DEFINITION OF THE CENTER OF GRAVITY OF PLANES.

The center of gravity of any given plane is a certain point placed within it, from which, if the plane is conceived by the mind to be suspended, it remains at rest while it is carried, and it preserves the position it had in the beginning, nor is it turned about in that motion.

ANOTHER DEFINITION OF THE SAME.

The center of gravity of any given plane is that point placed within it, around which the parts of equal moments consist on every side. For if a straight line be drawn through such a center, cutting the figure in any way whatever, it will always divide it into parts of equal weight.

Thus, just as the center of gravity is considered in planes, so also it will not be absurd to consider planes endowed with gravity. For if it were impossible to consider planes endowed with gravity, the center of gravity could in no way be conceived within them; and it is clear that the center of gravity can be admitted and designated within them, and therefore planes marked with gravity also. And if the mathematician considers bodies while setting aside their gravity and levity for a time; and the astronomer, considering celestial bodies which are neither heavy nor light, does not for that reason consider them to be neither heavy nor light by their own nature—for even if they were heavy or light, he would nonetheless consider them as being neither heavy nor light—if the mathematician can understand bodies of this kind in this manner, what prevents one from conceiving the same things again, as if they were such, neither heavy nor light; or as being heavy or light? Just as this will become clearer by this example:

[Diagram: A geometric diagram representing a balance. A horizontal beam is labeled with points A, B, and C. Point B serves as the central fulcrum or suspension point. From point A on the left, a triangle labeled D is suspended. From point C on the right, a square labeled E is suspended.]

Just as if we understand planes DE, which are equal, to be suspended from AC; and AC to be suspended precisely in the middle at B; why can we not understand in our mind that the space D is equal in weight to the space E, since they are equal? For if one of the planes, say D, were greater than E, then