the heavens were supposed not to encompass the earth, they would have no centre. When a round sphere is supposed, however, it must have a point at its middle, which is its centre. As for something that is neither round nor a sphere, the sphere’s centre—the point at its middle—is not its centre, whether it is placed above the round body or below it. Thus, nothing prevents a non-round thing from being above and below a round body. Nor does it thereby share with the round body the property of having the encompassing point as its centre.

Rather, the centre bears the same relation to every side of the encompassing entity. Its relation to what lies above or below that entity—if something non-round is supposed to lie above or below it—is not uniform. Instead, the centre, together with the encompassing entity, lies beneath this particular non-round thing, just as it may lie above something else. Thus, relative to the encompassing entity, the centre is below it, and the encompassing entity is above the centre.

Whatever is supposed to lie above the encompassing entity is certainly above all of it, and it is impossible to say that it is not above the encompassing entity. For sound reason plainly establishes that the air is above the earth and that the sky is above the earth. This is known before it is known that the sky encompasses the earth. Indeed, encompassing may even be thought to contradict being above. No one says that knowing something to be above depends on knowing that it encompasses, or that encompassing is a condition of being above. Birds are above the earth without encompassing it; clouds are above the earth without encompassing it; and every part of the celestial sphere is above the earth without encompassing it. It is therefore clear that being above is an intelligible concept that does not require encompassing, although encompassing does not contradict it.