limit in the past and the future—as some theologians maintain—so it also refutes the view of his fellow philosophers, who affirm the existence of the infinite, without beginning or end, in two distinct beginningless entities. Thus, they maintain that the motions of each celestial sphere are infinite and have neither beginning nor end, even though one sphere’s motions are more numerous and greater in magnitude than another’s.

They say, for example, that the moon completes one revolution each month, the sun one each year, and the encompassing sphere one each day. The encompassing sphere is therefore greater in size and faster in motion than the spheres of the sun, the moon, and the others. Since it encompasses them all, it is greater in size. Each day it performs the eastward motion by which it moves all the celestial spheres, and no other sphere completes a revolution every day. Its motion is therefore greater in magnitude and its revolutions more numerous than those of all the other spheres—the spheres of the sun, the moon, and the others—for days are more numerous than months, and months more numerous than years.

The motion of the body that revolves each day is itself greater in magnitude than that of a body that revolves each month or year. Yet, according to them, each of these motions has neither beginning nor end. It follows that something infinite, with neither beginning nor end—such as the motion of the sphere of the moon or the sun—can be increased many times over. Indeed, something many times its magnitude actually exists: the motion of the encompassing sphere. Thus, that which is infinite in