A heavy body lightens upon its support the more it becomes distant from the perpendicular that the fixing of the support has. This lightening has such proportion to the whole weight as the length of that distance has with the length of that support.

Let a b be the support of the weight; let b be the weight, and a the fixing of the said support; and again this a b is the perpendicular of the said fixing a. I say that the weight c lightens upon the support a c as much as this weight becomes distant from the perpendicular a b. Which distance is c d, which here is half the length of the support a c. And by this it follows that such a heavy body c is made half lighter upon its support than its natural weight.

It is proved by the fifth of the 9th, which shows that that weight will show itself heavier which is more distant from the perpendicular of the fixing of its support;

therefore because that part of the support resists less which is more remote from that fixing.

Again, when the support is in its perpendicular as a b, the weight attached at b is wholly upon the fixing of its support a. And when this support has its straightness in the situation of equality a f, then the support a f together with its fixing a feel nothing of that weight; and because from the whole to nothing there are degrees of pyramidal diminution, it is necessary that in the middle of the length of that pyramid there be half of all its base; therefore, in the middle of that diminution of the weight there will be half of such weight, which is at s.

Of bodies that bounce, always their heaviest part makes itself the guide of the incident and reflected motion.

The separation that the cord makes from the wheel is always at the extremes of the diameter of that wheel, in a right-angled disjunction.

Of the various figures of bodies which descend of themselves through the air, and of the resistance of the air against them.

The cord drawn along any line is altered by two equal and contrary powers, in whose situations one is interchangeably called power and the other resistance; and they are joined together in every part of the length of the cord.

What has been said is proved by this demonstration of the beams n m and m o; of which the cord n o resists equally the descent of each, and each by itself resists the descent of its opposite. Therefore the cord is drawn by the two equal powers, and they are all together throughout the whole cord, and all in every part of its length.

Here the half-real appendage a c e finds the potential arm d e of the balance d c and d e. Which arm is 4 times shorter than the arm d c, and consequently is 4 times more powerful than that arm d c; whence necessity loads it with 4 times more weight to resist the descent of the arm d c with its attached weight. Whence it is concluded: 4 pounds at a resist the descent of one pound placed at c; and because the cord a c d is drawn by two equal powers, that is 4 on this side and 4 on that, it sustains 8 pounds; which are 8 pounds of accidental weight, when such a cord were only tied by its ends without other counterweights. Then there is one pound of natural weight attached at c. Therefore the said cord sustains 9 pounds of weight.