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

For lie no where makes mention o( these, as neither does lie nn-nlion the eccentrics of the circles. For it would be ridiculous to make certain little orbs, moved m each sphere with a motion contrary to it, or to admit that they are parts of a sphere comprehend-

A mathematical table, in which the .annuls described lines and figures.

In llie original, m rijt tpieurr/r <r^mpu», i. e. in a sphere surrounded with ring's, which therefore is evideut y what the modern» call the ai mil/ari/ sphere.

l y the paiadigm, I suppose l’nn lus means an astronomical globe, or as it is now called, the celestial globe.

1 he astrolabe is a m.ilhcma tical instrument, representing nearly the whole of the celestial doctrine in a plane, w hence also it is tailed a planisphere.

book IV.]

TIM XUS OF PLATO.

l 295 mg indeed tin* centre, hut not mnvnl almnt it. For this would subvert the com¬ mon axiom of physics, that every simple motion is either about the mobile of the universe, or trom the middle, or to the mobile, lint this h\ pothesis of eccentrics, either divides the spheres into arches, moved in contrary directions, and destrovs the continuity of each, or introduces circles to the celestial bodies, of a nature different from them, and connects motions from things dissimil ir, and without sym¬ pathy with each other, through the dissimilitude of their compositions.

It is necessary however to consider whether those time's thus subsist. For again, we must give our opinion on this subject, which requires much discussion. I" or I’lalo moves the stars in different ways, not at all requiring contrivances of this kind, as unworthy of a divine essence. Hence [accordin'; to him] it is ne¬ cessary to suspend this variety from the motion of their informing souls, their bodies being moved swifter or slower conformably to the will of these, and not as the multitude think through imbecility. This inequality and diversity of motion also, is effected in orderly periods of time, the stars themselves being moved about their centre's, and proceeding variously through their proper spheres; m order that beini; mi dia between bodies that are inerratic, and those that are moved in a right line, they may have a mixed motion, being bone* along according to altitude and depth, and with a direct and retrograde motion, and this m orderlv periods ot time. For lie says that, “ the stars /iroctolhig u ith an ndnnnin if motion through the heavens, have rendulions.'' lint if they proceed through the heavens, it is evi¬ dent that all of them are moved throuirh tie ir spheres accordin'.; to the depth of them. 1 or bodies which proceed through a certain thing, do not abide in the. same place, but pass from one part ol that through vv Inch thev proceed, to another. If also, they have rotations, their all-various mutations are the revolutions of them in their spheres, according to breadth and depth. The spheres however, are alone moved to the east, and not about the same poles as the sphere of the fixed stars. For in the licpuhiic, he makes the one axis of them to Ik* the distaff', but the poles of the eight spheres to be the spindles, and he says, that about these there is one simple motion, just as there is of the sphere of the lived stars. After¬ wards, in that dialogue, he says that the Fates preside over these circles, and that a different Fate moves them differently. Here however, he convolves one of the spheres laterally, but the other diametrically, in the same manner as the cireles of the soul, in which he established the causes of the whole spheres them¬ selves, and the planets. On this account, he moved them obliquely, according to a diameter. Hence he says, that some of the planets are moved similarly, hut others, dissimilarly, in the same maimer as the spheres. The difference therefore

296 PROCLUS ON TIIE [book i*.

of the planetary spheres, anil the sphere of the fixed stars, is conformably to these things, and also according to a motion to the right hand, or to the left.

The difference therefore

296 PROCLUS ON TIIE [book i*.

of the planetary spheres, anil the sphere of the fixed stars, is conformably to these things, and also according to a motion to the right hand, or to the left.

Such therefore, is the fabrication of the sphere according to Plato, the seven spheres having a conjoint revolution, and possessing that difference which vve have mentioned, with reference to the one circulation [of the inerratic sphere.] Conformably to this also, tin* fixed stars are alone moved about their centres; but the planets are both moved about thur centres, and proceed through the depth of the spheres in which nut h is placed, variously revolving upward and downward, and with a rt trograde motion. Kuch of these likewise, and the poles of these, arc moved in another circle about the zodiacbut the spheres in which they exisi, are all of tlu-in moved similarly to the inerratic sphere ; \i/. they are moved about one pole w hu h is common to all of them. The sphere of the fixed stars also, is bv itself moved vvilli one motion; but the planetary sphere, with a twofold motion, one Ih mg the motion of itsi If, and which is oblupie, but the other being a revolution in conjunction with the nu rralic sphere. \\ ith respect to the stars how¬ ever, those that are fixed, revolve abom then own ecu ties, and have likewise an advancing motion, in conjunction with their sphere. But tin* planets revolve in conjunction with the iiurratic sphere, and each is moved together with its sphere to the east, and revolves bv itself according to breadth and depth, and about its proper centre, Tor it is necessary that each lieing spin rical, should be moved with this motion, imitating its proper wholeness ; ju>t as the fixed stars are eo-arranged with the inerratic sphere. To which may b< added, that proceeding through the heavens, they have also as I'lnto su>>, all-various revolutions.

These things therefore, being true, as we have l»efore demonstrated, the hypo¬ theses of epicycles, or eccentrics are not vain, hut they analyze various into simple motions, m order that we may easily apprehend the apocatastases of various motions, which are not of themselves easily understood, Imt are only to he compreheiided from the fixed stars. Hence it is an cm client contrivance to discover what simple, produce various motions, and through them to investigate the mea¬ sures of such as are various. Just as it some one, not being able to measure a spiral motion about a cylinder, but afterwards assuming a right line moved about it, and a point m the right line measuring its motions, should find what the quan¬ tity is of the motion about the spiral in a given time. To this therefore, the atti ntion ot those is directed, who employ evolvents, epicy cles, and eccentrics, through simple motions, from which they discover a various motion. These things

• For *tpi At gw* Lire, it u nccesiary to read wtpi Aigcv.

HOOK I*.]