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

If, therefore, ether consists of similar parts, but the figure of that which consists of similar parts is similar, and the similar is spherical, ether is spherical. After this manner, therefore, we may physically prove that the world is spherical,

If, however, it be requisite to elucidate what is said, by mathematical demons strations, let us summarily relate what appears to be the truth to those who are skilled in these particulars, In the first place, therefore, they endeavour to prove {that the universe is spherical] from the stars being moved in parallel circles, both the fixed stars, and the planets, the sections always becoming unequal, as we approach to the north; so that some of the circles touch the horizon; but others which are less than these, do not touch it. And, at last, there is a certain immoveable point, about which all the circulation is moved. In the next place, they infer this from the nights and days becoming unequal, conformably to the solar motions to the north or south. In the third place, from shadows. For whence is it that the sun when he begins to rise," and also when he sets, is more northerr. to us, and appears to pass beyond the crab, but when he is in the meridian, he sends the shadow to the north; unless from the universe being moved in acircle, which inclines to our motion? Farther still, they prove that the universe is spherical, from the stars which are not moved according to depth, always appearing to have an equal magnitude. For if the heavens were not spherical but cylindrical, or some other such like figure, it would be requisite that the sun, when he becoines more southern to us, should appear to be less, oir account of the inequalily of the interval.*| Nothing of this kind, however, is seen to take place. From these things, therefore, astronomers, in short, endeavonr te prove that the universe is splirical.

* For encyec here, it is necessary to read ἀνίσχει». ἢ For vrocracews in this place, it is necessary (o read arorrasews.

Tim. Plat. γον i. af

p. 450

Vv

From these things, therefore, astronomers, in short, endeavonr te prove that the universe is splirical.

* For encyec here, it is necessary to read ἀνίσχει». ἢ For vrocracews in this place, it is necessary (o read arorrasews.

Tim. Plat. γον i. af

p. 450

Vv

But that a sphere is the most capacious of all bodies that have equal perimeters, is also demonstrated by them. Likewise that all bodies of equal sides may be inscribed ina sphere, but not all of them in any one of the polyedra. Nor is there any occasion that we should transcribe what is demonstrated by them. For we write to him who has been sufficiently instructed in these particulars. At the same time, however, thus much must be related, that they demonstrate the superficies of the sphere to be more capacious than that of all other solid bodies of equal ambits, and they particularly demonstrate that it is more capacious than the bodies which are called by Plato, equilateral and equiangular polyedra; partly employing the propositions of Euclid, and partly those of Archimedes. As I have said, therefore, the demonstrations of this may be obtained from their writings. Ttais our intention, also, after we have commented on the whole of the Titmeus, to discuss more fully in a collection of the Mathematical Theorems in the Timieus, such mathematical particulars as are disseminated in the Commentaries; in order that the lovers of truth, by having a collection of these things, may be assisted in the all-various comprehension of the mathematical parts of the dialogue, But enough of mathematics.

Tet us therefore return to the words of Plato, and survey after what manner each of them is delivered. That in intellectuals! then, figure is after whole, and that Plato having demonstrated the universe to be a whole, very properly in what follows teaches us concerning the figure of it, we have before observed. Since, however, this proceeds into-the universe fruin the demiurgic cause, on this account he says that figure was given to it from thence. But the giver evidently possesses by a much greater priority that which he gives. The spherical figure, therefore, is in the Demiurgus, but mitellectually ; so that it is in all-perfect animal intelligibly, and in that which is still prior to the latter of these,* occultly. For if it be requisite to speak what appears to me to be the truth, where intellect is, there

> also the spherical peculiarity exists. For intellectual energy has an essence of such a kind as that to which the Athenian stranger or guest assimilates it.? But in one place, this peculiarity subsists unitedly and intelligibly, as those say who are divinely wise. In another place, it subsists intelligibly, indeed, but with a

* i.e. In first intellectuals, or in other words, in that divine order which is denominated intelligible and at the same time intellectual. 2

In another place, it subsists intelligibly, indeed, but with a

* i.e. In first intellectuals, or in other words, in that divine order which is denominated intelligible and at the same time intellectual. 2 i.e. In being itself, or the summit of the intelligible triad. ὁ Τὰ the Luth book of the Laws, he assimilates it to the revolution of a spnere fashioned by a wheel.

BOOK 111.]} TIALEUS OF PLATO. $51

more abundant intelligible division. In another intellectually, but accompanied with an all-various diversity. And in another sens:bly, accompanied with separation and interval, And _ this last, indeed, is not simply called by Plato spherical

(σφαιρικοην), but spheriform (σφαιροειδές), as being an imitation of the intellectual or intelligible sphere. For the universe also is moved in a circle, because it imitates intellect. Bul either the intellectual or the intelligible universe, will be most principally spherical ; and that which ts truly astronomy, will be conversant with these. For this

ἐξ fo astronomize above the heavens." Moreover, to be from all the parts equally distant from the middle to the bounding extremities, pertains indeed, to the sensible sphere, because all the lines from the centre of the earth to the extremities of the sphere are equal. For from all the parts is significant of distance according to the three intervals (of length, breadth, and depth}. It also pertains to the mathematical sphere. For there there is a middle, and the intervals are from all the parts equal. After another manner likewise it pertains to intellect. For to converge to ilsclf, and to be as it were of the same colour acoording to every part of étsclf, and to have all the powers in it conjoined to the one of itself, ἐδ the spherical peculiarity in intellect. Proceeding also still higher, it will no longer be possible to separate the centre from the sphere, on account of the ineflable and united nature of the intelligible* peculiarity. Le says, therefore, that it is the property of the sphere to have all the right lines every way equal from the middle, in order to distinguish it from the circle. For the term every way, or from all parts, does not pertain to this, since it has only two intcrvals.