John Buridan (ca. 1300 – ca. 1358) An Intermediate Position: Epicycles Denied, Eccentrics Affirmed

Translated by Edward Grant

in A Source Book in Medieval Science, pp. 524 – 529

From Buridan’s Questions on the Metaphysics of Aristotle


Book XII

Question 10

            In the tenth question, we inquire whether epicycles are to be assumed in celestial bodies.

            First it is argued that they are not to be assumed, by the authority of the Commentator [Averroes], who expressly tries to disprove them. Next by the authority of Aristotle, who, in enumeration the celestial motions and spheres in this twelfth book, did not enumerate epicycles. Indeed even in the second book of On the Heavens and World, in saving the irregularities (difformitates) of the planetary motions that are apparent to us, he says that these irregularities arise because several motions are brought together in the same mobile. Thus he does not assume that they arise by eccentrics or epicycles.

            Likewise, the Commentator argues that every celestial motion ought to be a simple motion and every simple motion is (1) away from the center of the world, or (2) toward the center of the world, or (3) around the center of the world, as is taught in the first book of [Aristotle’s] On the Heavens. Therefore, every celestial motion must be one of these [three possibilities]. But if the motion of an epicycle were assumed, it would be none of these. For it would not be away from the center, because that motion would be the motion of light bodies, namely an upward motion; nor would they move toward the center, because that motion is the motion of heavy bodies. Nor would it move around the center of the world, because this epicycle is not around the earth [that is, does not have the earth as its center]. Indeed it is above [the earth] in an orb and in this orb it has both its own center and circumference. Therefore, such an epicycle would not be around anything, since it does not have a center – except an indivisible [center or point] around which it is moved. Such an indivisible [entity] is not a natural center. Indeed it is nothing. Hence this motion is not around anything.

            Nevertheless, Ptolemy and all modern astronomers (astrologi) assume the opposite. For otherwise the appearances of the planets could not be saved, especially their approaches (approximationes) and recedings (elongationes) from the earth which we obviously and notably experience. Thus it is that sometimes the moon is so high that it cannot be totally eclipsed, but the cone of the earth’s shadow falls onto the middle of it, so that while it is seen to have been eclipsed in the middle, the circumference remains in light. And sometimes the moon is so near to the earth that it falls deeply into the earth’s shadow and remains totally eclipsed.

             It must be understood that in the world the natural center is this earth. Therefore, an indivisible center is not assumed except in the imagination. But nevertheless a point can be imagined in the center of the earth as if it were the center of the world, and then all spheres having their centers in the center of the earth are called concentric. But in all the spheres of the planets, the moderns assume a sphere which they call eccentric and which is wholly around the earth; it does not have its center in the center of the world, but outside it. And for this reason, it is called eccentric. Furthermore, they assume little spheres (spherulas), which they call epicycles, that are fixed in the width of the eccentric. The planet is fastened on these epicycles. But then it is necessary that the whole sphere of the planet be concentric, for otherwise there would necessarily be a vacuum between the total spheres of two planets. Indeed it is necessary to imagine two spheres of very nonuniform magnitude, [one] above the eccentric, the other below the eccentric, and each of them is very wide on one side and on the other side of virtually no magnitude. Then it is necessary to imagine that this whole sphere composed of all the things just mentioned is moved simultaneously with a daily motion from east to west, carrying the eccentric with it; but the eccentric is also moved on the poles of the zodiac between the two parts [or sides of the whole sphere] in a motion contrary to the daily motion, namely from west to east. Then, thirdly, the epicycle, carrying the planet, is moved on its [own] proper center in this eccentric.