After another manner, however, the same thing may be syllogistically inferred, physically in the way in which Aristotle endeavoured to prove it. For since the universe is moved in a circle, and it has been demonstrated by him that there is nothing external to the extreme circumference of the world, neither vacuum, nor place, it is necessary that the figure of the universe should be spherical, and not rectilinear. For if it was rectilinear, there would be a vacuum. For as the universe revolves in acircle, it would never have the same place through the alter- nate mutation ofthe angles and superticies. For since of every other figure besides a sphere, the lines from the middle are unequal, there will be a vacuum according to the less interval, where the bulk of the body is not. Whether therefore it be according to length, or according to breadth, there will be, during the revolution, a less interval, For a vacuum is perfectly equidistant; bat where there is no body nor figure, there will be a deficiency, In Consequence of the magnitude being less than the vacuum.’ Farther still, from secondary natures also, you: may assuine physically, that the universe is spherical. For the earth Is spherical, as is evident from all things every way tending to the middle of it. But water is dil- fused round the earth, and itis spherical. For there is a contlux of it into the concavity, till it comes into contact with the central part of the earth, The ar also surrounds the water and the earth, and the fire surrounds the air. It, however, this be the case, the heavens likewise will be spherical. For there will be a vacuum within them, unless they also spherically comprehend tire.
Again, nature distributes to the first of bodies, the first of figures, and a simple figure, to a simple body. For in each genus of things, ¢#e one is prior to the many, and the simple, to the composite. As, therefore, we distribute motions in a way adapted to their works, to simple works indeed, simple notions, but to composite works, Composite motions; thus also there is an allotinent of appropriate figures, one kind to simple, but another to composite bodies. Ligure, however, ts, as tt
were, the visible resemblance of form, the morphe of morphe, and as it were anafiation of
the peculiar hyparcis of each particular thing. Hence, that which is essentially simple, proceeds into a simple figure, but that which is variously mingled, has also a co-mingled idea of figure. Farther still, the celestial motion is the measure of notions ; but the measure in each thing is that which is least. The least motion, however, is the swiftest. But circulation is the swiftest of motions. If, however,
"Tustead of over ro σχημα ἐλλείψει, δια τὸ peyeNus, ἐλαττον ον τὸν KEVoU in this place, it is necessary
to read, ονὲς ro σχημα, ἐλλείψει, δια ro peyeOus ἔλαττον ον τὸν κενὸν.
Book 111. Tim Eus of Plato, 449
this be the care, the heavens are spherical. For the sphencal is the swiftest of motions, IN consequence, as the Elean guest says, of proceeding on the smallest foot. Again, of bodies, some consist of similar, but others of dissimilar parts. "To bodies, therefore, of dissimilar parts, dissimilar figures are necessarily distributed by nature. For polygonous and, in short, angular figures, are of this kind, and wiso those that consist ofmany superticies. But to bodies of similar parts, similar fizures are adapted contermably to their excellence. For the sphere alone among solids is a similar figure; since all the rest have dissimilar ficures. For some have two superficies, ἂς ibe cone, others three, as the cylinder, others four, others five, and others more than five, as pyramids on polygonous bases arranged in sue- cession. 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
450 ; PROCLUS ON THE {Book 411.
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 super- ficies 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 Comment- aries; 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.
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 separa-
tion 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 accord- ing 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 pecu- liarity 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.
Plato likewise uses the expression lo fashion as with a wheel, because bodies with us are rendered more accurately round throngh a wheel which cuts off the inequalities of the bodies. And that the simi/ar and the perfect especially pertain to the spherical peculiarity, is evident. The similar, therefore, is analogous to the one, but the perfect to the good, so that through both he refers the spherical pecu- liarity to the first principle of things, by saying that itis most similar to itself, and most perfect ; equallizing that which is most unical and most boniform. For neither the mixed perfect or similar, nor the right line, which always receives an addition and may become angular; but the spherical peculiarity alone, is most similar and most perfect. After this, he adds, which is evident, “ that the similar ts better than the dissimilar.” For similitude is of an uniting, but dissimilitude of a
* Which the Coryphean philosopher mentioned by Plato in the Thextetus, is said to do. * Instead of rns voepas cSuorgros in this place, it is neccssary to read ras voqrys ἐδιστητοε.
452 PROCLUS ON THE {[nooK 111.