vement. But as to the actual number of these movements, we now-to give some notion of the subject-quote what some of the mathematicians say, that our thought may have some definite number to grasp; but, for the rest, we must partly investigate for ourselves, Partly learn from other investigators, and if those who study this subject form an opinion contrary to what we have now stated, we must esteem both parties indeed, but follow the more accurate.
Eudoxus supposed that the motion of the sun or of the moon involves, in either case, three spheres, of which the first is the sphere of the fixed stars, and the second moves in BVB Trøjer the circle which runs along the middle of the zodiac, and the third in the circle which is inclined across the breadth of the zodiac; but the circle in which the moon moves is inclined at a greater angle than that in which the sun moves. And the motion of the planets involves, in each case, four spheres, and of these also the first and second are the same as the 2018 Christian Louboutin Loafers & Drivers first two mentioned above (for the sphere of the fixed stars is that which moves all the other spheres, and that which is placed beneath this and has its movement in the circle which bisects the zodiac is common to all), but the poles of the third sphere of each planet are in the circle which bisects the zodiac, and the motion of the fourth sphere is in the circle which is AFC Ajax Børn Fodboldtrøjer inclined at an angle to the equator of the third sphere; and the poles of the third sphere are different for each of Miehet Northface Denali Takki the other planets, but those of Venus and Mercury are the same.
Callippus made the position of the spheres the same as Eudoxus did, but while he assigned the same number as Eudoxus did to Jupiter and to Saturn, he thought two more spheres should be added to the Ecuador Fodboldtrøjer sun and two to the moon, if one is to explain the observed facts; and one Island Fodboldtrøjer more to each of the other planets.
But it is necessary, if all the spheres combined are to explain the observed facts, that for each of the planets there should be other spheres (one fewer than those hitherto assigned) which counteract those already mentioned and bring back Switzerland Børn Fodboldtrøjer to the same position the outermost sphere of the star which in each case is situated Saksa Pelipaidat below the star in question; for only thus can all the forces at work produce the observed motion of the planets. Since, then, the spheres involved in the movement of the planets themselves are — eight for Saturn and Jupiter and twenty-five for the others, and of these only those involved in the movement of the lowest-situated planet need not Deportivo La Coruna Fodboldtrøjer be counteracted the spheres which counteract those of the outermost two planets will be six in number, Guadalajara Fodboldtrøjer and the spheres which counteract those of the next 2017 Northface Miehet Takki four planets will be sixteen; therefore the Herre Parajumpers Adirondack Parka number of all the spheres — both those which move the planets and those which counteract these — will be fifty-five. And if one were not to add to the moon and to the sun the movements we mentioned, the whole set of spheres will be forty-seven in number.
Let this, then, be taken as the number of the spheres, so that the unmovalinks:
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