These two suppositions must be presented at first. The first is that the motive faculty which is internal and normal in any body does not seem to be of an inferior order, nor of weaker energy than the motive force which is impressed in some projectile by an external cause and through which the projectile then works by impelling the bodies opposing it with the same velocity as the internal motive force which propelled it. By its nature, the motive force does not seem to be anything else than the quantity of energy and violence of impetus by which not only the subject in which the motive force is present is moved but which, moreover, can be transmitted and distributed in other mobile bodies impeding its progress. Therefore, whenever the effect produced by two causes are equal, their effective causes are necessarily equally strong and of the same vigour. Consequently, if the same hanging body, indifferent to movement, is impelled at the same velocity by a blow delivered to it by some projected body, and by the fall of a heavy object or by the impulse of some animal, this intrinsic and natural motive force cannot be considered as weaker or softer than the projecting force. Otherwise the same effect of the velocity impressed into the hanging body would be produced by effective causes of unequal vigour, which seems completely absurd. On the other hand, I say nothing about the fact that the projecting virtue must be considered rather weaker and of an inferior order because it is not ever-lasting and persisting. Once weakened or destroyed, it cannot be restored by itself nor revivified. On the contrary, the motive force proceeding from a natural and intrinsic principle is never destroyed. If sometimes its action and the application of its operation are impeded, it revivifies by itself and acquires again its original energy. Therefore, in no way the projecting force must be considered of a higher order, and of greater vigour and energy than the motive force resulting from an intrinsic and natural principle and which impresses its degree of velocity into another body indifferent to movement.

Secondly, I suppose that the degree of velocity of any projected mobile, if decreased or slowed down by some external obstacle, cannot be restored and revivified by itself without the addition of a new cause which renews the impetus and which is again impressed into the body.

If indeed a body A moves at a velocity DC and its movement is slowed down by an external cause so that, for example, the velocity is halved and the body now moves at a velocity EC (Table 3.​1, Fig. 18), it is obvious that it cannot by itself, without the addition of a new impulse, move again at the initial velocity DC which is now extinct and absent, i.e. it cannot travel twice the space in the same time. Otherwise, the movement which by its nature is the effect and the result of some motive cause, would be created from nothing, which is impossible. Consequently, for the movement to be re-established in its double velocity, a new cause is required which increases the reduced velocity by a new impulse. This new impulse must come from outside. On the other hand, this is obvious in all projectiles. When a stone or a spear is thrown at a certain velocity, if its impetus is restrained or slowed down or extinguished by an external cause, we see that the spear does not resume its forces by itself and never moves in the absence of velocity. This principal property makes the difference between the impetus or natural motive force and the impetuosity of the projectiles. The natural motive force, even if impeded, slowed down and completely stopped, resumes its forces spontaneously so that heavy objects suddenly fall when their support is removed. This does not occur for projectiles. Therefore, the intrinsic and natural motive force can be considered as perpetual and immortal whereas the projecting motive force does not persist for ever and is mortal. When removed, it does not come back spontaneously to existence. After these premises it must be demonstrated that:

A body in movement, when striking a hanging body, impresses into the latter a degree of velocity, not successively and over some time, but altogether and instantaneously. But both bodies must be absolutely hard and rigid.

Let a body A moving at a velocity D collide at point C with a body B hanging, movable and at rest, and strike B at a perpendicular and median incidence towards G, impressing into B a degree of velocity EF (Table 3.​1, Fig. 19). Both bodies are very hard and rigid. Firstly, the body A is projected so that its impetus D does not originate from an internal motive virtue but has been transmitted to it by some external impeller. I claim that the body B acquires all the velocity EF together in one instant. If this is not true, such a degree of velocity is impressed successively over a time TV. A progressive diffusion of the impetus over some time cannot be understood without the impetus continuously growing from a very small and minimum degree up to the maximum impetus EF. Then, either this passage or increment of impetus occurring over some time is uniform, i.e. proportional to the elapsed time, or it is not. If it is proportional, in half the time TX, half the total velocity EH is acquired, and in a fourth of the time TZ, the fourth part of the velocity EI is acquired, and so on proportionally to the fractions of time. Finally, at the end of the time TV, all the velocity EF is completed. If actually the increment of velocity is not proportional exactly to the time, at least, unavoidably, in the portion of time TZ all the degree of velocity EF cannot be impressed in the body B. Necessarily some portion of it, whatever it is, is impressed if the whole velocity EF is supposed to be completely impressed at the end of the whole time TV. This being established, since this velocity is impressed from A into the body B over all the time TV and since an impulsive action cannot be conceived without contact, the body A, in permanent contact at C while moving forwards the body B, is forced to move together with B during all the time TV. Consequently, the body A is forced to move towards G at the same velocity as that of the movement forwards of the body B since during this time TV the body A is never separated from its consort the body B. Thus, during the time TZ, the body A cannot move at another velocity than that EI at which the body B moves. Therefore, as a result of the obstacle and impedance of the body B, the body A looses its previous velocity D and, at the end of the time TZ, has only a diminished velocity EI. On the one hand, the degree of velocity EI cannot increase by itself in the impelling body A. On the other hand, there is no additional new cause which could increase or restore the missing velocity, if some fluid environment cannot do it, as was shown. Therefore, during the following time, the impelling body A cannot possibly acquire by itself a greater degree of velocity than EI. But, by hypothesis, over a longer time TX both the body B and the impeller A acquire together a greater velocity EH and finally in the whole time TV they attain the maximum velocity EF, which is absurd. Consequently, the degree of velocity EF is not impressed into the body B from the impeller A over a period of time. It must thus be impressed instantaneously.