(1)
Mathematics in Naples, Naples, Italy
Deceased
Here by the way the opinion of Aristotle on the cause of the energy of percussion presented in his Mechanics can be refuted. He indeed seeks the reason why, if somebody puts a big axe on a piece of wood and adds over it a heavy wooden weight, whatever his attempts, he does not split the wood. If actually he raises the axe and strikes, he splits the wood although the weight which struck is much smaller than that which is on the wood and compresses it. He answers that everything is done with movement, and the weight itself of gravity is more in movement while it moves than when it rests incumbent. Consequently, a mobile does not move in an innate motion of gravity but actually it moves following gravity and following the action of a striking object. From this, his followers infer that a pouncing body acts not only through its innate gravity but also through the gravity which it acquires in moving, that the movement adds weight to the weight or that gravity is increased in movement. Therefore, it works more efficiently. This is certain, they say, since heavy bodies when falling also impel projectiles more in their progress, as if they were heavier.
Since this is in opposition to the theory reported above it is useful to point out the insufficiency of the peripatetic opinion.
Firstly, movement does not add weight to a weight. This appears from the fact that impetus and gravity are not quantities of the same kind. No more than a line added to a surface increases the surface, similarly impetus and movement will not increase gravity. This appears from what was demonstrated above.
Proposition CXXXIII
Impetus does not increase the weight of a heavy body.
Moreover, we will demonstrate the same point by another reasoning. The ratio of a body A to a body B is the inverse ratio of the impetus C of B to the impetus D of A (Table 23.1, Fig. 73). It is supposed that impetus and movement add to a heavy body a higher degree of gravity proportional to its movement. Thus adding impulses C and D to the weights B and A is as if new weights S and R equal to the impulses C and D were added to the weights A and B. If a heavier weight S exceeds the gravity of the bigger body A, the weight S will be the greatest and B the smallest of the four weights of a proportion. R and A are the middle terms. Thus the sum of the extreme terms S + B will be greater than the sum of the middle ones R + A. Therefore, the moment of the body B compressing with the impetus C will be greater than the moment of the body A compressing with the impetus D, which is absurd. Indeed, since the weights are inversely proportional to their velocities, everybody admits with Aristotle that their moments are equal. Thus, impetus does not add weight to a heavy body.
Proposition CXXXIV
The same point demonstrated by another argument.
Secondly, a heavy weight A is supposed to be supported by the subjacent plane, i.e. it is absolutely deprived of movement and impetus (Table 23.1, Fig. 75). A small body B is provided with an impetus. Since the impetus of B can be weakened and decreased down ad infinitum, a degree of impetus C can be found so small that, even when added to the weight B and increasing this weight, both do not overcome the energy of the immobile body A. Therefore, a percussion at a perpendicular and median incidence carried out by the hard body B with an impetus C will not overpower nor move the body A. This is untrue. It was indeed demonstrated that it raises A. Thus, movement does not add weight to the gravity of another body. Moreover, it must be noticed that the effort and compressive action of a heavy body do not push nor move it upwards or sideways but vertically downwards. On the contrary, an impetus impressed into it and the direction of its movement can be upwards, or downwards or sideways. Therefore, it happens that the effort of the impetus and that of gravity enhance each other when for instance both tend to descend in the same direction towards the centre of the earth. On the contrary, sometimes the impetus not only cannot increase the effort of gravity but rather weakens and cancels it, for example when the efforts and propulsions of the impetus and gravity act in opposite directions and collide with each other. One then impedes the impelling of the other. Then it appears impossible that the force of the impetus increases the force of the weight of the body. This of course occurs when a heavy ball is thrown vertically upwards since then the effort of gravity is opposite and is exerted downwards. The impetus of projection thus not only does not increase the degree of gravity and its compression but rather decreases it by its opposite action.
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