The Book of Mechanics

then the center D would coincide with the center of the world, and the figure C would be at rest around the center of the universe, just as it behaves around the center D. For the parts of the figure can have such a position that they can be in equilibrium among themselves, as is evident from the figures below. And it is even clearer if one understands a figure like E, bounded by both an exterior and an interior circle, the center of gravity of which will be at F outside the figure. This, indeed, will coincide with the center of the circles, around which (with the center F existing at the center of the world) the parts will be in equilibrium on all sides, since they all are equally distant from the center of gravity. Furthermore, in this figure E, perhaps it will not be inappropriate to assert that the center of gravity (although it is outside the figure) coincides with the center of figure and with the center of magnitude of that same figure. But indeed, figures AC will by no means have a center of figure and magnitude. And although it has been said that the center of gravity of regular bodies is their middle, it is not therefore to be said that it is the same as the center of magnitude and figure, except improperly; for "middle" is attributed to these improperly, just as is "center of figure," since the lines proceeding from it are not the semidiameters of those bodies (insofar as they are regular). Wherefore, the center of gravity can be found without the other centers, but not conversely. Again, the center of figure is more common than the center of magnitude; because, besides the circle and the sphere, which have both a center of figure and of magnitude, some figures have their center of figure within them and outside them; within them, as an ellipse, whose center is held inside; a semicircle also and a half-sphere have their center on the boundary. Outside the figure, however, such as the center of a hyperbola, which exists outside the figure, namely where the diameters concur. All these are indeed centers of figure; but they are by no means centers of magnitude. But perhaps someone will object at this point