Make the experiment of it, and then the rule.

a, b, c, d, e

By this reasoning, if the angle a is double the angle e, the angle e will shoot double what a does. And this would be false, because if the angle a shot one span, it would shoot 2 spans.

I claim that this power is pyramidal, because if I leave the crossbow unloaded in its natural bend and give 10 pounds of weight to its string, it will descend one ounce of a braccio, that is to say 1/12. And if I add another 10 to it, it will not then make another ounce of descent. And if, little by little, I keep adding ten by ten, the degrees of the descent will never be of equal diminution, but will be almost of the diminution of perspective.

The proportion of the motions made by the bolts will be similar to that of the angles which the string that shoots them makes, when it is drawn from its bow at different distances. Such will be the proportion of the angles made by the crossbow's string as will be that of the various weights or forces that cause them. And likewise, the proportion of the weights of the bolts should be similar to that of the angles of the string that drives them, or of the weights that are the cause of such angles.

If you load a crossbow with such a weight that its power exactly ends together with the resistance of the crossbow's string, when that string finds itself precisely upon the nut of the said crossbow, and that this weight be 400 pounds, and the bolt 3 ounces, and the motion made by that bolt be 400 braccia, I say: if you double the weight and the resistance of the string and the weight of the bolt, then in the same primary motion that bolt will make exactly a double journey, being of equal length to the first, or double.

When the powers that move and the resistances of the moved strings end exactly upon the nut of the crossbow, the derivative motion will be such as was the power of the weight.

Among primary motions of equal lengths, that one will bring forth the greater derivative motion which will be made with more brevity of time.

Primary motion is that which the string makes, during the time it touches and drives the bolt. Derivative motion is that which follows after the primitive, that is, which the bolt makes when it is released by the string that has driven it. That primary motion will be made in briefer time which is caused by greater power of weight or of force.