The Book of Mechanics

that he is about to treat of plane equilibriums or of the centers of gravity of planes; since those things which must be in equilibrium must also have weight; if planes must be in equilibrium, it is necessary that they be endowed with some weight. Which greatly abhors the nature of planes, since weight pertains to nothing but bodies, and not even to all of them. Yet he himself, while he promises that he will explain plane equilibriums or the centers of gravity of planes, openly assumes that planes and surfaces are heavy—a thing indeed entirely imaginary and in no way corresponding to the nature of the thing itself. So that Archimedes seems to have taken up a task concerning those things which are entirely contrary to the nature of the thing. But if, however, we look more accurately at the mind of the Author, we will find that he has taken up to treat a truly excellent matter, and one most consonant with the nature of the thing. For although planes, insofar as they are planes, have no weight, it is not alien to the nature of the thing, nor to reason, that we can find the centers of gravity of planes and surfaces, from which, if they were suspended, the parts of the planes would remain consisting in equal moments on all sides. Since the center of gravity is of such a nature that if we conceive in the mind that some thing is suspended at its center of gravity, it would rest and remain in that very manner in which it is found, as we previously declared. And although in reality and in act planes cannot be found separate from bodies; in them, however, this equilibrium of theirs around the centers of gravity can easily be reduced to act. Let there be a solid AB prism,