297 than on bd: it is also asked how much faster the mobile goes down on ba than on bd, and how much faster on bd than on be. In order then that we may be able to attain this, what we noted above {1} must first be taken into consideration: namely, that it is manifest that what is heavy is carried downward with as much force, as would be necessary for pulling it upward by force; that is, it is carried downward with as much force as that with which it resists going up.
If then we find with how much less force the heavy thing is pulled up by force on line bd than on line ba, it will then have been found with how much more force the same heavy thing goes down on line ab than on line bd; and, similarly, if we find how much more force is required in order to impel the mobile upwards on line bd than on be, it will then have been discovered with how much more force it will go down on bd than on be. But we will know how much less force is required to pull the mobile up by force on bd than on be, when we will have found out how much greater will be the heaviness of this same mobile on the plane along line bd, than on the plane along line be.Let us proceed then to a careful investigation of this heaviness. And {1} let it be undestood a balance cd, whose center is a, and at point c a weight equal to another weight which is at point d. If then we consider that the line ad, remaining fixed at point a, is moved towards b, the descent of the mobile at the initial point d will be as if on line ef; that is why the descent of the mobile on line ef will be according to the heaviness of the mobile at point d. But then again, when the mobile will be at point s, its descent at the initial point s will be as if on line gh; that is why the motion of the mobile on line gh will be according to the heaviness the mobile has at point sAnd again, when the mobile will be at point r, then its descent at the initial point r wll be as if on line tn; that is why the mobile will be moved on line tn according to the heaviness it has at point r. If,