The Book of Mechanics

...predominates over the other. From which it can be gathered that if anything heavy were placed in the center of the world, it is necessary that its center of gravity be established at the center of the world: since, for that heavy object to then rest, the parts surrounding it on all sides must exist and remain of equal moments. Wherefore, while it is asserted that any heavy object by natural propensity seeks its seat in the center of the world, nothing else is signified than that such a heavy object desires to make its own center of gravity fit with the center of the universe, so that it may be able to rest most optimally. From which it follows that the downward motion of any heavy object occurs along a straight line which connects the center of gravity of the heavy object itself and the center of the world. Since heavy objects are carried downward in a straight line. Whence it is manifest that heavy objects tend downward according to their center of gravity. Which we assumed in our book of Mechanics.

From all these things which have been said so far about the center of gravity, it is perspicuous that every heavy object gravitates properly at its center of gravity, just as the very name of the "center of gravity" seems to manifest that same thing. So that the whole force and gravity of the weight seem to be heaped up and collected in the center of gravity itself, and as it were to flow into it from all sides. For because of its gravity, the weight naturally desires to reach the center of the universe, but the center of gravity (from what has been said) is that which properly tends toward the center of the world. Therefore, the weight properly gravitates at the center of gravity. Furthermore, when some weight is sustained by some power at the center of gravity, then the weight remains at once, and the whole gravity of the weight itself is perceived by the senses. Which also happens if the weight is sustained at some point from which a straight line drawn through the center of gravity tends to the center of the world. For in this way, it is the same as if the weight were sustained properly at its center of gravity. Which, indeed, does not happen if the weight is sustained at another point. For the weight does not remain; rather, before its gravity can be perceived, the weight is surely turned until a straight line similarly drawn from the point of suspension to the center of gravity is carried along a straight path to the center of the universe. Which things are indeed manifest from the first proposition of our Mechanics...