Among bodies of various materials and of equal shape, the one that weighs more descends more quickly. Proposition. That spherical and heavy body will be of slower motion whose contact made by it with the plane where it touches is nearer to the perpendicular of its centre.

e – 20 – o b a – 5, 5, 10 – n m – 10 braccia – 20 braccia – f d.

s r – o; q. Proof of this proposition. You will see the proof of the above-said proposition in this way. Let us say that the plane where the above-said ball touches is the line d e, and that the contact of that ball with the plane is at n, and that the perpendicular of the line falling from the centre to the surface is at m. It is clear that the farther it is from m to n, the more upright the line d e will be; and the nearer m is to n, the flatter the line d e will be, and the more equal will be the weight from n onward to that from m back. I say that, the ball being found to touch the line d e at the point n, and the ball weighing 20, and the part from n toward the rise of the plane being 5, it is clear that 5 from n toward the descent would be equal with that toward the rise, that is, b would balance o, which would be 5 per part, making 10. Therefore half of this ball, being separated from the other, would be without motion, that is b o, and the other half therefore would be with motion. Whence one may conclude that this ball makes weight and motion of 10 pounds, falling along the line d e; and falling along the line e f it would make flight and weight of 20. Among bodies of equal shape and unequal weight, the one that weighs more falls more quickly. Therefore, the ball of 20 pounds falling along the line d e will weigh 10 pounds, and falling along the line e f it will weigh 20, which is double, and it will descend twice as fast. Whence, the line d e being 20 braccia and the line e f 10, the said ball will reach the line d f 4 times more quickly by the line e f than by d e.