Commentary on the Timaeus of Plato

* The original is, τοῦ yap αδιαιρετως παντὰ ovros, και rns δυαδος τῆς παντὰ ἐχούσης, μεσον ἐστιν ἡ μονας n Tarra ἐχϑυσα διηρημενως. But it appears to me to be neocssary to read, agreeably to the above transla- tion, τοῦ yap αδιαιρετως παντῇ ovros, καὶ τὴς ἑναδος τὴν παντα ἐχούσης διηρημενως, μέσον φστιν ἢ μονας ἢ ταντὰ ἔχουσα αδιαιρετωι. 380 PROCLUS ON THE [BooK 11. not be an intelligible animal besides it. For if there were, this would no longer be all-perfect, but a part. And that will be the whole of which this will he alone a part. For it is necessary that multitude should stop at the monad. Why, however, does Plato say, the second with another thing? For it would have been sufficient to have said, with another by itself, or the second, by itself. But he conjoins both, for the purpose of indicating that the nature which 1s co-arranged with another, and is not monadic, cannot as we have before observed, be the first. Perhaps likewise, it signifies the contrary, and that what is said pertains to thingsand not to words. For the form which is incorruptible natures entirely subsists with another. For the human form is in this individual, and in that, the participants being many, and on this account each is with another. That form, however, which is perpetual, yet not a whole, though it may be monadic, and on this account not with another, yet it is more imperfect than a certain whole. But that which is neither in many things, nora part with another thing, 1s not secondary, as being one and a whole, and not a part. Very properly, therefore, does the theologist produce Phanes, the only divinity bearing the seed of the lustrious Gods,’ from the God who 15 occultly all things ; and from Phanes gives subsistence to all the second orders of the Gods. For Heaven indeed proceeds together with Earth. But she,

Again th’ extended heav’n and earth? brought forth. Aud Saturn proceeds together with Rhea. For according to a third progeny, Earth produced [as the theologist says,] “seven pure beautifal virgins with rolling eyes, and seven sons that were kings, with fine long hair.” But the Demiurgus, who is the great Jupiter, is conjoined with Juno. Hence also, she is said to be of equal rank with him, and proceeds from the same fathers. Phanes, however, proceeds by himself alone, and is celebrated as female and father. 116 also produces the (three) Nights, and is present with the middle Night. For he Pluck’d the shorn flower of Night.’ According to this theologist therefore, all-perfect animal is not the second with another, but fills the orders of Night, and also fills the celestial orders with the > For θεὸν κλυτὸν here, it is necessary to read θεων κλυτων. τ, οὶ The intellectual Earth brought forth the sensible Heaven and Earth. 2 In the original avros yap ens παιδὸς ἀφείλετο covpipoy arfos, But for ens waséos, it appears from Eschenbach to be necessary to read τῆς Nu«res. Book 11} TIMUs OF PLATO, 381 allness of himself; in imitation of whom, Jupiter likewise, produces twofold orders, the super-celestial and the mundane. Phanes, however, gives subsistence to twofold triads, but Jupiter to twofold duodecads. For on this account bis sceptre is said to consist of four-and-twenty measures. Hence, the demiurgic is always assimilated to the paradigmatic cause, but proceeds into multitude from intelligible union. These things, however, are also elsewhere discussed.

But that animal itself rejoices in onlyness, is also manifested through the Orphic theologies. For as Phanes is the offspring of an egg, it is evident that he isan animal, At the same time also, he is called by Orpheus the happy aad venerable Metis, bearing the seed of the illustrious Gods; to whom Jupiter being analogous, is likewise denominated by Orpheus Metis and a demon. One power, one demon, the great lord of all. Thus too, the Oracles call this mighty God (i.e. animal itself] the fountain of fountains, and say that he alone generated all things. “ For from thence the gene ration of abundantly-various matter entirely’ leaps forth. Thence a fiery whirlwind sweeping along, obscures the flower of fire, leaping at the same time into the cavities of the worlds. For all things thence begin to extend their admirable “For again, another animal would be required about these two, of which they would be parts; and it might be more rightly said, that the universe is assimilated to this comprehending third, rather than to the This which is now asserted by Platu, may be easily demonstrated from the demiurgic goodness. For ifthe Demiurgus is good, he fabricated the universe with reference to all-perfect aniinal. Buthe is good and the best of causes, and therefore he assimilated the world to all-perfectanimal. Forit is necessary that the first Demiurgus should be intellective of the first paradigm ; and that being intellective of it, he should be the maker of that which is in every respect most similar to it. Forif there is nothing which is intellective of it, it will no longer have the order of a

paradigm, with respect to that which is fabricated by the first Demiurgus. If, however, you should say, that it is necessary there should be other secondary causes, which produce with reference to more partial paradigms, you say well * For Oey aby here, read ενθεν apdny. And for apvépow, αμνδροι. 382 τ PROCLUS ON THE [βοοκ τι. indeed, but at the same time you should preserve the universe one, For the fabrications of these partial paradigms are parts of the universe, in the same manner as the paradigms, and vice versa. As therefore paradigms are parts of paradigms, demiurgic’ are parts of demiurgic causes, and fabrications of fabrications, it is necessary that the wholeness of the universe should be the image of all-perfect animal; and that a!l-perfect animal should be the paradigm of the universe. Moreover, it has been demonstrated that animal itself is one, and alone, as being monadic. The world therefore is one and monadic, in order that it may perfectly imitate its paradigm. For as it primarily receives a simuar idea of it, how is it possible it should not adumbrate all the nature of it, im consequence of having been generated intellectual, perpetual, and monadic? “Tn order, therefore, that the world from its onlyness or being alone, might be similar to all-perfect animal, on this account the artificer neither made infinite, nor two worlds.”

Again, Plato reminds us of the Demiurgic cause, in order that we may understand also from this, that every thing which is generated by the whole fabrication, 15 monadic, perpetual, and intellectual; and that the Demiurgus is the cause of all things, in consequence of producing the monnds of them; but that he delivered the multitndinous and partial fabrication to the yunior Gods. | Farther still, he also latently teaches us who this all-perfeet intellect is, the name of which is so celebrated by the more modern philosophers ; viz. that it is intelligible intellect, in which the universe primarily subsists. Before, therefore, he called it distributedly “ according to all things perfect,” because he then celebrated its allness; but now speaking of it collectively, he calls it “ a/-perfect,” since his discourse is about the only-begotten. The infinite, however, in a certain respect is, and ina certain respect is not. Buta thing is said to be infinite ina three-fold manner ; either according to power, or according to multitude, or according to magnitude. The infinite therefore according to power isin divine natures, and in the world. For thenever-failing, and the perpetual, are the peculiarities of the infinite according to power. But the injinite according to multitude partly is, and partly ts not, Lor it has not an at-once collected subsistence, but exists according to a part. And the infinite according ta

Ἰ Instead of δημιονρ npura here, itis neccessary to read δημιονργικα, magnitude, neither erists according to a part,’ nor has any existence whatever Hence the infinite according to multitude, if it exists in the worlds, in the first place, will be without arrangement with reference to itself. For what order can there be in the intinite of things first and second, where there is no first? Jn the nevl place, it will not hace one producing cause. Lor if ithad, that cause would produce the one prior to multitude, and the whole prior to parts. For being itself one it would first assimilate to itself the things posterior to itself. For every cause which is effective of things according to nature, produces things similar to itself. But there is no first in those worlds, since they are infinite. And if they suppose other worlds consisting of others, either the causes of them will be unco-ordinate or co-ordinate. And if co-ordinate, it is necessary that the worlds should have one co-arrangement. But in the infinite there is no order. To which we may add, that the intervention of a vacuum in the middle, will separate the worlds. Bat if the causes are unco-ordinate, we must admit that there is a divided and unsympathetic multitude in the principles. This, however, will entirely abolish both all the causes themselves, and the things posterior to them. For the causes will be corruptive of each other, not being able to subsist in conjunction with, in consequence of being perfectly foreign from each other. But the things which proceed from them, collapsing, will stop, and will not have any thing from whence again they can be generated, the principles being destroyed.

Perhaps, however, some one may say that there is neither one world, nor infinite worlds, but many and finite. For we have heard of a certain Barbaric opinion, which the Cheronean Plutarch relates,’ placing in one equilateral. triangle the intelligible world according to the middle of it, in each of the sides sixty worlds, about the intelligible, and in each angle one world; all of them (except the intelligible) being such worlds as that in which we are comprehended, So that there are three leaders, and thrice sixty others, under them. For the angular are of a more ruling nature than the lateral worlds. "This opinion, therefore, introduces a multitude of finite worlds, and makes the intelligible to be one of them. Unless, indeed, you arrange the intelligible world in the middle, as the ' The words, ovée xara μέρος are omitted in the original; but, as it. appears to me, ought to be inverted. * These arguments, which possess an invincible strength, fully show the futility of that very popular theory of the moderns, that there are infinite worlds. For like most other modern dogmas, it is unscientific aud rambling. 4 See Plutarch’s Treatise on the Sileuce of the Oracles.

284 PROCLUS ON THE {Boox "1. root of all things, but the three angular worlds as connective of all things, and causing all things to be one, according to one mundane intellect, one soul, and one nature. Or according to the empyrean, etherial, and material world, For an angle is connective of the sides. But the three sixty worlds may be said to be the multitude according to each sphere of these. For the spheres are twelve in number; and the multitude in each is spherical, of which the pentad is a symbol, being the first spherical number. Hence there are thrice sixty worlds, because there is an intellectual, a psychical, and a physical series, accord - ing to each sphere of which the pentad is a symbol; or because there is an empyrean, etherial, and material multitude of Gods. If, however, some one shomld not admit that these things are obscurely signified (in this narration of Plutarch}, but should assert that the worlds are truly divided according to number, we ask him, whether it is better to make one world comprehensive of all things, or many worlds separated from each other? Por the former makes multitude to be connectedly contained by the monad, and parts by the whole ; but the latter dissipates production into an unco-ordinate multitude; though nature, and every cause of this kind, makes amonad prior to multitude, and a whole connective of parts. Jf likewise the worlds being spherical, touch each other, they will touch according toa point, but in the whole they will be separated from each other, and will be more unsympathetic than sympathetic.

Itis necessary however that things which proceed from one cause, should be co-passive with each other, and give completion to one lite. Butif they do not at all touch each other, they will be [entirely] separated. How also, Aristotle would say, will things which are upward be downward, and things which are duwnward be upward, interval being external to the worlds?) And how will this thing pertain. ing to the worlds be arranged here, but another there? For that which is upward to us, will be to others downward. Will not the earth therefore of the other worlds, and every thing there which is heavy, be impelled to this world, if the motion of that which is heavy tends downward? But at one and the same time, a body which in one of those worlds tends upward, will, as proceeding to this world, tend downward. And there will not be an order of motions, or powers, or of things which are co-ordinate in the universe. Unless some one should say in answer to this, that there is a different middle in each of the worlds : for the middle isnot the middle of a vacuum, but of a world. Each part therefore of a world tends cither to the middle, or to the circumference of that world, but not to that which is foreign to it. All the things, however, that are in other worlds, are

foreign to each other. If therefore, some one should think that these assertions are worthy of belief, let them remain as such. Plato however, has chosen the most principal and proper cause of their being but one world, viz. that which is derived from the paradigm of the universe ; but has omitted as concauses the above, and such-like causes. A demonstration also of this kind is definite. For it does not separately confute those who say there is a multitude of worlds, and separately those who introduce an infinite number, dispersed in different places, and intercepted by a vacuum, but at one and the same time he shows that the assertions both of the former and the latter are false, directly proving that the world is one from the onlyness of the paradigm. And farther still, he avoids the modes of argument which are derived from matter. Lor he neither demonstrates, as Aristotle docs, from matter being one, nor from places being definite according to nature, nor from essence, i.e. matter which is a body, being united, according to the doctrine of the Stoics. For Plato alone or especially employed, says Theophrastus, the cause which is derived from prooidential inspection ; beautifully testifying this of Plato. As we have said therefore, he ascribes the onlyness of the world to the paradigm. For if the paradigm is one, and the Demiurgus is one, it is necessary that the world should be one.

-Or rather, if the paradigm is one, and the world adumbrates the onlyness of the paradigm, the world is onc. But the antecedent is true, and therefore the consequent. For the paradigm is one, as he before demonstrated, and constituted the world conformably to the onlyness of itself, For as the intelligible paradigm was generated one from the one which is the good, so likewise with reference to itself being one, it constituted the world only-begotten. Hence the world is one. And neither are there many worlds ; for there are not many first paradigms ; nor infinite worlds ; for the infinite according to multitude, does not even exist in mortal natures, so far is it from having a subsistence in perpetual beings.

But it is possible, says Porphyry, to use the demonstration of Plato in all other principles. For through this, not only intelligible animal is demonstrated to be one, but also the first Demiurgus. And inshort, it may be demonstrated, that there are not many principles of intelligibles, but one priticiple. For again another principle of their being many would be requisite, through which the principles themselves are unbegotten. For every thing which is naturally inherent mmany things, is necessarily derived from one cause. He therefore who says, that God and matter are principles, must be compelled to admit that there is a certain 380 PROCLUS ON THE TIMZEUS OF PLATO. [woox τι. other cause prior to them. For neither is matter sufficient to itself, nor will God be comprehensive of all things [if there is another principle independent of him). It is necessary therefore, that there should be a cause prior to these which comprehends all things, and which is truly suthcient to itself, and is not in want of any other thing. “ But this heaven (or universe} was generated, is, and will be one and only-begotten.” The only-begotten indeed, adumbrates the monadic cause, and indicates an essence which is comprehensive of all secondary natures, and has dominion over wholes. Fur the theologist is accustomed to call Proserpine only-begotten ; ας presiding ina leading and ruling manner over all mundane natures, and as the cause of only-begotten animals, For the Goddess who ts posterior to her gives subsistence to the animals which are not only-begotten, as being irrational, The theologist therefore, on this account calls Proserpine only-begotten, though he produces another divinity from the same causes as he produced Proserpine, Unity however, ts imparted to the universe from the one unity of unities.

For as the being which ts every where, is derived from being itself, so the one! whichis in all things is from the one itself. But the words “ was generated, ts, and τοῦδ be,” manifest the temporal perpetuity of the universe, which is extended with the infinity of time. For the term weas, is indicative of the past, the term is, of the present, and the term will be, of the future time. Again therefore you have the term ove couformably to the image of the one being [the summit of intelligibles); but the terms was, és, and will be, conformably to the image of eternity. Bor the infinity ΟΥ̓ time imitates the eternal infinity. But all these are according to the image of animal itself. For this was) primarily monadic, and traly an eternal one. But the world is monadic and perpetual through the initation of it. Parther still, the term “was generated,” ts significant of perfection ; the term “4s,” of the participation of being ; and the term “will be,” of perpetual yencration, through which the world has a never-failing subsistence. So that of these, the first is from the one; for from thence perfection in imparted to all things, But the second is from the one being, And the third is from eternity ; for from thenee the never-failing is” inherent in wholes.

' For ro ey πᾶσιν ov here, itis obviously necessary to read ro es πᾶσιν ev. ’ y a THe present treatise in one way surveys the world according to the wholeness which it contains, conformably to which also it is similar to all-perfect animal, and was generated an only-begotten animal, animated and endued with intellect ; but in another way, according to the division which is in it; as when it divides the soul from body, and likewise things which have a more formal order, But how does the psychical breadth proceed from fabrication, and according to what kind of reasons? For since the world is an animated animal and endued with intellect, three things are exhibited in it, viz. a certain body, soul, and. intellect. ὦ Intellect however, is entirely unbegotten : for it is allotted an eternal essence and energy. But body is entirely generated: for it consists according to the whole of itself. in the whole of time, And soul is of a middle essence. As therefore, it is arranged in the middle of impartible and partible natures, after the same manner also, it is the boundary’ of unbegotten and generated essences. Hence it is generated indeed, as with reference to intellect, but is unbegotten, when considered with relation to a corporeal-formed nature. It exists also as the end of eternal beings, but ranks as first among things that are generated. On this account therefore, Plato delivers to us an all-various generation of body, producing it wholly from causes different from itself; but he produces soul both trom itself, and from the total fabrication and vivitication. He does not however, in words devise any generation of intellect. For neither is intellect produced according to idea, nor does it admit of any name of generation, being entirely unbegotten, and eternal. It is however unfolded into light from wholes, but abiding in them

* For epwshere, it is necessary to read opos. 388 PROCLUS ON THE [BooK "ι. inherently, it proceeds unitedly, together with its more total causes. Hence it abides impartible and undivided, being preserved by undefiled and inflexible powers, while another life is distributed and divided about the parts of the umverse. Plato therefore, delivers the first: hypostasis of the universe from fabrication, viz. an hypostasis according to wholeness; according to which it becomes animated, divine, and endued with intelleet, conformably to a similitude to allperfect animal. But he adds asecond hypostasis, which divides the world according to wholes, and the production of total parts; soul and the corporealformed nature existing according to this hypostasis. For intellect is entirely unbegotten, as we have said, because it is without generation and indivisible; except that it proceeds in an unbegotten manner, from the providence of the Demiurgus. But he calls the nature which receives intellect, the evolution ἡ itself into light of soul. For the Demiurgus himself places the circles of soul in intellect, unfolding it without division, as being impartible, and without figure, as being pertectly unfigured. And he delivers after this, the third hypostasis of the universe, dividing it according to parts, and giving perfection to each of the parts. For he delivers to us, how fire and air, water and earth are generated. But in the Jast place, he surveys the energy of fabrication which is effective of body ;

and neither in this does he descend to particulars," but abides in the whole elements. — For the total fabrication is the fabrication of wholes, and of total parts. But he delivers the formation of individuals, and of things which are truly partial, to. the junior Gods ; in order that imitating the providence of their father about wholes, they also may receive a similar fabrication about particulars, and may have that analogy to him which he has to the intelligible paradigm. For being intellectual as with reference to this paradigm, and having the order of intellect, as with relation to intelligible intellect, he becomes himself intelligible to the mundane Gods.

As we have said therefore, fabrication being triple, the first, according to wholeness, the second, according to a division into wholes, and the third, according to a division into parts,’ Plato now intends to deliver to us the middle or second fabrication ; having indeed a transition of this kind consentaneous from. things themselves 5 and having also an opportune progression to this from what had been " For aagaow here, read expavau. * For ra sadeora, read ra καθέκαστα. Ὁ In otber words fabrication is either Jovian, or Dienysiacal, or Adontical, as was before observed by Proclus. before said. For since he had defined the world to be one visible animal, comprehending within it all such things as are naturally allied to it; that the world indeed is one, he demonstrated from the onlyness of the paradigm ; but that it is visible, and that it is comprehensive of all kindred natures, is rendered manifest to us by the division of the universe into wholes. For if we can discover from what cause the world is visible, and how all the elements are co-arranged in it, and through what analogies, we shall easily perceive that it comprehends all kindred natures, and that there is nothing sensible which is not contained in the one ambit of the world. Perceiving this however, we shall sufficiently obtain the object. of investigation, For this was, how the world is visible, and how it is comprehepsive of all things which are naturally allied to it. For from what has been before said, we assume that the world is alone; but from these things, that it is all-perfect.

“Since, however, it is necessary that what is generated of a corporeal nature should be visible and tangible ; but without fire nothing can become visible, neither can any thing be tangible without a certain solid, nor solid without earth ;—hence divinity beginning to fabricate, constituted the body of the universe from fire and earth.” Plato having a little before given the definition of that which is generated, calling it that which is becoming to be, and which is perishable, he defined it to be that which is the object of opinion in conjunction with sense. But demonstrating that the world is generated, he converts the definition. For he says that sensibles are seen to be things which are becoming to be, and are generated. But now transferring that which is itself generated, to the order of a subject, he predicates of it the visible and tangible. For these are the extremes of sensibles, just as the sight and the touch are the extremes of the senses. Hence there, as 1 have observed in what he says respecting the world being generated, he converts the definition. But here he gives it according to nature. For that which is becoming to be was in the order of the indefinite. But as he said in the hypotheses, that which is the object of opinion in conjunction with sense, is to be assumed in the definition. Ie says therefore, it is necessary that what is generated should be | sensible, not indeed every generated nature, but that which we before called generated, viz. the composite nature, and which is always becoming to be through the whole of time. For soul also is generated, but the discourse is not about this.

200 PROCLUS ON THE [Boox 11. If however, some one should say that according to Plato material forms and qualities themselves are apprehended by sense, and yet are incorporeal, and at the same time have generation, let him know, says the divine Tamblichus, that these likewise contribute to the hypostasis of bodies, and are surveyed in conjunction with them. Since therefore the world has a certain corporeal and likewise an incorporeal portion in it, and this latter is two-fold, one being inseparable, but the other separate from body; since also the portion of the incorporeal, which is separate from body is two-fold, viz. psychical and intellectual; and further still, since the world also has the unbegotten and the generated, but the whole of every thing which consists of the unbeyotten and the generated, is generated, Plato very properly calls the whole world something generated and corporeal. formed. For if a whole consists of the mortal and the immortal, the whole is mortal ; if from the unbegotten and the generated, the whole is generated 5 and if from the incorporeal and the corporeal, the whole has the form of a corporeal nature. For if indeed, the incorporeal itself is co-passive with body, it becomes itself corporeal-formed, and not the whole only. Ty, however, that which is principally and properly incorporeal, is itself exempt and impassive, being raised above body, this more excellent nature is not indeed body, since it remains tn its own purity, but the whole may more justly be denominated corporeal-formed. Hence, since the world participates of many and blessed prerogatives from. its generator, but partakes also of body, itis deservedly called corporeal-formed, visible and tangible, according to the whole of itself Tor it is generated. But that which is generated is visible and tangible and has a body, as was rightly asserted before.

Plato beginning therefore from body, in the first place gives it to be sensible according to the extreme senses. In the next place, he imparts to it that which is more perfect than this, viz. the bond through analogy, which is connective of the bodies it contains, In the third place, he makes it to be a whole consisting of the wholes of the elements. Afterwards, in the fourth place, he gives ita spherical figure, in order that it may be most similar to itself according to form. In the fifth place, he shows that the world suffers all things in itself, In the sixth place, he distributes to it an appropriate motion. Afterwards, in the seventh place, he animates it through a divine soul. In the eighth place, he imparts to it atemporal period. Afterwards, in the ninth place, he establishes the senes ' For cepa here, itis necessary to read σειρα. βοοκ 111.] TIM.LUS OF PLATO. 391 of Gods in it, who conjointly produce the perfect year. And _ in the tenth place, he makes it to be perfect from all animals which are assimilated to the four ideas {in animal itself]. And thus through the decad he gives completion to the whole fabrication of things. ‘These particulars Lowever will be unfolded as we proceed.

Now therefore, we shall observe, that since the world possesses interval, and is apprehended by sense, it is known through the sight and the touch; being visible indeed, in consequence of being wholly filled through the whole of itself with light ; but existing tangible in consequence of being a solid. For itis sufficient for it to receive through these senses, all sensible aatures. The visible also, and the tangible conceived as always existing in the world in the four elements, are contraries. For these as being most distant from each other and under the same genus, are contraries. For both are sensibles, and this is their common genus, and they are most distant from each other, since the one is immediately sensible, but the other is not sensible without a medium. If however, we lvestigated the contraries in the elements so far as they are mutable, we should not say that they are fire and earth, but fire and water. For water especially extinguishes fire. Each also of the assertions is true. For it is common to both to have their contrariety consist in being extremes. And in this the assertions accord, as in senstbles indeed, carth being contrary to fire, but asin things of a mutable nature, water to fire. Hence also Plato opposes the visible to the tangible. Or, [it may be said] that he assumes the sensible clements, as not yet considering the mutation of them, according to which water is more contrary to fire than earth.

What Plato therefore here says, is not as Theophrastus thought, imperfect : for he doubts as follows: Why does Plato say that the peculiarity of five is visibility, and of earth tanzibility, but does not at all mention the peculiarities of the other elements? We reply, it is because we see the world, and also touch it, but we do not taste, or hear, or smell it. The world itself also is visible and tangible to itself. And as being luciform indeed, itis visible, perceiving itself through divine light, which is extended through all heaven, and is similar, as Socrates says in the Republic, to the rainbow. or this divine light is that which is primarily visible, and pervades through the whole world. For as the sphere of the sun is the sight of the soul which is in it, thus also the sight of the sphere" is that divine light, which pervades through all visive* natures, and operates on, and imparts life to things that are visible. You may likewise say, that this is

* For ψυχης here, it is necessary to read ogaipas. * Instead of eparwy in this place, I read σρατικων. 392 PROCLUS ON THE [Βοοκ 111. the first and most principal sight, but not that which subsists in conjunction with passion, and which is separated from visible natures. But again, the world as being solid and full of life, has what is called a co-sensation of itself. For we also have a co-sensation of the motions or passions which inwardly subsist in us. And through this consciousness, the world becomes tangible to itself. The most proper solution however of the doubt, is that which says, that Plato assumes the extreme elements prior to the others, because the latter subsist for the sake of the former. And he intends to show that the rest are constituted as the bond of the extremes. Orit may be said, that through the extremes he also comprehends the media. For as the universe is defined through fire and earth, and the media which are comprehended in these, thus also through the visible and the tangible he comprehends all the variety of sensible natures. This however, he employs as anaxiom. For it is usual with him prior to each of the subjects of discussion, to assume an axiom from which he demonstrates the thing investigated. Thus for instance he assumes axiomatically the sentence, “ Jn him who is good envy ts never ingenerated about any thing,” in order that he may demonstrate that the Demiurgus imparts good to all things.

And again, in this way he assumes the words, “ Jt neither was, nor will be lawful for the most excellent nature to effect any thing else than that which is most beautiful ἢ in order to show that the uniyerse is an animal endued with intellect and animated. This too, is the case with the words, “ That which is assimilated to an imperfect thing can never become beautiful ;” in order that he may survey what the nature of the paradigm is, according to which the Demiurgus constituted the world. After the same manner therefore here, previously assuming as an axiom, that what is generated ts visible and tangible, he demonstrates from this, how the elements contribute to the composition of the world, md how they are arranged in the universe. For if itis necessary that the world should be visible and tangible, fire and earth are necessary to it: for that which is primarily visible is fire. In the first place, indeed, because visible natures themselves are luminous substances: for all colours are the progeny of light. In the next place, because (he sight itself is light proceeding from an etherial-formed essence. And in the third place, because sight, and that which is visible, require the congregating power of light, in order to their existence in energy. ΕῸΓ what else Is it than light that collects both these together? So that the world will be in want of fire, in order to be visible. To which also may be added, that Pythagoras in what he says to Abaris, demonstrates that the eye is analogous to fire. For it ts the most elevated of the instruments of sense, just as fire is of the elements, and employs as well as fire acute energies. The conical emission also of its rays, has no

ποὺ κ 211.} TIMAUS OF PLATO. 393 small similitude to the pyramidal form of fire. Plato however, does not say that fire alone is vistble: for this is false in a twofold respect. For fire itself by itself, unmingled with the other elements, is by no means externally) visible, but is ouly visible in mental conception, And farther still, none of the other elements will be visible af tire alone is visible. It is) one thing therefore, to be visible through fire, and together with fire, and another for fire itself to be the only thing visible, Henee, he does not assert the latter, which may be confuted in a twofold respect, but the former, because nothing is visible separated from fire; from which also you may assume, that all bodies part'cipate of fire. But in different bodies there is a diflurent fire. For light, flame, and a burnins coal, are not the same thing. But fromon high there isa diminution as far as to the earth of fire which proceeds from a more immaterial, pure and incorporcal naturc as far as to the most matcrial and gross bodies. Vor there are streams of fire under the earth, as Empedocles somewhere says ;

Beneath the earth buro num‘rous fiery streams. Nor ought we to wonder how fire, though in water, is not extinguished. For all things proceed through each other, and that which predominates is different in diferent things. Light also is fire pervading through all things. Numenius therefore, being of opinion that all things are mingled, thought that nothing is simple. But Plato knew the mixture of things, and separately delivered the nature of each, fashioning the elements from figures, Perhaps however, the wonderful Aristotle will object to what is said, not admitting that every thing visible is such through the participation of fire; because the choir of the stars, and the great sun itself, though they do not consist of fire, yet at the same time are visible. But if some one should say to him, that with respect to fire, one kind is material, but another immaterial, as with reference to sublunary fire which is material; that one kind is corruptible, but another incorrupuble; that one is mingled with air, but another is pure; and in short, that there are many species of fire, perhaps he will assent to the assertion, and also to the theologists' who cals the suna fire which is the channel of pire, and the dispensator of fire, and all such-like appellations. For to what else can he ascribe visibility, than to that which is generative of light? But what except fire is a thing of this

"viz. The Chaldean Theurgists. See my collection of the Chaldean Oracles. Tim. Plat. | Vou. I. 3D 494 PROCLUS ON THE [Bpoow Itt. kind? For earth’ is effective of that which is entirely contrary to light: for it is the cause of darkness. And that which is more terrestrial participates in a less degree of light; but air and water are diaphanous, and are not of themselves visible. Hence each of these is a medium between that which is primarily visible, and that which obumbrates visible natures; cach being the cause of visibility to other things, but not to itself, so far as each of these is diaphanous, but other things are transparent through these. It remains therefore, that fire alone illuminates the things with which itis present, and makes them to be visible. If however, some one should say, that the celestial element which is visible and iluminative, is not fire, we ask him, whence does the fire which is here, become such as itis? Por if each of these is generative of sensible light, Why may not each of them be fire, though the one is immaterial, but the oiher material ? When, however, I say that the one 15 immaterial, [ mean as was before observed, that itis so when compared with the grossest* matter, which is not able to sustain forms, so as to prevent them from gliding away, and which is distinguished from the matter that mvariably remains im its Own proper form, For we learn that matter pervades through the whole world, as the Gods also say.

Hence Plato, as he proceeds, calls matter the receptacle of the universe. Such therefore, as are the kinds of light, such also are the kinds of fire; and analogy shows that the hight which is from the celestial element is from fire. Hence, it must be said, that Plato does not characterize fire by heat, nor by being, moved upward ; for these things are the peculiarities of the fire which is here, and which is not in its proper place; but that he characterizes it by visibility. For through this he comprehends all fire, the divine, the mortal, the caustic, and the vehement. Farther sull, the same things must likewise be said concerning earth, that earth is that which is primarily solid. For it must not be said that earth derives its sohhuity from some other place; but in sensibles, that which is especially solid, has this pecularity, prior to such things as are less solid; since also that which is especially hot, is hot prior to things which have less heat, and from this things which have Jess heat, participate of this quality. If therefore, earth is more solid than the other elements, but that which is most solid is the cause of things which are less solid being solid, and things which are less such are not the causes of: sulidity to those which especially and particularly have this power; —if this be

* Ynstead of πη in this place, it is necessary to read yn. * Lor Taxyvrarny here, itis necessary to read wayyraryy, the case, it is necessary that earth should be the cause of solidity to the other elements, having itself a subsistence contrary to fire. And if indeed, we assume things which are apparent to our senses, viz. heaven as fiery, and the earth on which we walk, as especially earth, the contrariety of these will be manifest, the former being always in motion, but the latter being immoveable; the former being transcendently visible, but the latter tangible: and the one being most attenuated through light, but the other most gross through darkness. But if we wish to survey the first elements of these, viz. fire itself so far as fire, and earth itself, so far as earth, we shall shortly after unfold all the oppositions of these, when we discuss the analogy of the four elements. “That visibility therefore, is the peculiarity of fire, and tangibility of earth, we may from these things assume to be most true, lence Porphyry says, that of demons some, being visible, have in their composition more of a fiery, in consequence of not having any thing of a resisting nature. But others, participating also of earth, are capable of being touched. Ile adds, that such as these appearing near Tialy about the Tuscans, not only emit seed from which worms are generated, but also strike against other things, and Jeave behind them ashes ;

from which likewise he shows that all things participate of earth. There is not, however, the same nature of earth every where, and in all parts of the world, but in some places it is more pure and immaterial, and without gravity. Lor not gravity, but tangibility, is the peculiarity of earth. But in other places, itis more material, and heavy, and is moved with difficulty. In some placcs likewise, it exhibits solidity alone; but in others, it receives other genesiurgic and material powers, after the same manner as fire.

If however, these things being asserted by us, Aristotle should doubt, how if fire isin the heavens it is moved circularly, and not in a right le, we must adduce in answer to him, what Plotinus says, that every simple body, when in tts proper place, either remains immoveable, or is moved ina circle, in order that it may hy xo means relinquish its proper place. For if itis moved in a different: manner, it will cither no fonver be inits own place, or will not yet be init. A celestial body therefore, being fiery, is necessarily moved in a circle. For earth also, if it were moved without leaving the place about the middle, would be moved in a circle. For when fire is moved to the upper region it is so moved in consequence of being ina foreign place. For the same reason likewise, a clod of earth is moved downward ; and in short, the local motions of the elements in ἃ right line, ure occa- * Instead of wa μη Se ws in this place, [ read wa μηδαμωε, 396 PROCLUS ON THE. (moun at, sioned by their being preternaturally disposed ; so that it is false to say that fire is naturally moved in a right line. For it then especially subsists according to nature when it possesses its proper place. — But when it tends to its proper plaice, it is not yet in a Condition conformable to nature.

This however being demonstrated, itis evident that the celestial fire when it is moved, is moved ina circle ; and nothing that has been said disturbs the Phatoute assertion. For if fire is moved in aright line,’ it is not yet in its natural place. Butaf itis in its nataral place, it will cither be immoveable, or moved in acirele, ΠΝ impossible however, that it should be immoveable: for all fire is naturally moveable. Tu its natural place therefore, it is alone moved in a circle. But let us return to the thing proposed to be discussed,

If therefore the universe is generated, itis necessary that it should be sensible. But if sensible, itis visible and tangible, And itso, it consists of fire and earth, But if this be admitted, it also consists of the middle clements. | For tire and earth areas much disjoined from cach other as the sight and the touch, and require the other clements as connecting media. Tfhowever, the world is visible, itis necessary there should be fire; and if tangible, 1Ὸ is necessary there should be earth, Bor that which is solid is tangible, and is also able to resist the touch; since that which is friable, and cannot sustain the touch, is by no means κι]. Tence Pythagoras calls the earth the sustainer, as being solid, and resisting the touch, and as moved with dituculty, and participating of stable power. If therefore, as we have said, fire is requisite in order that the world may be visible, but earth, that itimay be tangible, divinity beginning from fire and earth, made the universe, Not that he first made these ; for we have already reyected the generation which is according to time; but since every physiology commences from contraries, on this account Plato says that the composition of the universe orianated from fire and earth, in order that it might become visible through fire, and tangible through the solidity of earth, which with great accuracy he calls ὦ certain solid. Por ἃ physical solid is one thing, bata mathematical solid another, And the datter ts intangible, but the other, which the discussion now requires, is tangible, Por that solid is tangible, which as physical Pence those are absurd who doubt why earth alone ix solid: for, say they, water and air are also solids, Por it may be said, in answerto them, that resistance expecially pertains to earth; since tt is the support and foundation of the other elements. For earth supports water, and

* The words ex’ evOecas, are omitted in the original BOOK 111.} ΤΙΝ ῦ5 OF PLATO. 297 both earth and water support air. Earth therefore, is the first tangible, and the first resisting substance, and on this account is the first solid. We shall omit however to notice those who say that Plato here calls the three elements after fire, earth, For if this were admitted, it would not be possible to assign what is the medium of earth and fire. “ΤῸ is impossible however, for two things alone to cohere in a beautiful manner, without the intervention of a certain third ; fora certain collective bond is necessary in the middle of the two. But that is the most beautiful of bonds, which causes itself and the natures which are bound, to be one.” In what is here said, a bond is assumed as affording an image of divine union, and the communion of powers, according to which the intellectual causes of wholes effect their generations. But beauty appears to be assumed, as having an uniting and binding essence and power. For the words, “ to cohere ina beautiful manner, and the most beautiful of bonds,” appear to me_ to be significant of this. Beginning therefore from the duad, as allied to generation, progression and difference, Plato introduces union to the participants of it, and an harmonious communion through a bond, imparting to the world this as the second gift from the Demiurgus.

We shall however here avoid the introduction of such doubts as are adduced by those who do not rightly understand what is said by Plato. For neither do those who say that semicircles require no bond in order ἴο the generation of a circle, speak rightly; fora circle does not consist of semicircles, Lut on the contrary, the circle now existing, and not subsisting from these, the diameter being drawn makes the semicircles. And this is evident from the name affording a generation to these from the circle, but not vice versa. Nor do those speak rightly who assume the monad and the duad, which in a certain respect are opposites, and have no medium. For Plato does not absolutely say, that there is something between all things, in whatever manner they may exist, which gives perfection to the hypostasis of one composite. For he says, that two things alone cannot beautifully cohere without a third. But the monad and the duad are not contraries, since the duad consists of monads. Nor again, is there any rectitude in the assertions of those who introduce things that are corrupted together, as for instance, wine mingled with honey. For these no longer exist

498 PROCLUS ON THE (BooK τι, when the mixture takes place. We however, do not investigate how things are corrupted ; for this is not wonderful ; but how remaining what they are, they are co-harmonized with each other. For this bond‘ is the cause of safety to the things that are bound, but not of their common corruption and abolition. Nor do those speak rightly who adduce as a witness the communion of man and woman, which requires no third thing to its subsistence. For through ignorance they do not perceive the greatest bond, that of love, which excites to communion, in one way indeed, to a communion of the psychical life, and in another to that of the physical life. For the bond through animation is the medium in these. Nor are they right who adduce things which are melted together, as gold and silver. For of these there is the same essence; since both are water. ΑἸ these theretore, wander trom the conception of Plato. We however, again say, conformably to what has been before observed, that it is necessary these two things should be assumed, in the first place, in order to the g, and in the next place, in order that their coalition may not be corrupted. For they would no longer be bound, but would cease to exist, In the third place, also, it is necessary that they should truly be the clements of

composition of one thin that which consists of them. For having these conditions, they will entirely be in want of a certain third thing to their colligation, For what, since they are separate, divided, and most distant from each other, will collect them into one ? Por if nothing accedes to them, they will remain divided, and will subsist after the same manner as before. But if something accedes to them besides what they already are, this thing which accedes will become their bond. For it was this which collected them mto the composition of one thing. A bond, however, is said to be so ina threefold respect. For one bond is that which pre-exists in the cause of the things that coalesce. But another is that which is inherentin the things themselves that are bound, and which is co-ordinate to, and connascent with them. Anda third is that which exists in the middle of these, proceeding indeed from the cause, but presenting itself to the view* in the things that are mutually bound. Ifyou are willing also, one bond of an animal, and of the parts in it, is the one reason which is pre-established in the cause itself of the ammal. But the nerves and the fibres are another bond, connecting the parts of the animal, And another bond is the physical reason or productive and forming power, which

* For ov yap δέσμος ουτος, It is necessary to read 0 yap de opios ovros. * For evgau operos in this place, it is obviously necessary to read eppawoperos, Book 411] TIM ALUS OF PLATO, 399 proceeds from the cause of the animal, and employs the nerves, and all the inaterial organic bonds tor the colligation of the animal. For this bond is neither exempt from the things that are bound, nor yet ranking among things which are withont eflective power, is it destitute of the true cause. You must not therefore, understand the bond which is now mentioned by Plato, according to the first mode; for this is not attended with cause ; but cause is entirely exempt from the things which proceed from it, so far as itis cause. But Plato says, that the bond isin the middle of the things that are bound. That, however, which is in the middle of certain things, is not separated from them. Nor does this bond subsist according to the organic and Jast kind of bond. For the bond which is conformable to this, is not the lord of itself nor of its own proper union. Plato however adds, that the bond of which he is sneaking, makes both itself and the things which are bound to be one. Forit is possible for this to be arranged in the middle, But it possesses such a power as this through analogy, whichis the most beantiful bond, and which imparts to it a power that causes all things to have sameness and union.

This bond therefore, is inseparable from the things that are bound, and is analogy, which is different from all the natures that are bound, but has a subsistence in them. The demiurgic will likewise, is a bond, but is exempt from the things that it binds; “ 1/y τοῦ, says the Demiurgus, being a greater and more principal bond than those with which you were bound at the commencement of your generation.” 11 remains therefore, that we must understand the bond here mentioned, according to the middle mode, and as having a middle form, so us to be neither ellective nor organic.

Whence then is the conception of such a bond derived, and of what is it the symbol? Jt proceeds indeed from the one cause of wholes. For the power of imparting union is present to all things, from that fountain of all union, through which also intellect is conjoined to the intelligible, and which produces the light of truth, or the first of bonds, through which all things are connected with each — other, and become perfectly one thing through similitade. It is through this likewise, that things which have proceeded from their proper principles are converted to them. But this bond also proceeds from the one being, which is the first of beings, and which unitedly comprehends the causes of all things, according to the bond and divine union contained in it. It likewise proceeds from all-perfect animal. For every intelligible animal is by a much greater priority united to itself, than a sensible’ animal; and the causes of wholes which it contains, pervade * For ἡ το νοητὸν here, it is evidently necessary to read ἥ ro αἰσθητον. 400 PROCLUS ON THE [BooK 115. through each other prior’ to analogy; which analogy imitating, makes all things to be in all, and imparts the same powers to different things. It also proceeds from the connectedly-containing cause. For analogy inserts connexion, causing the natures which are bound by it, as Plato says, to be indissoluble by every thing except by him who binds them. Hence this bond proceeding from these causes, is connective, is the cause of the communion, and one union of separated natures, and is the supplier of harmony, and of the conspiration hastening to unity of different things; in order that it may be similar to the causes from which it was derived.

These things, however, being thus divided and defined, let us return to the thing proposed to be considered. For since it is necessary that the world being generated should be visible and tangible, it will be in want of fire and earth. Of fire, indeed, because it is visible. For vision? is of an etherial nature, on which account also it emits rays; and that which collects both sight, and that which is visible, is light. Batall lightis from fire; for it is not from earth, which produces darkness. As we have before observed, however, there are many kinds of fire. Because likewise, the world is tangible, itis in want of earth. For earth is that which is especially solid: for it is nore stable, and more of a resisting nature than the other elements. But that which is especially solid is especially tangible. For it in a greater degree sustains resistance, than that which is not solid. Hence earth is especially tangible. Let :t therefore be admitted, that there are primarily these two elements in the universe, and that they are contrary to each other ; fire indeed, being analogous to form, to the masculine nature, and to things of this kind ; but earth, being co-ordinate to the female nature, and to matter, Tfence, of these, which are thus oppositely divided, in’ their essences, powers, and energies, in the senses by which they are perceived, and in the places of their abode, there will not be one order, nor one world, unless a bond acecedes to them, and communion with each other. For it is impossible for two things to cohere in a beautiful manner without the intervention of a certain third. And Plato indeed adduces an universal assertion by saying, “a certam or some third thing.” But if you add the words, “ which are entirely contrary,” (immediately after the words, * or two things alone”) you will render whatis said mcontrovertble, and more acknowledged.

* For xpos ἀναλογίας in this place, read πρὸ ἀναλογίαν, *j.e. From the middle triad of the order of Gods called intelligible and at the same time intellectual, 2 For co oper here, itis necessary to read ro ὁρᾷν. nook 11} TIM.EUS OF PLATO, 401 For it is impossible for two things which are most contrary to concur into one composition with each other, without the intervention of a third. For either they collect themselves, or they are congregated by another thing. Being, however, contrary, and most distant trom each other, and secretly tlying from each other, through the fear of losing their own essence, they cannot bring themselves together. [lence they are congregated by something else. But this is a bond; so that they are in want of a certain third thing. The universe, therefore, proceeds from the duad to the triad. Por it began indeed from the duad, because all generation subsists in a way adapted to this principle. For difference, the infinite, and the Empedoclean strife [as being allied to the duadj are adapted to generated things. But the universe proceeds as far as to the triad, through the bond which is now mentioned. Again, therefore, a certain medium must be assumed between earth and fire, which is collective of both, And let this for the sake of an example be moisture, which is common toair andicater. Lor this' is connective indecd of carth, conglutinates it, and holds it together, so that it may not be dispersed ; but being as a subject to fire, it imparts to tt nourishment and permanency. From this triad, however, the tetrad will shortly atter be unfolded, because the natures which are bound together are solids. Hence it is rightly said, that a bond imparts beauty, and an harmonious communion and union, But what this bond is, and how it is inherent in the things that are bound, Plato shows through the following words.

“ This, however, analogy is naturally adapted to effect in the most beautiful manner.” Tt must be said, therefore, that this analogy is the bond which is now investigated 5 but that the middle or media, are after a certain manner bonds. For analogy is in those things which have the same ratio, and is naturally adapted to bind itself in conjunction with them; them indeed, through ratios; but. itself, through preserving the same form in things numerically different, and continuing to be one in multitude. For it has this from itself, and according to its own reason, and this consentaneously. For analogy proceeds from equality. But equality is of the co-ordination of unity. For as the monad is the fountain and root of quantity considered by itself; so is equality of all relative quantity, having the order of a monad, to all habitudes. For that we may omit other middles or media, which more recent philosophers have added, I mean Nicoma- ἡ For τὸν yap, tead rovro yap. Tim, Plat. Vou, I. ot ἜΣ 402 PROCLUS ON THE [Book 111. chus, Moderatus, &c.,’ we shall confine ourselves to the three media from which Plato constitutes the soul, arithmetically, geometrically, and harmonically.

It may be seen, however, how all these middles are generated: from equality, by the following method. Phe arithmetic middle, indeed, after this manner: and the third to the first, second, and third, Three monads therefore being proposed, there will be produced according to this method three terms, vin. 1. 2. 3. preserving an arithmetic middle. Bor this middle consists in equally surpassing according to number, and being equally surpassed.’ But the geometrical middle is produced as follows: Make the first equal to the first; the second, to the first and second ; and the third to the first, to twice the second and the third. For again, there being three monads, there will thus be generated the three terms 1. 2. 4. forming the geometric middle. Por the peculiarity of analogy consists in preserving the same ratio in greater and lesser terms. And the harmonic middle, which has the third order, is generated in the following manner : Three monads being proposed make the first equal to the first, and to twice the second; the second to twiee the first, and twice the second ; and the third τὸ the first, to twice the second, and thrice the third. For by this method the three terms 3. 4. and 6. will be produced, forming the harmonic middle. For the harmonic middle, according to the Platonte definition itself, consists ino surpassing and being surpassed by the same part of the extremes? All the middles, therefore, have their generation from equality.» But if this be the ease, they have the uniform, and a power which collects things, and causes them tobe one. For equality is analogous to sameness, to the monad, to bound and to similitude, through which communion is produced in’ beings. Hence Plato appropriately adds the words, ‘naturally adapted,” beewuse the analogies and all the tiddles have the spontaneous, Por they neither introduce an artificial, nor an adscititious bond, but present themselves to the view in) the

essences and powers themselves of things. “For when either in three numbers, or masses, or powers, as is the * For an account of these media, see my Theoretic Arithmetic. > fu the original, by some negligence of the transertbers, after ww δε urepeyopern, being equally surassed, the words κατὰ ψυσιν αὐτὸν ὁ yidoougys, Lumediately follow, which are obviously totally foreign to this place. > Thus 3 is surpassed by 4, by 1 which is a third part of 3, and 6 surpasses + by 2 which is a third part of 6. middle to the first so is the last to the middle; and again, as is the last to the middle, so is the middle to the first; then the middle becoming both first and fast, and the last and. the first becoming both of them middles, it will thus happen that all of them will necessarily be the same. But becoming the same with each other, they will be one.” Tn the first place, it is requisite to explain what is here said mathematically ; and in the next place, physically, as being that which is especially proposed to be effected, For it’ is not proper to separate the discussion from. its appropriate theory. There are therefore some who think that Plato in these words detines the geometric middle, and among other things which they assert, they say that the geometrie middle is properly exclusive of all the others analogy ;

but that the others may be justly ealled middles. — Nicomachus also is of this opinion, and he speaks rightly. 10) geometric proportion is properly analogy ; but it is requisite to call the ethers middle, as Plato also says further on inthe gencration of the soul, But the others are improperly" called analozics. Vo others, however, these appear not to have apprehended the meaning of Plato properly. For they say that it is not definitely asserted in these words, that there ought to be the same ratio; but thus much only is said, that it is necessary there should be such a habitude of the last to the middle as there is of the middle to the first. But this is common to all the before-mentioned middles, For as the monad is to the duad, according to the arithmetical middle, and the equal in quantity, so is the duad to the triad. | For by as much as the duad is surpassed by the triad, by so much is the triad less than the tetrad. And as the monad is to the duad, according to the geometric middle, so is the duad to the tetrad, For the ratio is the same. And as the triad is to the tetrad, according to the harmonic middle, and the part of the triad by whicn the tetrad surpasses it, so is the tetrad to the hexad. For by that part of the triad by which the triad is exceeded by the tetrad, by the same part of the hexad is the tetrad sarpassed by the hexad, Sach, therefore, is their opinion, though Plato clearly assumes the geometric iniddle. For itis the peculiarity of this proportion, that the first has the same ratio to the middle that the middle has to the third term. As, however, there are three middles, the arithmetic, the geometric, and the harmonic, and these being such as we have shown them to be, Plato very properly assumes these

* For καταχρώμενοι here, 1 read καταχρήστικωε. 404 PROCLUS ON THE (BooK 11, three subjects, numbers, masses, and powers. For the arithmetical middle is in numbers; the geametrical is ina greater degree conversant with continued (than with discrete} quantity ; and the harmonteal middle is in) powers, For it is conversant with sharp and flat sounds, And after this manner you may speak, distinguishing the middles according to their predominance, All of them, however, may be assumed in numbers, in masses, and Jn powers, And how, indeed, they may be assumed in numbers is evident; for it has been shown by us. But they may also be assumed in masses. For three equal magnitudes being proposed, you may be able, by using the before-mentioned three methods, to devise other magnitudes, at one tine producing an arithmetic, at another a geometric, and at another an harmonic middle. Jn powers likewise after the same manner. For let there be three equal powers, as for instance, three highest Aupateé (vraras) sounds, all of them homotonous, or of the same tone. You will produce therefore from these, the arithmetical middle, if you place the first sound, that is Aypate, equal to the first; but the second, to the first and second, as for instance, another sound emitting a sound the double of the first. And letit be nefe or the last sound, which has a double ratio to Aypate. But the third sound must be placed equal to the first, second, and third.

Por it will be a sound which wall have a triple ratio to Aypate, surpassing ucte by as much as γος surpasses Aypate. And these three sounds, Aypate, nete, trite-hyperholéon, Will avithinetically differ from cach other. But you will make the geometrieal middle, if the Aypate being posited, you make the first equal to the first, but the second equal to the first and second hypate. And let this sound be mese : for this is capable of emitting a sound the double of kypate. But if you make the third sound equal to the first Aypate, and to twice the second, and the third, you will have a certain chord which will sound wete-huperbolaon, For this will be capable of producing a sound the double of mese, and the triple of Aypate. These three sounds Likewise will form the geometric middle. ALL the middles, therefore, are seen to exist in numbers, im masses, and in powers. Number, however, is more adapted τὸ the arithmetical, bulk to the geometrical, and power to the harmonic middle. And hence Plato uses these three, viz. numbers, masses, and powers.

It is well, likewise, that assigning certain common ratios, he commences from the middle. For it is this through which all analogy consists, collecting the extremes according to ratio, from one power to the other. For analogy is that Which is principally and) properly a bond. Butitis a bond as that ¢hrough wehich, and the unddle. Por through the middle analogy binds the extremes. From this, therefore, he commences as most allied to the nature of analogy, and because habitude receives its completion through it. Hence, also, they are called middles, and because sameness is the end of all this analogy. | For since they proceed from equality, but equality is sameness, it converts all things to sameness. Sameness, however, may be properly and principally asserted of the geometric middle, for there is the same ratio; but equality of the arithmetic ; and similitude of the harmonic middle. And in the third place, the ascent is through sameness tounion, For analogy indeed is suspended from = equality,” being a πα ingenerated in the boundaries of equality. But equality is suspended from sameness, and sameness from union. It is necessary, however, after the mathematical resumption of these words, to direct our attention to the physical theory, For itis not fit that those who apply themselves to this discussion, should dwell on mathematical speculations ; for the dialogue is physical; nor that they should neglect such speculations, investigating only what relates to sense 3 but it is requisite to conjoin both, and always connect physics with mathematics ;

just as the things themselves are connected, are homogeneous, and of a kindred nature, according to the progression from intellect. For, in short, if the Pythagoreans arranged the mathematical essence as a medium between intelhgibles and sensibles, as being more evolved than intelligibles, but more universal than sensibles,* why is it requisite, omitting mathematics, to pay attention to physiology aloue? For how is the sensible nature adorned, according to what reasons is it arranged, or from what reasons does it proceed, exceptitrom those that are mathematical? These reasons therefore for productive powers], are primarily in souls, descending into them from intellect; and afterwards they are in bodies, proceeding into them from souls. Hence it is necessary not to remain in mathematical speculations as some do; for this produces false opinions in the auditors, and induces them to think that physical figures and numbers are mathematical. It is also in another respect absurd. lor the reaxons of nature do not receive the accuracy and firm-

* Tnstead of εξηρτηται yap ἡ μεν ex rns ἀναλογίαν, it is requisite to read in this place, εξηρτηται yap ἢ) μὲν ἀναλογία εκ τὴς ἰσότητος, * For των νοητῶν here, it is obviously necessary to read τῶν αἰσθητῶν. | ness of the mathematical reasons. To which may be added, that in so doing we shall not follow the demonstrative canons, in which it is said that) things pertaining to one genus must not be transferred to another, Neither therefore is it possible to survey physical objects arithmetically. Let us, therefore, if you think fit, discuss the theory of the proposed words - physically. ‘The first analogy then, according to which nature inserts harmony in her works, and according to which the Demiurgus adorns and arranges the universe, is one certain life, and one reason, proceeding through all things ; which first, indeed, connects itself, but afterwards the natures in’ which it exists 5 and according to whieh sympathy is ingenerated ἴῃ ἈΠ mundane essences, as existing in one animal, and governed by one nature, This life, theretore, which is the bond of wholes, total nature for nature which ranks as a whole] and the one soul of the world constitute, The one intellect ihewise generates it; and always more excellent beings, insert in mundane matures, a greater and more perfect union. Lat it be said, therefore, that the habit which predominates in material subjects, that material form, and the powers of the muddle elements, are bonds.

not participated, and are analogous to the middle in mathematical entities, through which habitude subsists in the extremes. But the lite of which we are speaking, which collects and unites all things, and is suspended indeed from its proper causes, but binds the things in whieh at is inherent, Is fru/y analogy, and preserves both its own union and the union Of its participants, Again, therefore, a bond is threefold, For the common powers of the elements are one bond 5 the one cause of bodies is anothers; anda third is that which as the middle of both the others, which proceeds indeed from the cause of bodies, but employs the powers that are divided about body. And this is the strong bond, as the theolowist says, which is catended through all things, and is connected by the yolden chain. For Jupiter after this, constitutes the golden chain,’ according to the But when your pow’r around the whole has spread A strong cocrcive bond, a golden chain ' This golden chain may be said to be the series of unities proceeding from the one, or the ineffable principle of things, and extending ay far as to matter itself, And of this chain, the light immediately

proceeding from the sun is au image. BOOK αι} TIM.EUS OF PLATO. 407 Physical analogy then being a thing of this kind, let us survey in what things, and through what, it is naturally adapted to be established. As Plato therefore says, It subsists in nambers, masses, and powers. — Physical mambers, however, are material forms divided about the subject i.e. about body}. But masses are the extensions of these forms, and the separations or intervals of them about matter. And powers are the things which connect, and give form [or specific distinction) to bodies. For form is one thing, and the power proceeding from it is another. For form indeed is impartible and essential, but becoming extended, and dilated into bulk, it emits, as if it were a blast from itself} material powers, which are certain qualities, "Thus, for instance, in fire, the formand essence of it is impartible,’ and is truly the image of the cause of fire. For in partible natures there is that which isimpartible. But from the form in fire which is impartible, a separation and extension of it take place about matter, from which the powers of fire are exerted, such as heat, or refrigeration, or moisture, or something else of the like kind. And these qualities are indeed essential, but are by no means the essence of fire. For essences are not from qualities, nor are essence and power the same ; but every Where the essential precedes power;

and from that being one, a multitude of powers proceeds, and that whieh is divided, trom that which is indivisible; just as from one power many enerzies proceed. For by how much more each thing proceeds, by so much more is it multiplied ἀπ divided, conformably to {the characteristic of] its principle and cause, which is impartible and indivisible, As in every body, therefore, there is this triad,’ T mean number, bulk, and power, analogy and the physical bond, occupy from on high the numbers, masses, and powers of bodies, and likewise congregate their partible’ essences, and unite them for the purpose of producing the one completion of the world. They also insert communion in forms, symmetry in masses, and harmony in powers. And thus all things are rendered eflable and consentaneous to each other. But this analogy proceeds from the middle to the first, and from the third to the middle ; from the first also to the middle, and from this to the last; and again, from the last to the middle, and from this to the first. Beeause, likewise, a bond of this kind imparts progression and conversion to bodies, it begins indeed from the

‘Instead of ro μὲν εἰδὸς αὐτὸν καὶ oumna, ἀμέρους ἐστε καὶ orros ἄγαλμα τῆς αἰτίας τὸν Rupes, It TS requisite to read, τὸ μὲν εἰδὸς αὐτὸν κας οὐσία «μέρες ἐστι, και οντῶς AYAAPaTHS αἰτίας τὸν RYPOS. δ For τὸν rpirov rovrov in this place, it is requisite to read τὸν rptagou rovroy. ? Instead of apepers here, itis necessary to read μέρισταν. 408 ᾿ PROCLUS ON THE {Book 111. middle, in consequence of being connective, and the cause of union, and is * defined according to this peculiarity. But it proceeds from the first through the middle, to the last, as extending and unfolding itself, as faras to the last of things. And it recurs from the last to the first, as converting all things through harmony to the intelligible cause, from which the division of nature, and the separation and interval of bodies were produced. For by converting them to this cause, according to one circle, one order, and one series, secondary being suspended from primary natures, it causes the world to be one, and most similar to. the intelligible [paradigm]. For as there all things are truly united to each other, 50 here all things are adapted to each other. And as intelligibles proceeding trom the good, are again converted to it, through the goodness which is in them," and through the intelhyible monads ; thus also sensibles: proceeding from the Demiurgus, are again converted to him, through this bond, whieh is distributed and pervades through all of them, and binds all things together, For in this respect it imitates the intelligible, But it) subsists intellectually in intellect, totally in wholes, and partially in partial natures,

After the same manner, therefore, as the intelligible, the sensible world has all things, according to all its parts. Por fire, so far as it is tangible, participates of earth, and earth, so far as itis visible, participates of fire, and each participates of moisture. For earth indeed is conglutinated and connected through moisture, and its dissipated nature is united through it; but tire is nourished and increased by it. So that the extremes are the middle, in order that what is said may become physically manifest in things that are Known by us. The extremes, therefore, are ina certain respect the middle, as preserving through it their proper idea, and remaining such as they are. And moisture itself, so far as itis coloured, participates of fire, and so far as itis re-Invigorated through heat. But again, so far as it is tangible, 10 participates of earth. So that each of the extremes gives perfection to moisture. These things, however, will shortly after become more known to us, But through this harmony and analogy, in the first place, sameness presents itself to the view, and in the next place union. For bodies themselves according to their own nature are partible, aud are subdued by differences and strife. “These, however, at the same time through harmony, are leagued in tdendship with sameness, and through sameness with union. For through analogy the universe 15

' Por ev avry read ey avros. BOOK 111. TIM.£Us OF PLATO. 409 completely rendered one, this having the power of making things that are divided to be one, of congregating things that are multiplied, and connecting things that are dissipated. Hence, theologists surveying the causes of these things in the Gods, enclose Venus with Mars, and surround them with Vulcanian bonds; the difference which isin the world being connected through harmony and friendship. All this complication and connexion likewise has Vulcan for its cause, who through demiurgic bonds connects sameness with difference, harmony with discord, and communion with contrariety. And this being eflected, Apollo, Hermes, and each of the Gods laugh. But their laughter gives subsistence to mundane natures, and inserts etlicacious power in the bonds. Let these things, however, as it is said, be preserved in sacred silence. But now, from what has been discussed, let thus much be manifest to us, that the physical bond being Vulcanian and demiurgic, (for the one and all-perfect Demiurgus comprehends also the production which is through necessity, as being Vulcanian and Dionysiacal, and causing each of the parts of the universe to be a whole,) is collective of contraries, and connective of material things; uniting their essences, measuring their masses, and harmonizing their powers. It likewise makes all things to be in all, and exhibits the same things in each other, according to all possible modes, empyreally, aerially, aquatically, and terrestrially.

“ Tf then it were necessary that the body of the universe should have been generated a superficies, and not have depth, one medium might have been suticient for the purpose of binding both the natures that subsist with it, and itself. But now it is requisite that it should be a solid, and solids are never adapted to each other by one, but always by two The scope proposed to us (in the Timeus], is, as we have before observed, to learn how the universe is constituted, and of what it consists. But this being the design, we may see in what a well-ordered manner the discourse devises. the composition of the four elements. For it is impossible that there should be one simple element alone; since there would not be generation. For all generation is ascertain mutation. But all mutation is naturally adapted to be effected in two things. All generation likewise is from contraries. But a simple element itself, is by no means contrary to itself: for it would be itself corruptive of itself. If, therefore, it is necessary there should be generation, it is Tim. Plat. Ὁ θῖν ἂν ᾿ 3F necessary there should not be one element only. For as Hippocrates says, if there was one element only, it would be impossible for things to be changed. For mutation and motion are not to the similar, but to the contrary. Hence there is not one simple element only.

If, however, there is not one, but two at least, it is necessary that these should be contraries: for generation 15 from contraries. It is necessary, therefore, that there should be two elements having in a becoming manner a nature contrary to each other. Hence, if they are contraries, they will be in want of a certain bond and medium, For it is impossible that two contraries can ina becoming manner coalesce, without a third thing ; since it is necessary that a bond should intervene, which is collective of both. For being themselves contraries, they will avoid communion with each other. Hence it is necessary, there should be another third thing which conjoins them and leads them to the completion ofone thing, But it is likewise necessary that this medium should be of a biformed' nature. For if the elements which were to be bound were superticies, one medium would be sufficient, But since they are solids, they are connected through two media. For the duad being the primary leader of solids, is also allotted the primordial cause of the bonds that are in them. Hence, likewise, Timieus calls a binding of this kind harmony, as inserting in the extremes ἃ symmetry of communion with each other. The analogy also which is in solids is introduced through two media. For two media analogously come between two similar solids. If, therefore, these things are rizhtly asserted, all the elements are four;

and there is neither one alone, lest we should destroy mutation; nor two contraries without a third thing, lest there should not* be a bond of things which are hostile to each other, Por there will not be order and ornament from two things most foreign to each other, Butif you conceive a certain thing of this kind, the solution of the doubt will be easy, Moreover, neither will there be alone two things which are not! contravies. For they will not be able to operate on each other, Por whiteness suffers nothing from ἃ line, but from blackness. Nor does heat suffer any thing from whiteness, but from cold,

Again, therefore, it must be said still more universally, reasoning from things known, that either there is one clement alone, or not one. If, however, there is only one element of the world, the variety of the phenomena, the opposition of the cir- » Por δεειδεν here, read &voedkes. > Ove is omitted in this place in the original. 2 Ory is also here omitted in the original. culations, and the war of generation, will be subverted, and either all things will be perpetual, or all things will be corruptible. Butif there is not one element only, there will either be two elements, or more than two. And if two, they will either be contraries, or not contraries. Tf, however, they are not contraries, there will neither be action, nor passion, nor opposition in bodies, nor will there be genera. tion in things which have generation. But if they are contraries, these will require amedinm. And if this be the case, there will either be one medium, or two media, Itis impossible, however, that there should be only one medium: for the elements are not superticies. Hence there are two media. But if there are two media of two things, all are four, That so many elements therefore in number are suflicient to the world, is through these things manifest.

Let us, however, if you please, concisely survey the mathematical meaning of the words before us, and afterwards adduce the physical theory pertaining to them. For how of two similar superticies or planes there is one medium, and of two similar solids two media, we will survey in number by themselves. For the primordial and spontaneous nature of numbers, is to be embraced prior to geometrical necessity. Tn the first place, therefore, let there be two square numbers 9 and 16, the less of which has for its side 3, and the greater 4, By multiplying these and making 12, we shall have an analogy in the three terms 9, 12, and 16." Let two numbers likewise be assumed, which are not squares indeed, but at the same time are similar planes, and Jet them be 18 and 3.2," the former being generated from the triad and hexad, but the latter from the tetrad and ogdoad. [{ therefore, we multiply either the triad by the ogdoad, or the hexad by the tetrad, we shall have for the product 24, binding in analogy 18 to 32, according to a sesquitertian ratio. This, however, is caused by their sides having the same ratio, If, therefore, the sides of the assumed numbers are found to receive no analogous mean or medium, all the planes generated from them will have but one medium, according to the before-mentioned mode,’ But if the sides themselves should be

* For as 9 isto 12, sois 12to 10. Ὁ The two similar plane numbers 18 and 32 here adduced by Proclus, prove that Gaston Pardies was greatly mistaken in asserting in his Elements of Geometry, “ that if two numbers are similer planes, the greater may be divided into as many squares as there are units in the less.” See the Translation of this work by Harris, p. 133. For 32 eannot be divided into as many squares as there are uoits in 18. And 32 and 18 are evidently similar plane vumbers, because their sides are analogous. For as 3 is to 6 so is 4 to 8. Υ 2 The sides of these numbers are 3, 6, 4, and 8, and they have no analogous mean. For there is no geometrical mean between 3 and 6, nor between 4 and 8, [lence the planes generated from them, vis. 18 and 32, will have but one medium, which is 24, 412 PROCLUS ON THE [BooR 11}. found to receive a certain analogous mean, the planes also produced from them, will necessarily receive more than one mean. For let there be two squares 16 and 81, and let the side of the former be 4, but of the latter 9. Since, therefore, the analogous medium between 4 and 9 is 6, according to a sesquialter ratio, it is necessary that more than one mean should fall between them. For the tetrad multiplied by the hexad will produce 24;

but the hexad multiplied by itself will produce the square of itself 36; and multiplied by 9, will produce 564. And there will be a continued analogy, in the terms 16, 24, 36, 54, 81." Hence, when the sides have an analogous mean, the planes produced from them, will have more than one mean. Hence, too, Plato appears to me to say very cautiously, not that there is entirely one medium in similar planes, but that it is possible for one to be suflicient. For more than one plane being produced, one medium would be sufficient to conjoin them, viz. 36 alone, according to the duple sesquiquartan ratio.” And thus much concerning similar planes.

Let us, however, now pass onto similar solids, and survey the media in these. In the first place, therefore, let there be two cubes 8 and 27, the former having for its side 2, and the latter 8. Of these cubes, there will be two media, the one being produced from twice two multiplied by three, 1. e. 12, and which on this account 15 (4exis) a Seam, but the other from thrice three multiplied by two, 1. e. 18, and which is therefore (πλίνθος ᾽) a tile. These will make a continued analogy with the before-mentioned cubes, according to ἃ sesquialter ratio.” And here you taay see how each of the media has two sides from the cube placed next to it, but the remaining side from the other cubes This however will be useful to us for the purposes of physiology. Again, ifthe numbers were not cubes, but similar solids, they will likewise have two analogous middles or means. For let there be two similar solids 24 and 192, the sides of the former being 2, 3, 4, but of the latter 4, 6, 8. And from the duad, the triad, and the ogdoad, 48 will be produced, but from the tetrad, the hexad, and again the tetrad, the product will be 96. Ilere too, each of the media will have two sides from that similar solid of the extremes which is next to it, but one side fromthe other cube, in the same manner

' For as 16 is to 24, sois 24 to 36, sois 36 to 54, so is 54 to 81, the ratio being sesquialter. * For 36 is a geometrical mean between 16 and 81, according to a duple sesquiquartan ratio, For 36 contains 16 twice, and a fourth part of it, i.e. 4also; aud 81 contains 36 twice, or 72, and 0 besides, which is a fourth part of 36. 3 For riiOus here, read Au os. * For 12 contains 8 once, and the half of 8. And ina similar manner 4%=1} and 77=11), δ Fos 12=2x 2X3, 2 being the cube root of 8, and 3 being the cube root of 27; and 18=3X3x 2. as in the media of the before-inentioned cubes. Hence between similar solids, two media are sufficient; just as Plato says, that two media adapt solids to each other, but never one medium. What then, some one may say, is there not one medium alone of the two solid numbers 64 and 729, which medium is 216? For G4 is a cube produced from 4, but 729 from 9. And 729 is the triple and superparticular ogdoan part of 216; and after the same manner 216 of 61. For each contains the other thrice, and three eighths of it besides.". And this will not only be the case in these, but also in other numbers: for these are the smallest numbers which admit of this.

In answer to this however it must be said, that the above-mentioned numbers are cubes and at the same time squares; the one, i. e. 64, being the square of 8, but the other, i. 6. 729, being the square of 27. Hence they have one mean, not so far as they are cubes, but so far as they have the tetragonic peculiarity, For the tetragonic side of 64, i. e. 8, being multiplied by 27, which is the tetragonic side of 729, produces the analogous mean 216, according to the method delivered [by mathematicians] of finding the mean between two squares, He who makes the objection, therefore, using solids not as solids, binds them together by one medium. But if he had surveyed them so far as they are solid numbers and cubes, he would have found that there are also two media between these, the one being 144, from four times 4 multiplied by 9, but the other 324, from nine times 9 multiplied by 4.

But Democritus + doubts, how it is said that one analogous medium falls between two planes. Vor by assuming four lines in continued proportion, it may be shown that the squares from them are analogous;’ so that two analogous media will fall between two extreme planes. He adds, that different persons have been involved in different difficulties through this doubt, and have been led by it to the duplication of the cube, and such-like investigations. Plato, however, does not say that one medium only falls between any casual planes, nor again two media between casual solids, but between those that are similar, and in an eflable ratio, and which have their sides arranged according to numbers. For * Thus 729 contains three times 216, i. ὁ. 648, and three eighths of it besides. For the eighth part of 216 is 27, and thrice 27 is 81, the difference between 729 and 648. And thus also 216 contains 64 thrice, i, e. 192, and 24 besides, which is three cighths of 64. ᾿ * This is most probably the junior Democritus mentioned by Porphyry in his life of Plotinus, " For let the lines be as the numbers 2. 4. 8. 16, which are in continued proportion; then the squares of them 4, 16. 64. 256 will also be analogous. Foras 4is to 10, so is 16 to 64, and so is

414 PROCLUS ON THE (BooK 111. the things generated by the demiurgic God, are effable with reference to each other, and are variegated by demiurgic numbers, as Plato says in another part of this dialogue. And it is requisite to assume similar planes, and solid numbers, and to survey in these the truth of the Platonic assertion. We shall show therefore at the end of these Commentaries, how itis possible, two right lines being civen, to find two analogous media, selecting for this purpose the demonstration of Archytas, rather than that of Menwchmus, because he uses conical lines, and in like manner rather than that of Eratosthenes, because he employs the apposition of a rule." With respect however to the things investigated, it must now be said that Plato appears to have perfect contidence in arithmetical demonstrations, since it is also possible to find in geometrical figures of two solids an analogous medium. For if there are three analogous right lines, a, 2, y, in a duple ratio, the squares from them will be in a quadruple ratio, as £4, ior, and ὃ. But the solids from them will bein an octuple ratio, as 913, 25, and y. Hence there will be three cubes, the extremes of which will have one analogous mean, And it is manifest that all cubes are similar to each other. For the angles are the same in each cube and are equal 5 and they are also comprehended by similar planes ;

and the multitude of them is equal. Moreover, we may thus demonstrate in the same manner as Democritus, that two analogous media fall between two similar solids. For that all squares are similar to each other is evident ; since the angles are the same in each, and are equal, and the sides are analégous. Hence it seems that Plato employing numbers, shows that solids are never co-adapted by one mean, but always by two media. For in these, as you see, the extremes are cubes, and at the same time similar planes. For 613, is from usr, and az. But the other of the extremes 7, is from Β, and 4, and there is the same ratio of the sides. There is therefore one medium of these, so far as they are similar planes, but not so far as they are solids. So that you will have the solution of what is said, by assuming numbers. Tor it is possible to find the same numbers which are at the same time similar solids and planes; but it isimpossible to assume geometrical figures which are at one and the same time similar planes and solids; since this also may be said, that all of them being cubes, the form of them is one. But Plato

* From the most unfortunate loss of the latter part of these commentaries of Proclus, this method likewise of his fiuding two analogous media between two given lives, is lost. poor 11 TIM.EUS OF PLATO. 415 assuming that the means are similar to the extremes, is thus confident in the theorem. For how would the extremes be in want of other bonds, if they had entirely the same form? And how would the media communicate with the extremes, and differ from them according to the sides, if they were all of them cubes? Hence it is evident that he assumes the media, as being truly media, and thus says, that solids are never conjoined by one, but always by two media ; every mediam containing the communion and difference of the things of which it is the medium. For to say universally, that all solids are connected through two media, makes the media to be infinite. It is manifest, therefore, that he assumes things which are most distant, and in every respect contrary to each other, and which have all the sides opposite to all; these in natural bodies being corporeal powers. But le does this, in order that of the media, one of them may have a greater communion with one of the extremes, but a less with the other; and that this may be vice versa with the other medium. Unless that also is true which is asserted by our preceptor.

For he says that it is necessary to assume the same ratio in the media or means, as there is in the sides of the extremes. Thus, for instance, if one of the cubes is 8, but the other 27, we shall find the media of them, if we take their sides 2 and 3, and multiply the square of 2, i. e. 4 by 3, and the square of 3,1. 6. 9 by 2, For then the media will be 12, and 18, which will conjoin the extremes through the sesquialter ratio, which is the ratio of the sides of the cubes. Hence, as there is the same ratio in the sides of the cubes, and in the media, Plato says that there is necessarily two media, and this in amanner more consonant to the proposed physiology. For in the powers of the elements, and in simple forms, the Demiurgus inserted communion prior to

_ things of a composite nature. We however conjoin the extremes through the octuple ratio, the sides of them not having an octuple ratio. For the mean being assumed in a duple ratio, the extremes will have a quadruple ratio. Thus, for instance, in the three proposed terms, if we assume a fourth analogous term, we shall find that as the side 2 is octuple of the side 16, so the first cube is conjoined to the fourth through the octuple ratio. For if you add 16, as a fourth term to 2. 4. 8, the cube from 16, is conjoined to 8, through the octuple ratio which 64 has to 8, and 512 to 64, and 4096 which is the cube of 16;to 512." So that the sides of the media receiving an octuple ratio, two media will fall between " If each of the terms 2. 4. 8. 16, is cubed, the four terms 8. 64. 512. 4096, will be produced, and C4 is octuple of 8, 512 of 64, and 4096 of 512; and the first cube 8 is conjoined to the fourth 4096, through the octuple ratio. 416 PROCLUS ON THE [Boox 111. the extremes. But ifa fifth analogous term is added, the sides will no longer be conjoined in an octuple ratio but in the ratio of 16 to 15 and on this account there will be three analogous media between the two cubes. What Plato says, therefore, is true according to the before-mentioned method.

Are not the sides also coadapted to his purpose? And it is requisite to say, that there may be one medium between two cubes, yet not according to harmonic ratios. Hence, when there is truly a colligation of the extremes through these ratios, then it is perfectly requisite that there should be two media. Through these things, therefore, it is manifest mathematically, that similar planes require one medium, and similar solids two media, and that they can never be bound by one medium alone.

Being impelled, however, by these observations, let us sce how physical conceptions accord with them, and let us adapt probable to scientific assertions. And in the first place, let us survey whata physical plane is, and how in planes of this kind, there is one medium, but two in physical solids. The divine Tamblichus indeed (for this man in a remarkable degree comprehended a theory of this kind, others being as it were asleep, and conversant only with the mathematical meaning of the words) appears to me to distinguish things simple from such as are composite, parts from wholes, and in short, material powers, and material forms, from the essences to which they give completion. And some of these, he calls superficies, but others solids. For as a superticies is the ultimate boundary of a mathe matical body, so likewise material form, and material power, are the morphe and boundary of their subjects. ‘These things, therefore, being thus divided, in things of a simple nature, one medium is suflicient, because there is [one] difference of the reasons and forms, and according to the common bonds of the reasons and the life. Lorin these there is one medium, Hence quality 15. uniformly connected with quality, and power with power, according to the difference and sameness of forms. But in things of a composite nature, there are very properly two media. For the duad is the supplier of all composition and separation. Every composite nature however consists of many essences and powers. Hence, there are many media. And these at least are two-fold. For there is one medium according to form, and another according to subject.

We however, conformably to physical principles, speak as follows, receiving auxiliaries from what Plato says as he proceeds. Or rather, let us speak from the beginning. There are some physiologists then, who ascribe one power to each of the elements ; to fire indeed heat, to air frigidity, to water moisture, and ’ ty earth dryness; in so doing entirely wandering from the truth. In the first place, because they subvert the world and order, For it is impossible for things to be co-adapted to each other, when they possess the most contrary powers, unless they have something incommon. In the next place, they make the most contrary natures allied to each other, viz. the hot to the cold, and the moist to the dry.’ It is necessary however, to make things which are hostile more remote than things which are less foreign. For such is the nature of contraries. In the third place, therefore, the first two powers will have no sympathy whatever with the rest; but will be divulsed? from each other. For it is impossible to say What is common to humidity and frigidity. And in addition to all these things, aa the elements are solids, they will not be conjoined to each other by any medium. It has however been shown that it is not possible for solids to be conjoined through one medium. Nor can they be conjoined without a medium. For this is alone the province of things that are perfectly without interval.

But some others, as Ocellus, who was the precursor of Timwus, attribute two powers to each of the elements, to fire indeed heat and dryness, to air, heat and moisture, to water, moisture and coldness, and to earth, coldness and dryness, And these things are written by this man in his treatise On Nature. In what. therefore, do these err who thus speak ? In the first place, indeed, wishing to discover the common powers in the elements, in order that tiey may preserve the co-arrangement of them with each other, they no more assign communion than separation to them, but equally honour their hostility and their harmony. What kind of world therefore, will subsist from these, what order will there be of things which are without arrangement and most foreign, and of things which are most allied and co-arranged? For things which in an equal degree are hostile and peaceful, will in an equal mode dissolve and constitute communion. But this communion being similarly dissolved, and similarly implanted, the universe will no more exist than not exist. In the second place, they do not assign the greatest contrariety to the extremes, but to things most remote from the extremes ; though we every where see, that of homogencous natures those which are most distant have the nature of contraries, and not those which are less distant. How likewise did nature arrange them, since they are most remote in their situation from each other? Was it not by perceiving their contrariety, and that the third was more allied than the last to the first? How also did she arrange the motions

δ For ro evayrwrara here, read ra evayrwwrara, and for ry θερμὸν re ψυχρῳ, το Oeppor, x. XA. * For arnprnyeva in this place, I read διηρημενα. Tim. Plat. Vou, I. 3G of them, since fire is most light and tends upward, but earth is most heavy and tends downward? But whence were the motions ofthem which are most contrary derived, if not from nature! If therefore, nature distributed to them most contrary motions, it is evident that they are themselves most contrary. For 45. the motions of simple beings are simple, and those things are simple of which the motions are simple, thus also those things are most contrary of which the motions are most contrary. And this may occasion some one to wonder at Aristotle, who in what he says about motion, places earth as most contrary to fire; butin what he says about powers, he makes the most remote of similar natures to be more friendly than those that are proximate, when they are moved with most contrary motions, Por as the clements have contrary places in- their positions, as they have contrary motions in dations, as they have contrary powers, eravity and levity, through which motions subsist in their forms, thus also they have contrary passive qualities. Aristotle Iimself likewise manitests that earth is contrary to fire. For wishing to show that itus necessary there should) be more bodies than one, he says: ‘ Moreover, af earth exists, itis also necessary that fire should exist. For in things, one of the contraries of which naturally is, the other likewise has a natural subsistence.” So that neither was he able afler any other manner to show that there are more clements than one, than by asserting that fire is contrary to earth,

Farther still, as the elements are solids, how can they be bound together through one medium? For this is impossible im solids, as we have before observed. Hence those who assert these things, neither speak mathematically nor physically, but unavoidably errin both these respects. For physical are derived from mathematical entities. Jundus therefore alone, or any other who rightly follows hin, neither attribules one nor two powers alone, to the elements, but triple powers ; fo fire indeed, tcnuity of parts, acuteness and facility of motion ; to air, lenuity of parts, obtuseness, and facility of motion ; to water, grossness of parts, obtuseness, and facility of motion ; and to earth, grossucss of parts, obtusencss, and difficulty of motion, But this is in order that each of the elements may have two powers, cach’ of which is common to the clement placed next to it, and one power which is different, in the same manner as it was demonstrated in mathematical numbers and figures 5 this different power being assumed from one of the extremes 3; and also in’ order that earth according to all the powers, may subsist oppositely to fire; and that For; cay here, it is obviously necessary to read exurepar,

the extremes may have two media, and the continued quantities two; the latter having solids for the media, but the forme., common powers. For let fire indeed be attenuated in its parts, acute, and easily moved. For it has an attenuated essence, and is acute, as having a figure of this hind ji. οὐ a pyramidal figure], and on this account.is incisive and fugitive,’ and permeates through all the other elements. It is also moved with facility? as being most near to the celestial hodies, and existing in them. For the celestial fire itself is moved with celerity, as is likewise sublunary fire, which is perpetually moved in conjunction with it, and according to one circle, and one impulse. Since therefore, earth is contrary to fire, it has contrary powers, viz. grossness, obtuseness, and difficulty of motion, all which we see are present with it. But these being thus hostile, and being solids, are also similar solids. For their sides and their powers are analogous. For as the gross is to the attenuated, so is the obtuse to the acute, and that which is moved with difficulty, to that which is moved with facility. But those are similar solids of which the sides that constitute the bodies are analogous. Tor the sides are the powers of which bodies consist. ence, as fire and earth are similar bodies, and similar solids, two analogous media fall between them; and each of the media will have two sides of the extreme situated next to it, and the remaining side from the other extreme.

ITence, since fire has for its three physical sides the triple powers, tenuity, acuteness, and facility of motion, by taking away the middle power, acuteness, and introducing instead of it obtuseness, we shall produce air, which has two sides of fire, but one of earth, or two powers of fire, but one of earth; as itis fit that what is near should rather communicate with it, than what is separated in the third rank from it.

Again, since earth has three physical powers, contrary to the powers of fire, viz. grossuess of parts, obtuseness, and difficulty of motion; by taking away diffeully of motion, and introducing facility of motion, we shall produce water, which consists of gross parts, is obtuse, and is easily moved; and which has indeed, two sides or powers common with earth, but receives one from fire. And thus these media will be spontaneously conjoined with each other; cominunicating indeed in twofold powers, but diflering in similitude by one power ; and the extremes will be bound togetiier by two media. Each element also will thus be in a greater degree conjoined to, than separated from the element which is * For vearioy in this place, read νπαικτικον τ" * Instead of axernros here, it is necessary to read evaeynror. 420 PROCLUS ON THE [ποοκ 111. near to it; and one world will be perfectly effected through all of them, and one harmonious order, through the predominance of analogy. Thus also, of the two cubes 8 and 27, the medium 12 being placed next to 8, will have two sides of this, but one side of 37. For 12 is produced by 2 Χ 2 Χ 8. But itis vice versa with 18 For this is produced by 3 X 3 X 2. And the side of 27 is 3, in the same manner as 2 is the side of 8. The physical dogmas therefore of Plato about the elements of the universe, accord with mathematical specalations,

Hence these things being thus determined, let us physically adapt them to the words of Plato. We calla [physical] plane or superticies therefore, that which has two powers only, but a [physical] solid that which has three powers. And we say, that if we fashion bodies from two powers, one medium would conjoin the elements to each other. But since, as we assert, bodies possess triple powers, they are bound together by two media. For there are two common powers of the adjacent media, and one power which is different. And the extremes themselves, if they consisted of two powers, would be conjoined through one medium. For let tire, if you will, be alone attenuated and easily moved; but earth on the contrary, have alone grossness of parts aud immobility, One medium therefore, will be sufficient for these. For grossness of parts and facility of notion, and tenuity of parts, and difliculty of motion, are all that ts requisite to the colligation of both. Since however, each of the elements is triple, the extremes require two media, and the things themselves that are adjacent, are bound toges ther throngh two powers. For solids, and these are things that have triple con-

trary powers, are never co-adapted by one medium, “Thus therefore, the divinity placing water and air in the middle of fire and earth, and rendering them as much as possible analogous to each other, so that what fire is to air, that air might be to water, and what air is to water, that water might be to earth, he bound together and constituted the heaven, visible and tangible.” Some of the Platonists, being impelled. by the assertions of Aristotle, extend through the whole world one passive matter, not at all different from that of the heavens, and in consequence of embracing certain barbaric opinions, give to the world a fifth body, end refer the doctrine concerning it to Plato, For Aristotle, following these opinions, introduced a filth element. And this ina certain respect he obscurely signifies, adducing the observations of the Barbarians as a testimony of the perpetuity and sameness of the motion of ether. But others assert, that the heavens are of a diflerent essence, as having a different form of life, a more simple motion, and a more perpetual nature ; but that Plato is now speaking about the sublunary elements, and adorns these by analogies. These menindeed, speak rightly, both with respect to things, and the opinion of Plato, in asserting that the nature of the heavens is different from mutable, and in short, material things; but at the same time ' they neglect the Platonic words, in which the philosopher says, that “ ¢he Demiurgus bound together and constituted the heaven [or the universe} through the analogy of the four elements ;”? and again, in another place, “ that he eluborated the idea of the stars, for the most part from fire.”

Let us therefore, if you are willing, preserving the opinions of both these men, perspicuously show, that the whole world consists of the four elements, and that the heavens are of a different essence [from the sublunary region]. And in the first place let us discuss the latter, For it is necessary, either that the heavens, should be entirely different from the four elements, being, as some sav, a fifth element; or that the heavens should consist of the four elements ; or from some one of the four; or from more than one. And if* the heavens consist of the four, they either consist of elements specifically the same with the sublunary, or of others. Tf however, that element is different from the four, how does Plato say that the whole world consists of the four elements? But if it is constituted from one of the four, how does he say shortly after, that the stars consist for the most part of fire? And if the world is constituted from more elements than one, [but not from all the four] how will it happen that a divine body will not be imperfect, and how wiil it possess all things, though the earth, and in short the sublunary region, have all things? Bat, if the world consists of all the elements, how does it happen, that in the heavens the composition of them is indissoluble, but in these [(sublunary] realms is dissoluble. For they will not be indissoluble on account of equal dominion. For whence, if there is equal dominion, is the variety in the heavens produced ? And how does Plato say that fire for the most part predominates there, if there is an equal domination? But if the heavens consist of four elements specifically different from the four sublunary elements, how, since they are composites, are the heavens moved with a simple motion? Where also are the wholenesses of the things which are there mingled !

' For ἡμῶν in this place, it is necessary to read opws. * Ecis omitted here in the original, 409 PROCLUs ON THE [BOOK ti. Such therefore being the doubts, it is better to say that all heaven consists of fire, which there predominates ; but that it also comprehends according to cause, the powers of the other elements, such as the solidity and stability of earth, the conglutinating and uniting power of water, and the tenuity and transparency of air. For as earth comprehends all things terrestrially, so the heavens comprehend all things according to a fiery characteristic. So that one thing [1 e. tire} has dominion, and the other elements are comprehended init) causally. Tt is necessary however to think, that the fire which is there, is not the same with sublunary tire, but that itis divine fire, consubsistent with life, and an imitation of intellectual fire. And that the fire which is here 15 wholly material, venerated, and corraptible. Genuine fire therefore, is in the heavens, and total fire for the wholeness of tire] is there. But earth is there according to cause, being another species of earth, and as itis fit it should, connascent with divine fire, possessing solidity alone, in the same manner as fire possesses an illuminative power, And as this celestial fire is not caustic, neither is the earth which is there gross, but the suminit of each is there. And as genuine and truly existing fire are in’ the heavens, so real earth is here, and the wholeness of earth 5 but tire is here according to participation, and materially, in the same manner as earth is primarily.

For that which remains is in each appropriately ; there the summit of earth (or earth according tu cause 5} but here the dregs of fire. But this is evident from the moon which possesses something solid and dark, and obstructing the light. For to obstruct is alone the province of earth, The stars also obstruct the sight, as producing a shadow above themselves. And it is evident this being the case, that since fire is in the heavens, and also earth, the diaphanous media between these, are likewise necessarily there printarily 5 air indeed, such as the most pure and agile air which is here; but water, such as the most exhaleable with us, and even still purer than

these; in order that all things may be in all, but appropriately in each, Lor on this account we characterize fire by visibility, which is deservedly the peculiarity of all fire. For as carth is primarily tangible, so fire is primarily visible ; because it is not in want of any one of the other clements, in order that it may be visible, as the others are inowant of the iluminative power of fire to their visibility. But fire becomes itself visible through itself. And this is common to all fire. Phe question therefore is solved. That all the progression of the elements however, may become manifest to us, and the gradations of them, itis requisite that we should begin the theory of them from on high, ‘These four elements therefore, fire and air, water and earth, υουκ I.) TIM AEUS OF PLATO. 423 subsist primarily, and uniformly according to cause, in the Detuinreus of wholes. For all causes are antecedently contained in him, according to one comprehension. Elence he comprebends the intellectual, divine, undetiled, and vicorous power of fire; the connective and vivilic cause of air; the prolitic and regerminating hyparxis of water; and the firm,’ stable, immutable, and unvacillating idea of earth, The theologist therefore, knowing these things, says of the Demiurgus,

ilis body's boundless, tim, and tiery-brights And, "The wide-extended all-pervading air, Forms lis broad shoulders, back, and bosom fair, Hlis middle zone ’s the spreading sea profound, Ihis feet, the roots deep-fix'd within the solid ground, But from these demiurgic causes, a progression takes place of these four elements into the universe, though not immediately into the sublunary world. For how can the most immaterial natures give subsistence without a medium, to the most material; and immoveable natures, to those that are in every respect moved? For the progression of things is nowhere without a medium, but exists according to a well-ordered gradation, The generations also into these material, dissipated, and dark realms, are effected through things of a proximate nature. For these are capable of being fashioned by the junior Gods, and especially so far as they have a tangible composition, But the Demiurgus is the father of greater and more beautiful effects. : Since therevore, the elements in the Demiureus himself are intellects, and imparticipable intellectual powers, what will be the first progression of them? Ts it not evident, that they will stil continue to be intellectual powers, but participated by mundane natures? For the progression from imparticipable intellect is proximately to that intellect which is participated. And in short, the progression from imparticipable causes, is to those that are participated, and from supermundane to mundane forms. These powers however, still remaining intellectual, but participable, what kind of diminution will they have? Is it not this, that they will no longer be

* For yovincsin this place, it is necessary to read povipos. intellectual? But I call intellectual natures, the forms of intellect, and of an essence truly intellectual. Being however, participable, but no longer intellectual, it is evident that they will not be immoveable. And not being immoveable, they will be self-motive. For these are proximately suspended from immoveable natures; and the progression is from things essentially intellectual, to those that are so by participation, and from immoveable beings, to those that move themselves. These elements therefore, will subsist in life, and will be intellectual according to participation, and self-motive. But itis evident what that is which will proceed from this. For the descent from life is to animal; for this 15 proximate to life. And from that which is self-motive according to essence, to that which is selfmotive according to the participation of life. And so far indeed, as the elements proceed from life to animal, they are changed; but so far as they proceed from that which is immaterial to immaterial natures (1 mean immaterial as with reference to mutable matter,) and from a divine life, to a divine essence, they are assimilated to truly immaterial essences. Here therefore, taking away the immaterial, and the immutable, you will make the material and the mutable. And through this they will be inferior to the natures prior to them; but through the order and symmetry of their motions, and the immutability in things mutable, they will be assimilated to them, If therefore, you also take away this order, and survey the great confusion and instability of the elements, you will have the last of all things, and those which are allotted an ultimate separation, being the dregs of all the elements prior to these.

Hence, of the elements, some are immoveable, intellectual, demiurgic ; others are intellectual indeed essentially, and immoveable, but are participated by mundane natures ; others are self-motive, and have their existence in lives ; others are self-motive, but live (i. δ. are animals], and are not lives only; others are alter-motive, but are moved in an orderly manner; and others, are disorderly, tumultuous and confused,

The difference of the elements therefore, being so great, what occasion is there to disturb what is here said by Pl: to, as if the elements existed only in one way ? For it is necessary to survey the clements in as many ways as there are media between the Demiurgus and sublunary natures; because their progression 15 through media. The elements therefore, are in the heavens, but not! after the * Ov is omitted here in the original. same manner as tn genesinrzic bodies 3 for neither do they subsist in the heavens, alter the same manner as in the Demiurzus. But prior to the sublunary elements, there are, the celestial fire (and this light manifests which is a species of fire) and celestial earth. Or Why does the moon being illuminated produce a shadow, and Why does not the solar light pervade through the whole of it? It is also necessary that the middle elements should. be in the heavenly bodies, but that ditl-rent elements should abound in different parts of the celestial regions. And in some places indeci, tt is necessary that tne fiery nature should widely scatter its splendour, on account of solidity, as in the starry bodies ; but in others, that it should be concealed from us, as in the spheres that carry the stars. Lence, the peculiarity of all fire is vistbility, but neither heat, nor floating, And solidity and tangivility, are the character-

“astics of all earth, but not gravity, sinking, and a downward tendency. It therefore, We assume these peculiarities, we shall find that fire and earth subsist also analogously in the heavens ; fire indeed, defining the essence of them, but each of the other elements being consubsistent with it. Por again, this also may be said, that causes and the efficients of certain things, every where antecedently comprehend the powers of the natures which are adorned and produced by them 3 and especially when they produce according to nature, For thus nature possesses the form of the teeth, the eves and the hands, through which also she gives morphe to matter, And not every eye possesses interval, but there is something in which it has an impartible form. Again, soul is one, and contains in itself that which is divine, and that whieh is irrational. And in the divine part of itself, it comprehends rationally the irrational powers, by which it governs, and arranges ina becoming manner irrationality. And neither is the unity of the soul, nor its multitude destroyed through different essences. For these things subsist in one way in the superior, and in another in the inferior part. Ina similar manner, the world also is one and many ; for the heavens are one thing, and generation another. And ceneration ts adorned from the heavens ; and these elements are in the heavens, but celestiaily. For they are in soul, psyehically, in intellect, intellectually, and in the Demiurgus, demiurgically. For how could the sublunary elements be governed by the etiluxions from these natures, unless they also subsisted in them after another manner? Thus also in the arts, we may see that the physician does not preside over the carpenter ; for the physician does not anteccdently comprehend in himself the works of the carpenter. Nor does the mechanic preside over the cook ; for the former does not antecedently comprehend things pertaining to banquets. But it

Tim. Plat. : Vou. I. 41] 426 PROCLUS ON THE ; [8οοκ lt. is the province of that which antecedently comprehends the whole power of a thing, to govern it. Hence it is evident that the mechanist entirely presides over the carpenter, and the physician over the cook. If therefore, the heavens govern all generation, the elements will be contained in them primarily. The Pythagoreans however say, that the clements may be surveyed in the heavens in a twefuld respect, in one way indeed prior to the sun, and in another after it: for the moon is ethereal earth. This therefore, the theologist clearly asserts. Lor he says: Another boundless earth besides he made, Which Gods se/ene, mortals meae call, With num’rous houses, ties, mounts adorn’d. But they say that the planct Mercury is ethereal water, Venus air, and the sun fire, And again, that Mars is eclestial fire, Jupiter celestial air, Saturn celestial water, and the inerratic sphere celestial earth. And thus speaking ina divided manner they make the extremes to be every where fire and earth, but conjoin the ethereal natures through media, viz. through Venus and Mercury: for both these have a collective and unifying power. But they conjoin the celestial natures, through Saturn and Jupiter: for through these that which is connective of wholes, and the commensurate, accede to all things. What we now say, however, is conformable to the history delivered by many [of the Pythagoric doctrines], For that this mode of distribution is not Platonic, we may learn from this that Plato arranges the sun immediately above the moon, afterwards Venus, and then Mercury.

It is necessary therefore to understand, that all the elements are in each of the celestial spheres, since in the sublunary elements also, each participates of the rest. For fire participates of earth; since being moved with facility, it would most rapidly perish, ifit was entirely without stability. And earth participates of fire; for being moved with difficulty, it requires heat to resuscitate and restore it. As this therefore is the case in these sublunary elements, much more must all the elements be in each of the celestial spheres, though some of the heavenly bodies participate more’ of fire, others of air, others of water, and others of earth. Again therefore, from the beginning we must say, that the elements being con- ‘Madey is emitted in this place in the original, ev aa ae Sen eee oe te ee! ee δὰ τρια» ceived in one way as unmingled, but in another as mingled, the first’ mixture of them produces the heavens, which contain all things according to a fiery characteristic. [But the second mixture of them produces the sublunary rezion]," in which all things subsist according to a middle characteristic. And the last mixture of them produces the subterranean realins, in which the dregs of all things are contained, Pyriphlegethon, as they say, and Acheron, Ocean and Cocytus. Hence it may be said, that the four unmingled elements are every where, and that there are five, all heaven being assumed as one element;

but that the last elements are comprehended in she earth. The five elements however, are said to be the elements of the world ; and on this account the world derives. its completion from them. But it must be said that the four elements are the elements both of the heavens and of generation. Hence the heavens are of a fifth essence, besides the four elements ; but are mingled from the simple elements. For these sublunary four are not in the heavens, but the summits of them are there, and all the four elements unmingled, and separated from each other by their proper forms. And these assertions are most concordant with Plate, who at one time says that the heavens consist of the four elements, bound together by analogy, and that the whole world is constituted from these; but shortly after fashions the five fizures, and calls them five worlds. For these things give a fifth essence to the heavens, introduce a tetractys of the elements, and accord with truth. For all things are inthe heaven according to a fiery mode; and on this account it is a simple body, different from that which is sublunary, and. truly comprehends all things pertaining to these material masses. We must not therefore admit that all earth is heavy, nor that all fire is light; but sublunary earth aud fire are perhaps things of this kind, while those in’ the heavens subsist after another manner.

For the solidity and stability which are there are derived from earth. And hence each of the spheres is not moved according to the whole of itself [but revolves round an immoveable centre]. But the celestial light, and facility of motion, are derived from fire. The connective and transparent nature of the heavens are from air 5 and their equability and smoothness, from water.