and is fontal, subsists between the impartible ami partible essence; of which the former is universal intellect, but the latter is divisible into atoms. Hence the first soul is the medium between these, as subsisting from both which are prior to it, and becoming one whole from the three middle genera. Hut the second, and which is universal kind, is divided into parts, and is harmonized For the first soul, abiding wholly in itself, a division is produced, which is a progression from the soul that is a whole prior to parts, into the soul that consists of parts. And the third soul is that which is fabricated through right lines and circles. Form this the division manifests a diminution from that soul which is a whole prior to parts. Hence he divides the whole of this discussion concerning the psychogony into three parts, conformably to the three souls that have been mentioned; one subsisting according to the mingling, another according to the harmonizing, and another according to the forming energy of intellect. Having therefore, made this division of the psychogony and souls, he considers the distribution into parts, and the seven terms, as alone pertaining to the universal soul. Re¬ ferring likewise thc-a» terms to the division of the universal soul, lie thinks it necessary that celestial natures should be produced bv this soul from the duple, but sublunary natures from the triple order. For he distributes appropriati num¬ bers to each of the elements, to earth indeed 7, to tire II, to water!), and to air 13. For the geometrical.proportion, which is l, 2, 4 [and the sum of the lernisof which is 7] pertains to earth ; perhaps indeed on account of the name ; and jrcr- liaps also, because' as e-art h contains tbe remaining elements, so tin- geometric comprehends the' other middles. Hut the arithmetical proportion which pertains to wate r, is ‘2. 3. 4; through ‘2 communicating with earth, and be cause likewise, it is especially friendly to multitude, and consists of an element which is the most multitudinous of all others, viz. the* icosaedron. And theharmonieal proportion, which pertains to air, is 3. Lti; because this communicates with the arithmetical, according to two of its te*rins 3 anil I, which are the greater in the former, but the less terms m the* latter, proportion. Since, however, the' harmonic middle is (wo- fold, consisting e it tier in the* duple* ratio of the* extremes, or in the* triple- ratio ; lor Plato assumes it as the middle of either duple* or triple* terms;—hence, making the e'xtivmes to be 3 and <>, according to tbe double* <*f the extremes, [i. e. accord¬ ing to a duple* ratio] he* obtains the* peculiar element of the air, viz. the ortaedron, which has 0 according to the* angles, but 4 according to the base of the* two pyra¬ mids, ami 3 according to the superficies of the nrtnedmn, which is trigonir. But according to the other harmonic middle, which is 2. 3. he obtains the ele¬ ment of fire; U'causo these? according to the two tonus 3 and (i communicate with the tonus prior to them [3. 4. 6], which are there the extremes, but are here the
greater terms; and moreover, because the element of fire has 0 sides, but twice the tetrad, in its angles and HiijR-rficies, and a triangular base. Very properly, therefore, does 7 pertain to earth, 9 to water, 13 to air, but 11 to fire; the ratios being assumed iu the above-mentioned numljers, from which they are pro¬ duced. For 7 consists of 1. 2. and 4 ; 9, of 2. 3. and 4 ; 13, of 3. 4. and (J; and 11, of 2. 3. and 6; each having two terms in common with the number next to it, just as the elements have two sides in common. From the composition how¬ ever of these, a triple order is effected. And of the middle terms of the propor¬ tions proximate to each other, the one is gn atcr than the other, which is also the case with the extremes, as is evident in earth and water, and in fire and air,* as is evident in the given terms. Again, he attributes the iuiiiiIm r 15 to celestial natures; the monad indeed, to the crcle of same, but the double hebdomad to the circle of different, on account of the twofold circulation of each, viz. of the spheres themselves, and the stars contained in them, which are seven, the spheres being also seven. These things, how ever, which are mathematically asserted, bring with them a certain not inelegant theory, lhit how they are assimilated to the things which are now discussed, and how they may Is* Py thagorieally interpreted, is not at all noticed by Theodorus, in stu h a way as to be able to satisfy him who does not negligently attend to what Plato siys. All these particulars are indeed ele¬ gantly invented, but ho refers the analy sis of the Platonic diagram to monadic ntmiliers, not looking to the ratios resulting from them, so as to assume every¬ thing, viz. the middles, the sesiptialtcr ami sesipiitertian ratios, the sesipiioctaves and leiminas ; it being by no means possible to diseovi r these m tin* first num¬ bers, which he emplovs iu the above-mentioned distributions, into the elements and tin heavens.
After these, therefore, let us survey another mode of dismission, which is adopted by our preceptor, is generative not of one only, but of many and admir¬ able conceptions, and which we also made use of liefore. lie says then, that each of these things may be considered iu a twofold respect, in the w hole soul of the universe as one, according to union, and m the many ratios, and in ihe multitude contained in it, according to division. For the soul is both one ami multitude, one reason, and the numlier of all-various forms, and imitalesthe demiurgic whole¬ ness, and the* separation of the powers of the father. In the first place, tin re fore, we must understand what it is according to the whole of itself, abiding, and pro-
• Thus tu the nunilrt r* 1 i. 4, w Inch |>ertain lo chi ill, and in 2. 3. 4, w hit h pertain to water, t lie mid¬ dle term 3 ii greater than the middle term 2, and lint is also the case in I lie niiiuhers 3. 4 and 2 I, ft, the former of which pertain I j air, and the latter to fire. In the extremes also, the extreme 2 is greater than 1, aud the extreme 3, than g.
BOOK lit.]
TIM.FATS OF PLATO.
U.l
ceeding in itself, ami returning to itself, and also providentially attending in one way to the immaterial and pure forms of mundane natures, hut in another to all bodic s, and the partible essence. Understanding this likewise, we must say, that it abides according to the run: or first part; but proceeds according to the second, the progression being conceived to l>e divine, and not according to passion or imbecility; and that it returns according to the third part. For the perfective accedes to beings from this. Hut being all-jM'rfrct, and established* in iutelligi- Idcs, and abiding eternally in intellect, it also providentially attends to secondary natures. And in one way indeed, it providentially inspects the natures that are proximate Iy suspended from it, hut in another, solid masses themselves. It like¬ wise attends to each of these in a two-fold respect. For tin* natures which proxi¬ mate!) participate of it proceed from, and return to it; proceeding indeed, ac¬ cording to the prolific power of the fourth part, but returning to their one cause, according to the re-elevating power of the fifth part. We may also survey these solid numbers in corporeal masses; which proceed indeed, according to the octu¬ ple of the lir-t part, this numlier Iveing dyadic and solid, and at one ami the same time prolific, and capable of proceeding to all things ; hut they return according to the number twenty-seven, this being a solid conversion, as triadic, and as per¬ taining to the nature of sameness. For such is the odd number. Hence, there are three progressions, ami three regressions, about the one and united perma¬ nency of the soul. Hence too, there are three even and three odd numbers, proceeding from the monad, and complicated with each other; because the sold itself abo proceeds, and returns. And proceeding indeed, it produces the first receptacles of itself, and that whic h is primarily invested with figure. Producing it also, it imparts interval to it and bulk. Put in its regression to itself, it causes it to be spherical, and on this account causing it to be a thing of this kind, it produces the world in it; ellerting the progression of it according to the even • number, but the regression according to the odd number, and both these cubic- ally, lieeause it is the generation and regression of solids. The progression therefore, and regression are triple; the first being unligured, the second accom¬ panied with figure primarily, and the* third secondarily; but ail these as in numbers.
In the next place, we must pursue the theory, conformably to the multitude which is in the soul, and say that the ratios in it are comprehensive of ratios.
■ For twcpryitvifv here, read triipKp o-ijr.
* For apuKvi ill (Inn place, read apr iarwi.
* It is occeaury here io mpply (he word* rpwrm, ( it.
And some of them indeed, are divided in it, after the manner of wholes, hut others after the manner of parts.* And some are total, others generic, others specific, and others partial. The total indeed, are such as the ratios of the middles ; but the generic, are those which are found in the duple, or triple terms; and the tqseeific, are those which are under these.* For each of them has a multifarious subsistence. Hut the partial ratios are those of the sesquioctaves and leimmas, into which, as parts, all the sesijuialter ami sesipiitertian ratios are di¬ vided. We must also say, that the soul cont tins tin one union of the ratios, through the essential monad ; but the diiision of the ratios, through the* progression of the duael ; ami the comprehension of them , 1 through the multiple terms. I'or these are comprehensive of the super particular ratios, and have an essence more total than these ratios; just as the super-particulars comprehend the sesqtiinckives ami leimmas; the former having the relation of species, but the latter being arranged in the order of parts. ] or to make the geometrical proportion alone comprehensive of the other two middles, m the first place, causes the whole essence of the soul to be as it were demiurgic geometry. For elsew here, Plato calls this analogy the judgment of Jupiter. In tin next place, it show s that these two mid¬ dles, when surveyed with the geometric middle, and comprehended m it, dispose wholes in an ordi rlv manner according to justice; but that when separated from it, they are the causes of confusion ami iuju-ti« e. For a distribution of tin* equal to things unequal, is entirely unjust; as is aho, the conjunction of eontraries to inch other, without a certain geoinetrieal equality Hence tin* harmonic middle is in w ant of the geometric analogy, in order that it may bring together contraries elegantly, just as Plato did, m harmonizing lire and earth, through tin* two elements [of tnr and water]. Jin* arithmetical middle likewise, energizing together with this, possesses rectitude in its operations. For thus the unequal in uiu*qual things is equal.* Distributing therefore equals to iiiiequals, it preserves tin* peculiarity of itself, and exhibits distribution according to desert, which is the prerogative of the geometric middle.
Farther still, we must say, that the soul imitates the first principles of things.
' For firpi here, it n ubuuuslv necessary to read utpvr.
* i. e. They are llie livpologi, uliuh have been before explained.
* llctweeii Am and rcWaiXurnuH lure in I lie original, st is necessary 1o insert, conformably to the version of Tlloinxus, the words rrjv fen ?m -roiintov, ij Ae rue Auyue irepio^ij Am. e. A.
* Thus in the terms 1 2. 3 0, wlinli are in geometric pioporliou, the terms 1. 2. 3 also being in arithmetic proportion, the difference is uni rpial between the terms 2 and 3. and the terms 3 and fi, and also between the ternib 1 and ?, and 3 arid t>, but the ratio is ecpial ; and therefore, by the union of the arithmetic with the geometric middle, the unequal in unequal numbers is equalized.
book III.]
TIMfEUS OF PLATO.