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

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.

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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

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.

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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.

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

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