The Book of Mechanics

whose sides AE, CF, DB are erected to the horizon, and the upper base ACD, just as the lower EFB, is equidistant to the horizon; let there be G, the center of gravity of the plane ACD, from which G, if the whole AB be suspended, it is evident that the plane ACD remains equidistant to the horizon, and therefore is in equilibrium around the center of gravity G. Which indeed, although it needs demonstration, at the end of the first book is omitted for the present, and is to be shown below in its own place. Let it be enough for us now to have shown that these things can be reduced to practice and can (as they say) be handled by the hands. And if these things are so, such a consideration will not be vain, nor to be rejected as useless. But let us progress further still, and let us say that, since the plane ACD, insofar as it is joined to a body, must remain equidistant to the horizon; if we understand it apart from the body, as if ADC were suspended from its center of gravity G, then in whatever manner it might be found—that is, whether equidistant to the horizon or less so—we can understand that it will nevertheless remain the same, with the parts consisting everywhere of equal moments. Nor does Aristotle attribute moments only to heavy things, but also to light ones; and the same thing (as Eutocius reports in the commentaries on these books) pleased Ptolemy as well, as is contained in the book (which we however desire) which he wrote on moments. Furthermore, other philosophers also seem to have felt the same, which is indeed consonant with reason, for those things which are light fly upward. And if it be conceived in the mind that the same figure is of something light, then if it be held at G, the parts would consist everywhere of equal moments, and G would be (so to speak) the center of levity. Since, however, we consider equilibrium around the center of gravity, for that reason we conceive in the mind that planes, as they appear to us, have weight. It is not therefore alien to reason to understand and conceive of equilibrium in planes, considered as heavy things. Nor does it hinder us in the least that the definitions of the center of gravity brought forward earlier explained the centers not of planes but of bodies, such that the center of gravity is to be referred to bodies, not to planes. For this was done because the center of gravity properly regards bodies; yet it does not therefore regard planes improperly, but because it primarily regards bodies, in which it is found to exist in act; therefore, the same definitions can be adapted to planes also in this manner.