The Commentaries on the Timaeus of Plato — trans. Thomas Taylor

And thus far Porphyry, who, in what he here says, allords us an oc< asion of collecting something true concerning the soul

IJnf the divine lauiblichiis celebrates these numbers with all his power, as ex¬ hibitin'' - certain admirable peculiarities. And he calls indeed the monad, the cau-e ofsanieiu» uni union ; the iluad, the supplier of progression and separation; and the triad the leader of the regression of the things that have proceeded. lie aUo >avs, that the te»rad is truly all-harmonic, containing all ratios in its< If, and unfolding in itself the second orderly distribution of things; and that the euuead is effective of true perfection and similitude, being perfeet from pet feet numbers, and participating of the nature ol sameness. But ho calls the ogdoad, the rinse of universal progression, and of pervading through all tilings. Lastly, he says, that the number twenty-seven is ef¬ fective of tin- regression nt tin last of things to the lirst, in order that on ouch side ot the tetrad, there may he permanency, progression, and regression, there primarily, hut here secondarily. For the ennead has ail alliance to the monad, bi > iu ,r it iwu.’ one (*v y!ov c>a a ); hut the ogdoad to the duad, being the cube of it, ami the number twenty-seven, to the triad, through a similar cause. Through the former numbers therefore, the soul imparts to more simple natures, permanencie s, progressions, and regressions, but through the latter it imparts these to more com¬ posite natures. But tlie tetrad being the middle, because indeed, it is a square, lias permanency ; but because it is eveiily-even, lias progression ; and because it is tilled with all ratios from the monad, has regression. 'I In se, however, are symbols of divine and arcane things.

After this explanation, which i v thus admirable, the philosopher I heodorus, proceeding in a certain path peculiar to himsclt, say s, that the soul is tin* third principle after the one principle of all things, one soul lieing fontul, another uni¬ versal. and another the soul of this universe, lie also says, that the lir^t ol these is indivisihle, the second divisible, and that the third possesses all-various divi¬ sions. Since therefore, there is a triple difference of soul, that which is soul itself

BOOK III ]

TINLFA’b OF PLATO.

p. 03

and another the soul of this universe, lie also says, that the lir^t ol these is indivisihle, the second divisible, and that the third possesses all-various divi¬ sions. Since therefore, there is a triple difference of soul, that which is soul itself

BOOK III ]

TINLFA’b OF PLATO.

p. 03

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 jrcrliaps 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 (wofold, 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

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

p. 94

PROCLUS ON TIIK

[BOOK III.

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.