Thus, if two unequal bodies are impelled by equal motive forces, their velocities will be inversely proportional to the magnitudes of the impelled bodies.

Let two unequal bodies A and B be considered (Table 3.​1, Fig. 13). The motive force of A is R which moves the body forwards at a velocity D. The motive force S moves the body B at a velocity C. The motive forces R and S are equal. I claim that the ratio of the velocities C/D is equal to the ratio of the bodies A/B. It is supposed that another body E equal to B is pushed by a motive virtue V at the same velocity D. Since the bodies A and E move at the same velocity D, the ratio of their masses A/E is equal to the ratio of the motive forces R/V. Then, the two equal bodies B and E move at unequal velocities C and D. Therefore, the ratio of the velocities C/D is equal to the ratio of the motive forces S/V. But the motive forces R and S were assumed to be equal. Therefore, their ratios to the same motive force V are equal. It was shown that the ratio of the mass A to the mass E or to the mass B equal to E is equal to the ratio of the motive forces R/V. It was also shown that the ratio of the velocities C/D is equal to the ratio of the motive forces S/V. Consequently, the ratio of the body A to the body B is equal to the ratio of the velocity C of B to the velocity D of A. Q.E.D.

The inverse of this proposition can be demonstrated easily.

Impetus of the Throwing Subject Is Distributed and Transmitted…?>In the collision of two bodies, I speak of perpendicular and median incidence of one body on the other when the line of the movement of the former body not only is perpendicular to the surface of the latter body but also passes through the centres of gravity of both.

In the following propositions it is dealt with the straight movement of bodies and not with a circular movement. Whenever two bodies in straight movements collide, it may occur that the incidence of one is perpendicular to the surface of the other. But the straight line of incidence must not necessarily pass through both centres of gravity. Actually, the straight lines drawn from these centres of gravity to the point of contact can be inclined and form an angle. Consequently, in short, the straight lined incidence which occurs perpendicularly to the surface of the other body and which passes through the centre of gravity of each of the two bodies will be called perpendicular and median incidence.

Any hanging body at rest, indifferent to movement, can be moved by any motive virtue however small.

Let a body B of any size be at rest, movable and balanced, i.e. indifferent to movement, and unimpeded by the density of air (Table 3.​1, Fig. 14). A body A moving at any velocity X collides in C with the body B at a perpendicular and median incidence. I claim that the body B must be impelled and displaced from its position by the body A. A body C is supposed to be equal to B. The ratio of the velocities X/Z is equal to the ratio of the masses of the bodies C/A. The body C at the velocity Z collides with the body B at a perpendicular and median incidence. Obviously, the body C moving at the velocity Z must propel its equal, the body B, deprived of impetus and indifferent to movement. The motive force of A is equal to the motive faculty of C (since the bodies A and C are inversely proportional to their velocities) and the body B gives way and is pushed not by the mass but by the energy and the motive force of C. Consequently, the body B at rest, movable and absolutely deprived of velocity, must be displaced from its position and propelled by the equal motive force of the body A impelling at the velocity X. Therefore, etc.

Any movable body at rest does not resist at all any motive force.