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 toge- ther. [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 gene- ration 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, how- ever, 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 inhe- rent 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 inves- tigated 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: Make the first number equal to the first; the second to the first and the second 3 and the third to the first, second, and third, Three monads therefore being pro- posed, there will be produced according to this method three terms, vin. 1. 2. 3. preserving an arithmetic middle. Bor this middle consists in equally surpass- ing 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, form- ing 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 ana- logies 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 sur- assed, 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.
Rook 411} Timeus of Plato. 403
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 requi- site 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 ha- bitude 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, ac- cording 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,