“An example of this” is that they determined that one celestial body lies below another because the lower eclipses the upper, but not vice versa. From this they inferred that the upper body lies in a sphere above the lower one. Likewise, they inferred from differing motions that the spheres are distinct, even positing several spheres within a single sphere, such as the epicycle and others. As for anything existing above these for whose existence they have no evidence, their method gives them no knowledge of either its existence or its nonexistence.

Likewise, the assertion that the motion of the “ninth” sphere is the source of events is erroneous and misguided even according to their own principles. For they say that the “eighth” sphere, together with the fixed stars it contains, has a motion peculiar to it, and that this motion has two poles distinct from those of the “ninth.” The same applies to the “seventh” and the “sixth.” If each sphere has its own distinctive motion—and the differing motions cause the various celestial configurations that arise, while those configurations cause events in the lower world—then the motion of the ninth is only one component of the cause, just like the motion of any other sphere.

The configurations that arise in the heavens—a celestial body’s conjunction with another at the same degree; its opposition to it when they are separated by “half the celestial circle,” namely 180 degrees; its trine with it when they are separated by “a third of the celestial circle,” namely 120 degrees; its square with it when they are separated by “a quarter of it,” 90 degrees; its sextile with it when they are separated by “a sixth of the celestial circle,” 60 degrees; and other such configurations—arise only through differing motions, each distinct from the others. For the distinctive motion of the “eighth” is not the same as