A heavy body is lightened at its support as much as it becomes more 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 to 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 also a b is the perpendicular of the said fixing a. I say that the weight c is lightened at the support a c as much as that weight becomes more 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 at 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.

Also, when the support is in its perpendicular like a b, the weight attached at b is entirely on the fixing of its support a. And when that support has its straightness in the site of equality a f, then the support a f together with its fixing a feel nothing of that weight; and because from all to nothing there are degrees of pyramidal diminution, it is necessary that in the middle of the length of that pyramid be half of all its base; therefore in the middle of that diminution of the weight will be half of that weight, which is at s.

Of bodies that bounce, their heavier part always 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 rectangular disjunction.

Of the various shapes of the bodies that of themselves descend through the air, and of the resistance of the air against them.

The cord pulled along any line is altered by two equal and contrary powers, in whose sites reciprocally one is called power and the other resistance; and they are united together in every part of the length of the cord.

What is 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 pulled by the two equal powers, and they are all together throughout the whole cord, and all in every part of its length.

Here the semi-real appendix 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 pulled 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 at 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.