of irrational natures, tending to

externals as it were in a riiiht line, as never being able to convene to itself, and as having an appetite directed to other things placed externally to itself. For the self-motive nature is moved from itself to itself, >ee> itself, and is present with itself. Hence also, such a form of life as this is circular. For in a circle, the same thing is the end and the beginniiiir, in the same manner as in that which is converted to, begins from, and ends in itself. The right line therefore and the circle ofthe soul, are without interval ; the former beinii the image of life [simply ', but the latter of life convertive to itself, and not absolutely of all lite. For both these may be surveyed in souls; the ri.uht line indeed, according to the transi tions of appetites; but the circle according to a circumduction from the same things to the same. And this Socrates knowing, savs in the Pha-drns, that souls are carried round in a circle, revolving under intelligibles as ohjecLs of desire, ln-ing at different times happily affected by diflerent things, and returning from the same objects to the same. "Why therefore, should we any longer fear those skilful Peripatetics, who ask us, what kind of line Plato here assumes ? Is it a,

LOOK in.] TIM. EL'S (>r PLATO physical line? But this would he absurd : for this is the end of bodies. Is it then a mathematical line? But this is not self-motive, and is not essence. Plato how ever says,1 that the soul is an essence, and is separate from bodies. We say therefore, that they in vain make tin se inr|iiiries. For lonp; before this, \\c havenot ceased asserting that this lino is essential. And prior to us Xenocrates calls a line of this kind indivisible. For it would be ridiculous in any one to think that there is an indivisible magnitude. It is evident however, that Xenocrates thought it requisite to call the essential reason of a line an indivisible * line. But Plato, for the sake of concealment, employed mathematical names, rr.s -ceils of the truth «f things, in the same manner as thcofagists employed fuhlcs, ami the Pythagoreans symbols. For it is possible in images to survey paradigms, and through the former to pass to the latter. Against such men however, as these Peripatetics, who are contentious, no arguments are sufficient. But let us return to the words of Plato, and direct our attention to each of them.

Since therefore, the soul is one, is dnided according to its parts, and is both one and many, Plato denominates it (his, as heiri'4 one, hut till, as being multitude, and coi»j:r,\ifif)n, as both ; which iilso shows that the essence of it differs both from things dixTele, and things continuous. For these are without communion ' with o.ich other, Hut the soul is one, and at the same lime multitude, and is discrete, and continued. Sine*- however the psychical reasons are Informed ; for the soul is of an ambiguous nature, (^Mv/Troaoj) anil /ni.i tiro faces, co>ifonnabl>f to its paratli^m, so that it intellectually perceives the impartible essence through the circle of ///c finite, but contains and connects the partible essence, through the circle ai the different ; — hence Plato calls it double. But because it has the same reasons or ratios, above and beneath, and not as some fancy, the duple ratios here, but the triple there, on this account, he delivers it to us divided according to length. For this duision alone, preserves every where the same ratios. But the scission itself exhibits demiurgic section, which is appropriate to the Pemiurgus. For the duad is seated by him, and is refulgent with intellectual sections, as some one of the (iods says.* Moreover, the words " middle to middle " indicate perhaps, that the division and contact of things intangible, are adapted to the psychical middle: for they subsist in a middle way. For in intellect also there is division, liecause there is difference, but it subsists primarily, and as it were occultly, and indivisibly. In sensible* likewise there is division, but according to an ultimate distribution in-

1 For tyaaiv lirrc, I rr:i<l i^itv. * The word arofiof i» omiilcil in i lie original. 1 For «u-i» ijra lirrr, it is necessary to read a^oifoftfrai * This is asserted in ouc of the Chaldcau oraclet. 1MIOCLUS ON THE BOOK m.J to parts. Hence also the union in these is obscure and evanescent. But in the soul both have a middle subsistence, in a way adapted to it. And if indeed Plato had spoken concerning intellect and soul, he would have said, that the Demiurgus ap plied the first to the middle, and if about body and soul, that he applied the middle to the last. But since he teaches us concerning the psychical duad, he v.iy> that the Demiurgns applied middle to middle. Peihaps too, he says this, bccau>e the con tact of the soul is pro|»erly of a middle nature. For the last part oftlic dianoetie. and the summit of the doxa>tic pouer, form the media of all the p>ychic;d com position. But (hoc are conjoined to each other, and conformably to then-, one union is produced of the-e two lives. For in every order of heing>, the bases of first are united to the Mimmit> of secondary natme<. The figure X however, pro duced by this application, has a great allinity to the universe, and also to the soul. And as 1'orplnini relitlei, u character (>J this kind, r/'r. X, surrounded b>i a circle,1 /v i/1//// tlit F.^ii])tians a .M/i/il/ul of 'the mundane ton!.

For perhaps it signifies, through the right lines indeed, the biformed progre>-«ion of the soul, but through the cir cle its uniform life, and regiv»ioii according to an intellectual circle. \\emust not however conceive, that Plato thought a di\ine essence could be discovered through these things I 'or the truth of real beings cannot, a> >ome fancy, be known from characters, positions, and \ocal emissions. But these are jilter an other manner svmbols of di\ ine nature-. Fur n* a certain motion, s<> likewixe a certain figure and colour, are symbols of this kind, as the initiator* into mysteries say. For diflerent i'haraj'ters and also diflerent signatures are adapted to different (lods; just as the present character is adapt* d to the j-oul. For the complication of the rijjht lines indicates the union ol a biformed life. For a right line it-elf al<o, is a symbol of a life which flous from on hi:Ji. In order houever, that \\e may not, omitting the things themse!\e*, be too busily employed about the theory of the character, Plato add> "ax it it ere," indicating that this i> a>Niimed as a \eil, and for the sake of concealment, thus endeavouring to invest \\ith figure the unfigured nature of the soul.

" Afterwards he bc-nt them into a circle, connecting them both with tliemselves, rind with each other, in sucli a manner that their extremities might be combined in one, directly opposite to the point of their mutual intersection/' That \v hat i> said by Plato manifests through right lines the progression of ' lu^tt-aJ of ii/kXoi in tliis place, it is requisite to read ii'iXf-. BOOK in.] TIM /ML1 S ()!• PLATO. ll.'f the soul, and its providential attention to alter-motive 7iature*, is I think evident from what has l>een already observed. And I also think it is proper to deliver the inflection into a eirele analogous to these things. For sinee regressions are in continuitv vtith progressions, recalling [to the principle] tilings which have proceeded from it, hence Plato says, that the right lines wen- In-nt into circles. And sinee also, the \\(;\\ nature of the soul is intellectual, and apocatastatie, and evolves intelligible multitude, hence it is restored to the same tiling again. liecause likewise, it moves alter-motive natures, the soul being converted to, and moving itself. . arc. mlinu' to all these particulars, circulation j)ertains to it. For the progression of it is in continuity \Mtli its regression ; since it is not imperfect. And the motion of alter-motive natures is suspended from the self-motive life. As the one of these also, is not sub\< rted, but perfected by the other, after the same manner the composition of die right lines is not destroyed through the in flection into circles, but the former remaining, the circles are generated.

For all things subsist at once in the soul, so that as the continuous is simultaneous with tin- discrete, thus also tiie circular \\ilh the rectilinear. For it is necessary that tin- n.J. l and the circular should remain, just as the impartible and the partible sub sist ti'^'-ther in the soul. For the Pemmrgus makes eternally, so that the things which are generated by him, are entirely perpetual. Hence the rii;ht and the circular line are simultaneous in the soul, whatever each of them may be.

What therefore are the twofold circles, and how are they in the highest decree adapted to the soul ? If then the essence of the soul proceeding: from intellect, was such as to be entirely different from the intellectual peculiarity, the circular form would not be adapted to it. lint since it is intellectual according to par ticipation, and an evolved and Informed intellect, on account of its intellectual nature.it is a circle nnfigured, without magnitude, and self-motive ; but on ac count of its dyadic ' nature, it is a twofold circle. For its progression al«o, in the same manner as its regression, is twofold, and its reason is twofold ; so that its intellectual participation is twofold according to its lives. Since however, these lives are conjoined according to their first progression, but in proceeding are divided from each other, but after the progression are again converted to their principles, hence they are again conjoined according to the peculiarity itself of regression ; the first adaptation of the lines manifesting permanency ; but their separation from each other by division, their progression ; and their inflection,* \\w\tregrwion again to the name thing. For the more divine life which subsists

' for (tiH-iibiKov \\ctt, it i» olmoinlv Morc»sary to read bvuluor. * . \flcr r>,. iv» on-' oXAqXwr 0^91*1 tn Unoriginal, (lie worili r^v xpooloi', r»ji £c r dcnlU wauling. PROCLl'S ON THE [BOOK in. according to regression, conjoins the end of itself with the beginning ; and the more subordinate life converts the progression of itself to that which abides. Hence it converts this progression to the one intellect both of itself, and of 'the more excellent life. The conjunction, therefore, of the two lives is there the contact of the one, being in an opposite direction to th:it of the other; because the union of the one is according to progression, but of the other, according to re- •Tession, and regression is contrary to progression ; for the latter pertains to the nature of sameness, but the former to that of difference. The latter also imparts a collective similitude [but the. former, division in the progression*.1] For their opinion must not In? admitted, who contend that the figure of (lie soul truly con sists of two circles. For if the circles are without breadth, how is it possible to cut one of them, since it has no latitude >. Hut it' they are certain rings, how can the soul if it consists of these, be every \\ay extended from the middle to the ex treme heaven ? For after what manner can rings be extended through the whole of a spherical body!

To which may b«- added, that these circles bem- corpo real, "ill exhibit to us a certain body external to the universe, and will also pro duce a certain vacuum in the superficies of the sphere, in consequence of surround ing it, as is evident in the rings of spheres. And if they are circles ihe\ must have profundity together with the body of the universe, on account of their station from the middle as far as to the extremities of the world. It is necessary there fore to conceive this vivitic figure of the soul to be uutiguivd, and without inters al, unless we intend to fill ours, Ues and also the theory of Plato with much absurd ity, such as that which is noticed by Aristotle, who on the supposition that the soul is a magnitude, demonstrates that as Mich it is alone partible, but by no means impartible, though its essence, together \\ith partibilitx, has also impaitibiJity. But whether it is a circle, or a ring, it \\ill alone ha\e a partible, and by no means an impartible nature.

" ile likewise comprehended them on all sides in that motion which is convolved according to the same and in the same." The mode of conception of the divine lamblichus in what is here said, is truly di\ine, and firmly adheres to the meaning of Plato ; since he does not, like the I interpreters prior to him, think that the motion \\hich is convolved according to » Tbt- wonU witliin the bracket* an- wan(in» in Hie original, but are <,ii|>|>lic <l from llie \orM.m of Thom-AU-,. II i- uce alter llie worth TJ t( <ri/» uyu^o* o/joiorijra ci Muo.r, it i> lutcsiarv to in cit v.r biaifitoiy run »ptt^o^». • in.] TIMJEUS OF PLATO. ,21 •:K: sa.ue, and in Uio same, should be understood as pr>rl,Miiin,r to flip -onl. For || r<i •• Pi.etion of the soul is now in it, and uol about it. ]}.. conr^ne*. tj, ,. |,,;v. i - .a! lit.- motion now spoken of pertains to intellect ;unl ihe intdlrrjiul life, or in no part of the remainder of this Dialogue tin,-* 1'lato appear (0 conjoin Kic MV.J! IM inldkct. It is wo ssary, however, t!iat he should, in order that by <li.- :n\ •.](•.. /.i I,,, may demonstrate the nni\erse to he an animal endued with soul i. IM! :vrt. We mu^t th'Tefore conceive the motion which is convolved accordii, (.. (lit; same, and in the same, to be intellectual. For this comprehends lli, soul in the same manner as the soul circularly covers the heaven as with ;i \eil.

Intellect, h(»\ve\er, is indeed an immoveahle motion; for it subsets wholly ami uuuMlly at ..nee. i5ut soul is a self-mr»\ed motion. And the former is uni form, Iml tin- latter l.ilormed. The former also is one and indivi-ihle, hut the. latter divides and multiplies itself. The soul, however, participates of intellect solar as it is intellectual; and through it is conjoined to a di\ me intellect. For the soul of the universe participating of intellect, ascends to the inlelii-ihle. It is necessary, therefore, that the motion which isciicmnu.hed in the s;ime and about the same should In- intellectual, hem- dillerenl f,-,,,,, the motion of the; two circles, since it comprehends them. \\ e must say, therefore, either that this motion per tains to a participated intellect, which is proximatoly seated above the soul, or that it should he the motion of the Demiiir^us of the soul. The latter however is impossible. Hence it must he admitted that this is (he motion of a participated intellect. Hut that the motion \\luch is coinolvecl according to the same, and ia the same, bein- intellectual, and above the soul, i< not the motion of the Demiur^Mis, may be learnt by considering, that he mnde the inmerse to be endued with intellect, not -ivin- himself to the uiuuT>e, in the same manner as the soul, but imparting to it another participated intellect, which we h:ue before demonstrated to be seated above the soul. For placing intellect in soul.' but soul in body, he fashioned the universe.

Arid it is c\id. nt that he did not effirt ihi> by placinhimself in soul. Fur it would IM- ridiculous that If should co-arrange himself with soul, beiu^ separate from it. Pl;.,o therefore says, in what follows, of all [true] hem-, thai neither doe> any other tiling proc.-ed into it, nor does it proceed into any other thin-. JJut this beinj; true, the Demiur.uus will not place himself in soul ; and before he constitutes soul, subsistin- by himself, he will -enerate another being, which' when lie had generated soul, he placed in the soul. If, however, this be true, the motion of that intellect, which is circumvolved according to the

' For nvv\»> km*, it is ncrr.isarj to rc;id ft- <r>>\>i. * Iti» ucccswry here Jo supply .". Tim. Plat. VOL. II. j4>2 PROCLUS ON TI1K [BOOK in. same, and in the same, will comprehend these psychical circles, and not the motion of him who constituted both this intellect and soid, and who shortly after is said to abide in his accustomed manner, exempt and separate from the universe. The mundane intellect therefore, is the intellect of which we are speaking, the life of which comprehends the psychical li\es, vi/. the uniform life comprehends the Informed lives, arid the eternal life the; lives \\hich are not eternally moved. Hence the whole boiil proceeds after this manner, l»eing a monad and a duad, and at* is evident from what has been said, without difference with respect to itself. That which remains therefore, Plato delivers in. what follows, viz. how from the demiurgic divisions, one of the circles contains in itself that which is more di\ine, but the other, that which is more subordinate. For we have assumed these things fur the sake of perspicuity. But let us hear what is next said by Plato. " Ami he made one of the circles to be external, but the other -) (- internal. IJe denominated iheretbie, the lation of the external circle,

the motion of the nature of same ; but the lation of the internal, the . motion of the nature of ditlercnt." The divine Jamblichus refers these divine circles to the intellect which is sepa rate, and to the intellect which is inseparable from souls, and to the motion which is convolved in the same, and on all sides comprehends them; so that one of the circles comprehends the two souls, but the other is in them ; and the one is unruiuglcd with the other life and the powers of the soul, but the other is mingled with and governs them; from which cause likewise, the whole soul, stably energi/es, and i.s united to the Demiurgus himself. \\ e however interpret the two circles to be the two-fold lives of the souls, vi/. the providentially energi/ing ' and convertive or regressive lives; and also to l>e the two-fold powers, the dianoetic and doxastic. 1'or the soul of the universe has both these; since Plato likewise in the Pluedrus says, that of the horses, one pertains to the nature of sattn; but the other to the nature of different, though ho also attributes horses to the Gods,* but such as. are good, and consisting of tilings that are good. Here therefore the external circle is dianoetic, but the internal doxastic. For the I)e-

1 I'nr i- i/rmu ill lliif |ilace, it i* u<n^.ir\ to read »•/,,,> <,i/r n u». For the MIII! 01' the uuivrric a!«.i\» fiirrjMzt •> l>olli |iru\iilriiiij||\ and t un\ciii\i ly, and the hitter riiiTyy ii inu-lltclivc. llciicr, there Mould In- a tjuti>ln>:\ in t»\ini>, the iittrllectire (>u»jrnu») and cvmeriivt lives. 1 I'nr roi/k 0«oi'« IK-IC, it ii nccosiiry to read rou 0»ou. miurgus imparted to the dianoetic circle a power, according to which it is more divine than the doxastic circle. For it is more united, and is intellectual. For you must not suppose that to denominate, is the mere position of a name, hut in the dianoctir circle is a participation of power, effective of sameness; and in the doxastic circle, of difference. Prior to this, therefore, Plato taught us the similitude of the soul itself to itself; hut now he adds the transcendency and diminution of it with reference to itself, which it possesses, and received from the Demiurgus; who made one of the circles to lx> external, so far as he rendered it more similar to intellect and the intelligible ; for they are properly c.itcrnal, as being e.rcmpt from oil secondary nature*; hut the other internal, as being container! by the more ex cellent circle, as being that which ou^ht to be go\erned by it, and as being of ;t subordinate nature. It \\as very far therefore from the intention of Plato, to adumbrate these circles mathematically, who, though they are equal, makes them to be unequal, and though they subsist similarly, renders them dissimilar, attributing to them f«>r their essence, the demiurgic will.

Some, however, here doubt, how, since the soul consists of similar parts, one of the circles pertains to sameness, but the other to difference, and the one is denominated internal, but the other external ; for these things subvert similitude of parts. Porphyry, therefore, directing his attention to sensibles, and material mixtures, adduces as instances, water mingled with honey, and honey mingled \\ith wine; the whole consisting indeed of similar parts, but in different persons producing a different passion. For some are more affected by the vinous flavour, but others by the sweetness. Our father [i. e. preceptor] however, thinks we should survey the mixture of the genera in a manner adapted to immaterial and incorporeal natures. Hut this is not according to a confusion of forms, nor according to a corruption of powers, but they I >eing preserved, the mixture is according to a union and penetration of them through each other. For corruptions and the diminu tions of pouers, sire in material natures, matter not being able to preserve in herxeli'lhe dilli-rent peculiarities unconlused stud genuine. For the peculiarity of immaterial mixture is for the same things to remain united and separated, and to IN- co-mingled and unmingled [but in material mixture, the things which are mingled, are said to be confused, and without separation from each other, because this mixture is through computrefaction, and corruption].1 It is easy likewise to call to our remembrance such-like immaterial mixtures xs we speak of, from the sciences, from physical reasons, and from a multitude of lamps. For the many

' In thr original lierc, tin re i-. nothing more than, ro ra /if/iiy/irKo »«t a&iajcjptra UT' aAXiyXwr ccfat. The rest in tin- altovc translation is *ujtj>Uc(l from the vcniou of T 1MIOCLUS ON THE [BOOK in. liphts \\liicli produce one li^ht, at tin' same time remain unconfused. An<! tlie multitude of physical reasons subsisting all of them at once, are. at the same time separated from each otlier, according to physical difference. The many sciences also are in each other, and an- unmiji'..rl< d \vitli each other. But this \n e\ident from their energies. For it is impo»ilile for things that are confused to employ their pn»i>er energies with purity. Hut the sciences t-nergi/e appropriately each \vith purity in i I self. If then-. ore the genera of the soul are immaterially mingled, tliev are in each oilier, and are established in themselves. By their subsisting lik.ewi.-e in e;u-h other, they cause the whole soul to he as it were of a similar colour. Hence every part of it con-ists «,f ihe-e genera. Hut throu-h the genera lx-in;4 established in them-elve-, and preserving their proper purity, diirerenf pro perties shine forth, according to the dillen nt powers of the soul, and >ome things prevail more than oilier.-. For in thin1;* which are mingled through the \\hole of iheinselvc-, ami are corrupted together, (here is eiilii- !y a similitude of pails, and lli< re i- al-o a similar form. Hut \\ here I here is the unminulrd m the mixture, the unconfused in the complication, and purity in the separation, then it i- possible for wholes to pervade throu-h w holes, in order that each part may consist of all ;

and for each pail to remain in it-< It' in order thai one tliin- may ha\e dominion m another. Hence, it is not at all wonderful, since all the -eiiera pervade though each oilier ill ihe soul, and pic-i rve at the same lime the idea of themselves, that in one place sameness should pn-dominale, hut in another, the nature of dill'dcnce, and thai the ^eims of essence should bo common, d. liniu- the one middle of Ihe soul, according to which il is a medium l.etvvcen l!,e imparlilile «— .nee, and llial which is din-ilile ahont hodi. -. llnice too. the ,-,.ul is one life, as Item- one e.s-elice, (ml the life is Informed, in ihe »'iine III, mm r as the essence is tvvtifold, on account of the two genera. Ami ilia-, much iu answer to the doulit.

Hut it i- evident that the words " lie »itti!<" are ni">l propuly a - i.nied liv IMalo, iu order that a^ain the form of the middle nature may !»e preservi-d in the same manner as lieiorewheii he said, ihe Demiiir^n^ " t< 'irp!, -.tcly jilU'd" ami " <;>-i/iiii^u<!.n The expression too, " lie i!cn»niin<ili-<!~ i- in!r"di! - cd appropriately to llie things proposed to 1 e dUcu-sed. For since naiiu s ue .iiveu to the circles, ;K •cnidil'L; lo (hat which piedoiniliale-, ihe expression " In ,'i /"'///,//,/<«/' m.iln - -ts That tin- appellation i- uiven to them, not from the whole hvpan.is, hut fr-.m that tvhich preilommates in them. To assign names likewise iifler l!:<- pro<luctioti «.f the < iides, inanife-ls thai names properly -o called re^anl llie nature of ihinj;*. 1'or the Demiurgus does not thus denominate (hat which i • .< -t t'ie < ii-cle of the same, Nut that which was con-tituttd such hy him. Dr ralln r, l.is piodticfivu HOOK in.] T1M.EUS OF 1'LATO. 125 cnenry possesses the most principal cause of the name. And the position of the name is an ell., -clue eiiei_iv, -nice intellection there is not separated from fabri cation, but tin; God.- produce by the very energy of intellectual perception [i. e. their intellectual perception is cflective]. For thus also by giving names to, they cons!iiui(; thiiv;s lhem.-,-I\e$. And if it be requisite for me to gi\e my own opinion, we ;r,ay through these thii^s perceive the arcana of the theory of Plato.

For he 1101 only delivers the Deiniurgus as a nomenclator, who fu>t gnes names to the I wo circulations of the soul ; but prior to these; unfolds the essential cha racter of it, \r/.. two separate n Jit li ics, and the y produced from them, and also the two circles. ;or;':.;:i f, mn l;;"-i- lines ; which things theurgy likewise unfolded after him,1 i;i«in_ co;Mi'h tion to the character of the soul from chiasmi * and .-e* micirct' s. P.-.\n;ical ii:-;tv •.. therefore and characters were first delivered to us by Plato. w!iic;i In ir:U lie ci'.uilly saw, and which the wise men po.-lerior to inn, embraced. For it i- nee. -sary to think, that there are psychical characters, and not only such as are common, like these, but such as are peculiar, and which are different in different soul-; such for instance as those of ii. miles, Penthi us, Atreus, and of Plato himself, dcliicred to us by the Gods them-el\es. These however, it belongs to the Gods alone both to know and to unfold ; but the cha- .racter which i> common to every soul, beginnitm from the soul of the universe, Plato first beheld, and committed to writing, lie also shows that the J)< :nmrgus is the maker of this, who inscribes in the essence of the soul its ' \i\iiic cha racter; gi\es names as we ha\e said to its two intellectual circulations, and assumes the-e from his own essence.

For it is the Demimmts himself, who is especially characterized according to these genera of name, i mean the same and Ihc (liji\rcnt ; since one of these eminently pertain- to him, as irivinir form to mat' ter, according to the terminations of forms ; but the other, as collecting multitude to the one idea of the fabric of the ir.ii\er>e as one production. I letter; also with Orpheus, the J^emiurgus p-.irticularly iiuerro^ali-s Ni^ht concerning these things, and says,

Tcil me iinw .ill tliin-s w.ll a^ one subsist, \ ct i ;n i. il - i, .it in r •< | '.ii .id1 |ins(i\cr For tl." l^i mi::!''jus cau-c- each thing to pr» -serve its nature, -e[>arate from others through <ii!!'ni»i:i.e, but he makes .dl things to IK- one through sameness. The Oracles like* '*e, by asserting, that the Demiur-us is refulgent with intellectual ' For /IT' ui/-<,.f hrr«', it i> n-<}iiiiilr to riM<l fi<r' avrcy, anil li>r Ufw^yiri (Jti)r(iyin. * C/^'•/^^'ll, i. e. figure:) iu I lit- form of tlie littery. 1 It i- ;.iTiisaij licre iu the word* rov zwyoviwv mr' aw»;» )^a^ai.rr;f»i, to t \jnuifj? nr'. 126 PROCLUS ON THE [BOOK in. sections, manifest that power of him which is effective of difference. But he fills all things with Io?e through the power which is effective of sameness. Hence lie very proj>erly gives these names which are demiurgic signatures, to the circles of the soul of the universe from his own esssenee. This name therefore, " (he circle of I he saint," is a divine name, as bearing the signature of the intelligible cause of sameness, as is likewise, " t)ie circle of the different" as possessing the symbol of the nature of difference. For with reference to the genera of being, one of these circles is allied to sameness, hut the other to difference ; but \\ith reference- to the intellectual Cods, one of them is suspended from the paternal, connectedly-containing, and immutable causes, but the other from the prolific and \ivific causes. And as with reference to intelligible*, the one in a greater degree participates of bound, but the other of infinity. These signatures therefore from all the orders, cause one of these circles to obt'iin

such a name, but the other, a contrary name. Some i ne however may say, what, then, is the one essence- of the soul destroyed in the ditision of these twofold circles? \N «• reply, by no means. For in divine natures, ditision is second to union, and progression is the medium Iwtween stable power, and the |>erfection subsisting in conversion or regression. But .since the soul is a monad essentially and a iln.ul, one and multitude, abiding, and at the same time proceeding and returning, and is also united prior to division ; — hence the mixture of the soul subsists one whole, prior to the many parts, and being divided according to progression, is again united according to regression. The less therefore, is comprehended in the greater circle. For as intellect comprehends the soul, illuminating it with its own light, thus also the circle of the same ' imparts union and perfection to the circk of the different, rendering it uudt filed in its providential energies, united in its progressions, and in a certain resjject intellectual in its knowledge of sensibles. Hence likewihe, in an admira ble manner, one of the circles subsists, and is denominated according to tht same, but the other according to the different. But the essential as being common to Inith, is omitted, and is attributed to no one of the parts. Hence the soul accord ing to thi> is one, but according to the two circles is bi for mod, these being after a certain manner opposed to each other.

" lie likewise convolved the circle of llie name, laterally towards the ri^ht hand, but the circle of the dijf'cnnt, diametrically towards the left hand." 1 For a*, on h ir, it is ucceuacv to read ravraw. BOOK in.] TLM/EUS OF PLATO. 127 What is liorc said, as that which remains to be discussed, is concerning the psychical powers, and the demiurgic separation of them from each other. For power is after essence; hut energy has the third order, as we have before observed. This also IMalo himself manifests to us, denominating the motion of these circles, the lulhn of f/ic snmc and the lation of the different, but not the essence of these. From these two circles also, he generates different powers, and afterwards unfolds to us what kind of energies they possess. Such things as these likewise, he asserts in the Plr.rdrus, concerning the better and the worn* of the two horses of the soul, \\hat therefore does he hem say concerning the powers of the soul of the universe? In the first place, as I have said, he di\ides the whole powers into two, I mean into the power of (lie same, and the power of the different ; the former being analogous to bound, but the latter to infinity. Afterwards, lie di\ides the power of the different, according to other peculiarities, and a^ain collects them into less numbers, and through sameness unites the multitude. In the next place, he attributes things more excellent and divine to the Ix'tter, but things less excellent to the subordinate powers.

Thus, lor instance, he attributes a convolution towards the right hand, to the lation of the circle of the tuna-, but to the left hand, to the lation of the circle of the different. And to the former he attributes the lateral, but to the latter the diametrical. For in the two co-ordinations of things, in the more excellent series there are [the same, the right hand, the equilateral and the rational ; but in the less excellent series]1 the contraries to these, the different, the left .hand, the longer in the other part, and the irrational. Such therefore, is the whole meaning of the words In-fore us.

1^1 us however see what the truth is of the things; and in the first place, if you are willing, let us show how the right and the left hand subsist in the universe. For I know that the da-moniacal Aristotle calls indeed the eastern part of the world the right hand, but the \\estern the left hand; since the first motion is from the eastern, but the motion posterior lo this, from the western parts. In all animals, however, the principle of motion is on the ri^ht hand. And in this thing Aristotle accords \\itli the doctrine of Plato, and also in what he assorts concerning the same and different. He says therefore that the merratic sphere is the cause to all things of sameness of subsistence, but the planetary spheres of a subsistence different at different times. This* however appears to me to be the illustrious peculiarity of the Platonic doctrine, that it does not define these things according to our habitude, but delivers these pro[K-r- ' The words within the brackrl* are omitted in ilicnripn.il, but art- Mi|»|>lir«l from t lie version of Thomarui. Hence after llie word* twt piv rr)i xptiTrovut ftmr attpnt in (lie original, it is wcessary to tdd, TO ravror, ro ix$u>r, rv ivo-r\tvpoft r» XoyuoK* twt tt riji ^eipoj-ui, K. X.

,.,U PKOCLUS ON THE [BOOK in. ties as proceeding from the fabrication itself of things. For if the Demiurgus himself inserts in divine; soul* the right hand and the left, each of these did not proceed into the world, either according : to our position, or as a mere hal.itude, but they are essential peeuliarilH'.- *, just as the paternal and maternal in the Gods, are the jH-culiarities of divine essences. For even in partial animals nature does not constitute some of the parts on the right, and others on the left hand, accord ing to mere habitude, but according to phvsical powers. And this is evident from her fashioning some of the parts on one side, but others [different from these] on the other side; and making this to be the principle of motion, but that not. This being thecasc, what ought we to think concerning the fabrication itselfof things' Is it that it exhibits one thing on the right hand, but another on the left, according to habitude alone' But how is this possible, if we admit that it produces by its very existence that which it produces, or that a divine soul is an r.-sence exempt from every tiling which introduces accidents ? Or must we not a.-sert, if this is granted, that the nature of the fabrication of things is in a greater degree gene rative of essence than a divine soul is \ Hut as it appears to me, we must say that this soul physically inserts in bodies the right hand and the left, and sus pends from itself in a greater degree the right hand as the principle of motion.

Hence, by a much greater priority, it is lit that the maker of soul should pro duce, both the.M- demiurgically in himself, and the right hand an image as it were of himself; and thus m the world, that the inerratic spin-re should he circumvohed to the right, but the plain tary sphere to the left ? the former having a prim ordial life, acme of power, and cilicacions energy ; but the latter being prolific and \arious, and from another source than itself jcceiv ing the principles ol mo tion. Hence also in the universe the inerratic sphere has dominion over all thin"*, convolving all things according to one circle; but the planetary sphere is mul tiform, and as we have said, is the cause of difference to generated natures. And the one is the imag" of intellect, but the other of soul ; for the circle of tin' sume is intellectual. In the soul of the universe however, the ri-ht hand is that which is eomethd to intelligible* , to truly existing beings, and the Gods : tor it i> a power which fills the soul with diune life. Hut the left hand is that which is converted to the care, ami orderly distribution of sen>ibles: for it is a power, motive of all M-condary nature*, and subvcrtive of inordination. It also produces separation and \.iricty in demiurgic works.

Farther still, the being convolved dunnctricallii uccord'nt" to tin- left hand, may be said lo compr« In ml the motion from the we.>t to the east, and the motion to the oblique parts, UnM!;_h the obliquity [of the zodiac]. But you may say that in the soul iiclf, the circle of difference, being gnostic of all sensible natures, at once no,,K in.) TIM/EUS OF i'LATO. j-29 comprehends the quadruple order of things, through the four centres, ac cording to which the visible motion of the bodies that revolve to the left hand and diametrically is effected; just as the circle of the same, knows in- (elligibles as primordial causes, as snpernally unfolding all secondary na tures, and convolving according to one union the various order of sensible*. Again also, these things accede to the soul according to its similitude to tjie rchu/e vivification.* For as the soul is a monad and duad according to this, so likewise it is allotted through it the right hand and the left. For in the irholc vivijication, these things first present themselves to the view, and are derived from it ; one multitude being produced from the right hand, but another from the left hand parts, whether you call than hcnilx,ur hands, or intestines. For according to all these, theologists deliver to us the prolific powers of the Goddess. These things however being appropriately asserted, it is evident that it is not the same thing to say that a certain thing is moved on the right, or on the left hand, and that it H moved towards the right or the left hand parts.

For the latter of these, assertions is attributed to things that are moved in a circle, manifesting that to be moved to the right hand parts is to be moved to that part to which the right hand moves, and also that to be moved to the left hand parts, is to lx> moved to that part to which the left hand moves. Since therefore, the ri^ht hand and the Irft are called the east and the west through the before-mentioned causes, so that the former is the beginning of motion, but the hitter follows, and in a similar man ner, the one being a power iu the circle of the same, but the other in the circle of the dijjcrcnt, from which the motion of each is derived, the words " tmcards the ri«ht and the left hand," are very properly introduced by Plato. But to bo moved on the right hand or on the left, pertains to things that are moved in a right line, these being the boundaries * of the motions according to breadth. Hence Timicus, having before separated the six motions in a right line, from the motion in a circle, and l>eginning in what is now said, from the soul, deservedly gives to it the difference of the motions towards the right and the left hand. And thus much concerning these motions.

Let us, however, consider the remaining opposition. For Timaeus, as in the world, convolves the inerratic sphere according to the side, but the planetary sphere according to the diameter, jiibt as in the soul he convolves the circle of the game laterally, but the circle of the different diametrically. In the first place, therefore, this must be considered mathematically, by drawing in a quadrilateral figure a 1 i. r. To Ceres, or Rliea, who contains in her right hand part* Juno Icfou ntam of »oulf, md in her lofl VcMa the fountain of virtue. ' For rape ra o»-rn here, it U necessary to read vrparn o»r«. Tim. Plat. VOL. II. R FHOCLUS ON THE [BOOK tu. diameter, and conceiting that the circle of the tame* is convolved according to the side, hut the circle of the different, according to the diameter of the figure. The quadrilateral figure, also, must l>e adapted to the two circles, i. e. t«> the sum mer and winter tropics; and we must concede, that they are moved with the motion towards the right hand part-*, accord in-jj to the two sides which are simi larly positt-d in lx)th the circles ; and also that the middle [or the circle of the same] is mou-d according: to the ureatot of the two circles, but that the circle of the different, which is oblique with reference to both, is moved according to the diameter of this quadrilateral figure. For the oblique circle [i. e. the zodiac] is described about this, according to which all the period of the circle of the different is convolved.

Leading however the mathematics, let us consider what the peculiarities are of the dianu-t.T and the (side. For we shall find those of the latter to be, the unoblique, the enable, the comprehensive, and that which is connective of angles ; but on the contrary those of the former to be, obliquity, the irrational, the com prehended, and that which divides angles. For according to all these peculiari ties, the side diners from the diann-ter. And lln^e also are inherent in the cir cles of the soul. For one of these cirrles is alKrd to simplicity, bound, and end ; but the other to variety, multitude, and the nature \\hich possesses infinite power. The one likewise is connective, but tin- oilier is the cau>e of division. And the one is allotted tin- dignity of comprehending, but the other that of being comprehended. Hence the one is very propi-rly said to !>•; convolved according to the side, as im mutable,1 as united, and as uniform ; but the other according to the diameter, as rejoicing in progression, and multiplications, and as effective of difference. For the diameter is greater in power than tin.- side, divides the angles, makes many spaces from one, and is situated obliquely. Hence in what follows, Plato says, that the lation of the circle of the tlijf'crcul is oblique. But all these particulars are indications of the nature of the infinite.

" But he gave dominion to the circulation of the same and similar. For he suffered it alone to remain undivided." This is the demiurgic sacred law, intelligibly proceeding from on high from intelligibles ; viz. that more simple should predominate over more various natures, • The circle of tht tame, is in the universe llie equinoctial circle; and the circle of tht tlifftrtnt, »» ihe zodiac. * F«.r uirap«.Ai<ru» in lllis j>lace, read a«-apaXAa*roi. HOOK MI.] TIM.EUS or PLATO. ,3, the more uniform over the multiplied, linites over infinites, and the more orer tinless intellectual. As then-lore in intelligible*, bound has dominion over the infi nite, in intellectuals the male over the female, in supermundane natures sameness over difference, and similitude over dissimilitude, thu.s also in the soul, the period of the satne predominates over the circulation of the different. Hence also in uensiblos, the planetary is under the dominion of the inerratic sphere, «nd everv multiform genus of life is contained by the uniform genera. Hence from these things likewise it may be assumed, that sameness i.s better than difference ; that again similitude appears to lx> more excellent than dissimilitude; and that the opinion of the generality of IMatonists is not true, that difference is better than sameness and dissimilitude than similitude. For on account of the form itself of sameness, the circle of the same is more divine. For the undivided, signifies divine union, an indivisible life, and uniformity in powers.

Why therefore, some one may say, if this is better, did not the Demiurgus suffer the whole soul to be undi vided ? We reply, because it i.s requisite" that the soul should possess all forms, and all the reasons and causes of mundane natures. And that which is compre hensive of twofold circles, i> more perfect than that which is defined according to one power. For that which is after such a manner the same, as in sameness to comprehend difference occultly, is more excellent than that which subsists ac cording to the psychical middle. But it pertains to the essence- of the soul to have dominion over difference, in conjunction with sameness. For the intelligible and intellect, are as it were the circle of sameness alone. But the sensible essence, is as it wore the circle of difference alone. For in the former, difference subsists occultly; but in the latter, sameness has nn obscure and superficial subsistence. And the soul i« a medium between both, being a duad, and having twofold cir cles, one of which pertairis to intellect, but the other to the sensible essence. It likewise possesses twofold reasons, the one intellectual, but the other effective of the world ; and the one proceeding to truly existing Ix-ings, but the other coming into contact with sensible*.

• ' But as to the interior circle, when he had divided it six times, and had produced seven unequal circles, each according to the interval of the double and triple ; each of the intervals being three ; he ordered the circles [i. c. orbs] to proceed in a course contrary to each other ; three of them indeed revolving with a similar celerity, but the other four dissimilarly to each other, and to the three, yet in a due proportion." ' For rJn hrrt, read •£««. 132 PROCLUS ON THK [BOOK in. In the first place, if you are willing, let us now surrey what is said by Plato, astronomically. For this mode of doctrine is appropriate, and let us conceive the depth of the planetary spheres, as one thiuir, and throughout similar to itself; because, as those who are skilful in things of this kind say, it consists of one matter; but is divided into seven orbs, which revolve in a certain respect con trary to each other. Or as some say, because the sun and the moon are similarly moved in their epicycles, revolving in their orbs with a motion contrary to that of the inerratic sphere. But others make one lation of the equable and the ano malous. Or [there is one depth of the planetary spheres,] because as others say, Saturn, Jupiter, and Mars, make the first eastern phases,' after their conjunction with the sun, in consequence of the sun beiim moved with greater celerity than these planets in cons, queiitia ?