(1)
Mathematics in Naples, Naples, Italy
Deceased
The logic of the theory requests that we enquire on the nature of that force which is diffused by the throwing subject and transmitted to the projectile, and on what effect of velocity it produces. The motive virtue of course seems to be of the kind of those which can be increased not only in intensity but also in extension. The motive force can expand and contract according to the size of the subject in which it is present. Moreover, it seems to be able to increase and decrease in intensity in one and the same subject.
I at first wonder every time I notice that a whole stone is moved at a well-determined velocity. I perceive clearly that its different particles are displaced at an equal velocity. Since the whole stone is impelled by some well-determined motive virtue, it appears necessary that any particle of the stone be impelled by a particle of the motive virtue. Therefore, the motive force is considered as subdivided into as many equal particles as there are particles in the displaced body. Each of them moves forwards a corresponding particle of the body at the same velocity by a distinct effort which is its energy. As a result, the displacement of the whole body is carried out at this same velocity. I cannot believe that some particles of the stone only are provided with small portions of motive force destined to move them forwards whereas other particles of the stone are not propelled by any portions of motive virtue and are deprived of them, since the effect of velocity which they exert cannot originate from nothing but necessarily results from its effective cause which is this motive force. Consequently, if the stone is divided into two equal parts while moving, the whole motive virtue will also be divided into two equal parts. Each of them would impel one half of the stone as quickly as previously the whole velocity moved all the stone forwards.
Consequently, we can accept this assertion without any hesitation.
Axiom I
If two bodies have an equal mass and an equal consistency and if they are impelled by equal motive faculties, they necessarily move at an equal velocity.
Axiom II
Conversely, two bodies equal in mass and in consistency, and carried at an equal velocity, are necessarily impelled by equal motive faculties.
The truth of both assertions is obvious. If the effective causes are absolutely equal and the subjects in which they act are also equal to each other, it appears impossible for the effects which they produce not to be also equal to each other. Conversely, equal effects in subjects absolutely equal and similar can only result from effective causes equal to each other. Equal motive faculties are the effective causes of the movements and velocities of two equal and similar bodies. Therefore, their effects, i.e. the velocities transmitted or produced in these bodies will be absolutely equal to each other, and conversely.