(1)
Mathematics in Naples, Naples, Italy
Deceased
If the movement was the matter, it is clear of course that a huge material mass could be moved slowly by any small corpuscle impelling quickly, as was said. If the impulse which generates vibration was the matter, the impelled body could also move at the same velocity as the impeller. But to assert that a slowly impelling body can move a body more quickly seems absolutely impossible since no cause can produce an effect greater than itself. Therefore, a slow movement of the impeller does not seem to be able to provoke a very quick movement in the struck body. Nevertheless, it will be shown that this is possible according to the principles presented above. Since a more impetuous and quicker force can produce a weaker and slower movement, it results that a weaker and slower impeller can generate a quicker impetus. This actually seems paradoxical.
But, firstly, it must be supposed as established and known that any motive force, however small and slow, can move any immobile and movable body, as was demonstrated.
Secondly, I suppose that if two bodies move simultaneously while being always joined together as if they were carried in a boat, the escaping body behaves in relation to the pursuing body as if the former was absolutely immobile since they are always touching each other as occurs when the former body is immobile. The former immobility can be called relative whereas the latter is absolute.
Proposition CIX
A small motive force of gravity can produce an effect greater than itself, i.e. an impetus by which a heavy body can be propelled in the course of its fall.
Firstly, the intrinsic and natural motive force by which heavy bodies fall should be considered. Although these bodies are moved by a very small motive force impelling continuously, however, since both are carried together like in a boat, the moved body itself must be considered as being immobile in relation to the impelling virtue transported with the body itself. Since, in movable immobility, any small impelling force can displace any huge material mass, this small motive force of gravity can move the heavy body in which it is present in a relative and movable immobility. The motive force of gravity, because it is always active, continuously repeats its blows and thus continuously creates new impulses. These, since they are indelible result in a very quick impetus by which the heavy body is finally carried and agitated. Consequently, a small and little motive force of gravity can produce an effect greater than itself, i.e. a greater impetus by which the heavy body can be propelled in the course of its fall.
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