“ And with respect to the seven bodies, some of them being slower, but otlicrs sw ifter; those that revolve in a less circle, revolve more swiftly ;* but Saturn revolving in a greater circle, moves more slowly."
Plato says this, looking to the apocatastases of the planets. Hence, he says, that they revolve swifter or slower, and not that they simply proceed swifter, hut revolve slower. For when, as circle is to circle, so is time to time, then the
* Tor ti<ri lien*, it is necessary to read x-poeiirt.
’ Here likewise. for tm, read tpoutn.
1 This portion of the text is omitted in all the printed editions of the Tirowus. The original is as follows: ciictrni ra oera <rwpara, ra fitr (ipabvrrpa o era, ra br (tarrv. ra ptr eXarrw wep<ioi ra cwXor, dnrwpov (Itff Oar-roe) erpinne c b* gpoyot ftnSm wtp iwr ftpabvTtpor. This portion of text, appears also to have been wanting id the Fledicean manuscript from which Fionus made his translation of Plato, for be has not translated it.
IMtOCLUS ON THE
[book IV.
‘2 id
liodie* winch arc movetl are equally swift. For let one circle he double of another, and one time of another, then the "renter circle which is moved in the double line, w ill lie moved [over the same space] in half the time of the less, but the less will be moved in half the time, over the same space. Hence, they are equally swift. For things are equally swift, whit h arc mn\ed o\er the saint; space in the same time. Hut when one circle is to another, in a "renter ratio than one time to another, the motion of the "renter < irt It* is the swifter. For let this | H . so, anti let it he us circle is to < ill le, so is time to a certain time, which will then fore In* less than tin tune from the liisl. lor the same thin" will have a "rt alt r ratio to the less. The greater * ir* le tin n fore, m this less time, which is less than the time from the first, will pass over the same span* as the less circle. I'or it has l»ecii ih inoiistrati d, that it t in 1* is to circle, as time to tune, (lit motion of the less ts equally swill with that of the greater lilt le. Moreover, the motion of the h ss eirele Inmi the first was performed m u less time than the tinio from the first, ileiice the same interval, is passetl over by the one circle in a greatt r, hut hy the other in a less time. The motum therefore of the less circle, is slower than that of the "renter. Again, if the ratio of one circle to another, is less than that of onetime to another, the motion of the greater circle will Ik- slower than that of the 1 « >s. For if you make as circle is to circle, so is time to another time, you will make it tube ton greater time. Fur the panic thing has to the greater a less ratio. So that tin; greater circle will in a "reatt r tunc pass o\er 11 it* same space, than the less circle. It is therefore slower. Hence, these things thus subsisting, 1’lato does not now investigate what the con¬ dition is of the planets with respect to swiftness and slowness; for this requires a more ample consideration; but he adds, that there is a diflerciit apocatastasis of diflerciit plain ts, and of some slow* r, but of others more swill; the swiftness and slowness, being produced, either from the anomalous nature of the motions, or, which is more true, from the stars* Ining all of them moved with equal cele¬ rity, hut ore cueh having to another a greater ratio, than one time to another.
In short, thus much ought to be know n concerning the motion of the stars, that thev have not a rolling motion alone on their spheres. I or this motion is foreign to spherical bodies. Nor do tin v alone remain fixed. For bow would they be a „v longer of a circulating nature! Hut they circulate about tin ir centres, lini- tatui" the universe, according to the opinion of Plato; without being at all in want of the hypotheses employed by astronomers, as I bate In-lure observed. I'or if Plato thinks that the fixed stars are thus movt tl, through an imitation of the
1 i. e. Let what has been before demonstrated be admitted. 1 Fur arfpwv lure, read ocrr^iwi*
hook i* ]
TIM/HUS OF PLATO.
universe, much more will lie "rant that those stars which are allotted the government of the universe, and a leading dignity, imitate the whole world. These therefore, are moved about their centres; hut the spheres in which they are contained, and which are as it were moving rulers, convolve them either swifter, or slower. Except that Pluto gives to them a more various motion, because they are media ls-tween things that jut treed in a right line, and tilings that by themselves are alone moved in a (irele, and moves each of them about its centre, anti through its proper sphere, so as to become elevated, and near the earth, and to revolve about the northern and southern parts; by which motions they are inferior to the fixed stars, though they are otherwise allotted a liberated dignity and power.
“ But from the lation of the circle of the same, the orbs which compre¬ hend, appear through the circulation of those that move more slowly, to he comprehended. For all the circles of them revolve with a spiral motion, because at one ami the same time they arc moved in two contrary directions; and in consequence of this, the sphere which has the slowest revolution, is nearest to that to which its course is retrograde, and which is the sw iftest of all the spheres."
Circulation, as wo have frequently observed, 1 m ing twofold, one from the cast to the west, hut the other from the west to the east, lie who understands hotii these circulations, w ill know what is the common, and what the peculiar motion of the stars, and which of them are moved swifter, and winch more slow. For he will look to their jMVuliar motions, and will know that those are swifter which are in comerjuentia ; and thus, he will not admit that Saturn is swifter than the Moon, hut he will see that the Moon is more eastern, and that Saturn is comprehended, but the Moon comprehends. But he who fancies, that there is onl\ one simple motion ot all the stars, which is from east to west, when he sees that Saturn and the Moon, are at one time together, hut that .it another time Saturn is more west¬ ern, as Ir.ning moved to a greater extent, w ill say that tin Moon is comprehended by Saturn, n/,. the swifter by the slower. The cause however of this e rror, arises from alone looking to the period of the circle of the same, which possesses much y power and strength, anil not considering the peculiar motions of the planets, nor perceiving that they do not make their transition in nntea dentm , but in coiiM t/ucnlia. l or asserting this also, the Athenian guest or stranger illumes the multitude and those who are ignorant of astronomy. “ For it is disgraceful,” says he, “ if we survey a stadium, and do not know which of the racers runs swifter, anil which
[book I*.
Hlower; am! he must be considered as absurd, who fancies that the swifter is the slower course. But it is much more disgraceful for those who perceive truly Olympic races, not to know the swifter and slower period, through ignorance of astronomy." For the bodies that revolve with the greatest celerity, appear to l>e comprehended by tho^e that revolve more slowly, though they in reality will he wen to comprehend, by those who are able to look to their proper motion. But the latiou of the circle of the same, vanquishing the body which is nearest to it, causes it to appear most rapid in its motion. That however, is nearest to it, which is the b ast distant from it. I or let, if it should so happen, the Moon and Saturn be near tin* Cor la-onis, or heart of the Li m; then the Moon being moved with its jieeuliar motion, will depart from this fixed star; but Saturn for many nights will be su n about the same place. I he astronomer there fore, knows that the M oon departs from this star more rapidly, on account of the motion of the Cor Ltmis in consequentia. But he w ho is ignorant of astronomy, w ill fancy that the Moon and Saturn being moved with the universe towards the same parts, do not make theirapocatastases after the same manner; but that the one, as swifter, arrives at the west before the other ; but tliat the other as slower, arrives at a more western part. This then fore, would be the conclusion according to the opinion of the multitude. This may however, happen to be true, I mean that Saturn is the swifter; if, as we have before ohsi rved, the ratio of the circle of Saturn, to the circle of the Moon, is greater than tin* ratio of the apoeatastasis of one time to that of the other. For the body which is nearer to the sphere of the fixed stars, will be sw ifter, for the before mentioned reasons.
But what i> the meaning of the assertion, that the planets “ revolve uith a spiral motion , bet au.se at one and the same time theif are moved m two contrary directions And how are we to admit of contrariety in a circular motion? For each of the planets being moved with two local motions, i* not the cause of the spiral motion ; but this arises from their being moved in the oblique circle [i. e. in the zodiac] towards the equinoctial. Thus, if some one supposes that the Sun is moved with the universe towards the equinoctial, the cause of this will not be a spiral motion, though there is an anti-circulation. IVor must it l>c simply admitted that the motion which is contrary to a circular motion, is another motion [i. e. is a motion of a different kind]. For many beautiful arguments have liecn urged against this opinion. May not therefore the words, moved at the same time m two contrary directions nu-an, that they are not only moved at one and the same time to the east and west, but also that they become both according to breadth, and according to depth, nearer to, or more remote from the earth, and more northern, or more southern ? For these two motions, make a spiral, in conjunction with the lation
Book Iv ]
TIM/EUS or PLATO.
of the universe. The spiral likewise, is adapted to the planets, which are media between the fixed stars, and snhlmiary bodies; the former being moved according to a circle alone, and the latter, in right lines. Just again, as it is natural to the planets being media, to be moved both anomalously and equably, according to length, breadth, and depth ; in order that they may have the paradigms of the natures that are all-variouslv moved posterior to themselves, and may imitate through circulation the uniform subsistence of the natures prior to them. These things then fore, are manifest to every one.