If, of two bodies present on the same plane, one is immobile in one position and the other arrives to the former in an uniform movement, then either the plane with its associate bodies is immobile or it is moving. The travelling body always remaining parallel to itself arrives to the stable body and strikes it with the same impetus.

Two bodies A and B adhere to the plane CD. B always remains immobile at the same place C of this plane (Table 7.​1, Fig. 40). A is carried from D towards C in an uniform movement. I claim that either the plane CD is immobile or it is moving together with the adhering bodies A and B, transversely towards E. The plane CD always moves parallel to itself. The body B is struck with the same force and energy by the other body A. The transverse movement from C towards E, since it is common to the plane CD and to the adhering bodies A and B, does not modify the particular movement carried out in the plane CD, i.e. A does not move more quickly or more slowly towards B when the bodies are carried by the subjacent plane as if it were by a boat than if the plane CD was maintained immobile. Whether in movement or immobile, the sign C of the plane is the arriving point of the particular movement of the body and the sign D is its starting point. The distance CD, along which the movement is carried out as if it were in a boat, is also always the same straight line CD and does not change. The order of the bodies or their arrangement in the common transverse movement are not changed nor from what they were in the plane which was maintained immobile. But the particular movement through DC carries out on B a percussion with a well-determined force. Consequently, whether the plane is in a common transverse movement or whether it is immobile, the percussion of B by A is carried out by the particular movement and impetus DC, thus with the same energy.

After this premise, if two bodies move uniformly away from the same straight line perpendicular to the underlying plane, in the same direction, and one of them moves on the underlying plane on which its surface always is, and the other body arrives in an oblique movement and collides with the former, the percussive impetus of the mobile travelling obliquely occurs in the same direction, the impetus being determined by the straight line in which the said bodies started their movement.

The straight line CD is perpendicular to the underlying plane CE (Table 7.​1, Fig. 40). At C and D there are two bodies B and A which move uniformly in the same direction. One of the surfaces of B is in the underlying plane CE from which it cannot be separated. A follows an oblique route DF until the two bodies collide at E. I claim that, in this collision, the body A carries out a percussion on B with an impetus determined by the route of the uniform movement DC and as strong as if it occurred with the straight line CD immobile. The movements CE and DE are supposed to be uniform. Leaving from the points C and D at the same instant, they arrive t their mutual collision at E, also at the same instant. Thus, at any intermediate instant before the collision, for example when the bodies are at F and G, the ratios of the distances are

DG/CF = DE/CE. Therefore, at any intermediate instant the straight line FG is parallel to the straight line CD. Consequently, the two bodies A and B are always on the same line CD moving evenly through CE and always parallel to this. The line carries with itself the two bodies A and B. Consequently, the percussive impetus with which A falls on B at the point E (according to the preceding proposition) is exactly the same as the one which occurs in the plane CD immobile. But when the plane CD is immobile the percussive impetus is determined by the particular movement and impetus DC. Consequently, the force of percussion of the body A falling obliquely at E on the body B, itself moving, is measured precisely by the impetus of a fall from the height DC.