299 a perfectly spherical shape would be, and, of the hardest material, or else fluid like water.If all these things are thus disposed, any mobile on a plane parallel to the horizon will be moved by a minimal force, indeed by a force smaller than any given force. And this, since it seems quite difficult to believe, will be demonstrated by the following demonstration.
And so let there be a circle, whose center is a, and a balance bc that can move about its center a, and which is parallel to the horizon; and let the perpendicular ad be drawn from the center a, directed towards the center of the world; and let us imagine that some weight is suspended from point d. It is then manifest that the weight at d, as it is moved in the direction of c, goes up necessarily. I say, then, that any force applied on point b can move the weight at d, and that it necessarily moves it.For consider a weight, however small, suspended from point b, and as the weight at d is to the weight at b, let line ba be to another line, to which it is assumed that line ae is equal. Now if d is suspended from point e, then it will weigh equally with the weight in b; neither one will be moved by the other, nor will the balance incline. [see my notes below]But the weight at d suspended from a is lighter than if it is suspended from e, since it is weighed not only nearer the center, but suspended from the center itself: it is necessary that the weight at d, suspended from a, is moved by the weight at b, and that the balance inclines on the side of b and that d goes up. Therefore, if by any force any weight at d not only is moved, but even is raised, what wonder is it, that the same weight d should be moved, on a non ascending plane, by the same force or even a smaller one, than the force at b?Furthermore: a mobile, having no extrinsic resistance, will go down naturally on a plane inclined no matter how little below the horizon, with no extrinsic force applied; as is evident in the case of water: and the same mobile does not go up on a plane erected no matter how little above the horizon except violently: it therefore remains that on the plane of the horizon itself it is moved neither naturally nor violently. Now if it is not moved violently, hence it will be able to be moved with the minimum of all possible forces. We can also demonstrate this differently: namely, that any mobile, subject to no extrinsic resistance, can be moved {1} on a plane which is directed neither upward nor downward by a force smaller than any proposed force whatever. To demonstrate that we presuppose this: namely, that any heavy mobile can be