If two bodies move at an equal velocity along the same straight line and in the same direction there is neither resistance nor percussion.

Let the bodies A and B move along the same straight line ABCD in the same direction at an equal velocity (Table 7.​1, Fig. 26). I claim that A delivers no blow nor percussion to B and B does not resist at all an impulse of A. A and B are supposed to touch each other (indeed, unquestionably, without contact no percussion occurs). Since the actual velocities are equal, if the body A travels a distance AC in a given time, B in escaping travels also the distance BD equal to AC. B neither impedes nor slows down the movement of the body A. Since, if the body B was removed and absent, A would not travel more distance than AC in the same time, thus the same distance is travelled by A alone as it is by A conjoined with B. Therefore, the progress of A is not more impeded by the body B than by nothing. The progress of A thus is not impeded at all. But, if the progress of A is not slowed down, neither percussion nor resistance of B can be conceived. Consequently, A does not strike B nor does the latter resist the former. Therefore, A touches the body B with the same placidity as if both were absolutely at rest in the same position in the world space. Q.E.D.

From this it appears that, if the movement of the escaping body B is quicker than the movement of the pursuing body A, there will be neither percussion nor resistance. If the slower body A never succeeds in touching the quicker body B escaping, neither percussive action nor resistance can be conceived.

And this is a second way of preventing percussion. Although A is carried by a true movement in the space of the world, with its velocity and impetus, because A lacks movement and impetus relative to B, there is thus no percussion.

If two absolutely hard and rigid bodies, in opposite movements along the same straight line, collide at a perpendicular and median incidence, the ratio of the percussion which would affect the body travelling more slowly if it was at rest and movable, to the percussion during the opposite movements is equal to the ratio of the velocity of the striking body to the sum of the two opposite velocities of the bodies.

Let two bodies A and B move in opposite directions along the same straight line so that they collide at a perpendicular and medial incidence on their respective surfaces (Table 7.​1, Fig. 27). The velocity of A is CD, the velocity of B is EF. The straight lines GC and EI are drawn perpendicular to CD and EF. The ratio GC/EI is equal to the ratio of the mass of the body A to the mass of B so that the perpendiculars represent the masses of the bodies A and B whereas the other lines CD and EF represent their velocities. The rectangles GD and IF are completed. Their ratio is the product of the ratio of the velocities and the ratio of the magnitudes of the bodies A and B. Therefore, these rectangles represent the motive forces of the bodies. The ratio of the sum of A and B to B, (A + B)/B, is equal to the ratio CD/CL. By dividing and inverting: B/A = CL/LD, the rectangle GL is completed. Similarly, (A + B)/A is equal to the ratio of the velocities FE/EM. By dividing: B/A = FM/ME. The rectangle MI is completed. The rectangle CO equal to FI is superimposed on CD. Since B/A = FM/ME = CL/LD or the ratio of the products FK/IM and, similarly, the ratio of the products CP/LO. By combining the products: FI/MI = CO/LO. The nominators FI and CO are equal. Consequently, the denominators IM and LO are also equal. Then, the ratio of the masses of the bodies R/A is equal to the ratio of the velocities CD/EF. It must be demonstrated that the ratio of the rectangles GL/LO or GL/IM is equal to the ratio of the velocities CD/EF. The ratio of the rectangles GD/IF = GD/CO is the product of the ratio of the sides CD/EF = R/A which is the ratio of the velocities, and the ratio CG/EI or the ratio of the bodies A/B. The ratio of the rectangles CN/ND is equal to the ratio of the bodies B/A, and the ratio of the rectangles ND/LO or of the rectangles CH/CO = CH/IF is equal to R/B. Consequently, the ratio of the rectangles CN/LO is the product of the ratios B/A and R/B. Therefore, B being eliminated, the ratio of the rectangles GL/LO is equal to R/A or to the ratio of the velocities CD/EF. It must be shown that the rectangle CN designates the partial percussion of A against B and that LO represents the partial repercussion exerted by B on A. If B was at rest and movable, i.e. indifferent to movement, the body A moving at a velocity CD would carry out on B a percussion designated by the rectangle CN, i.e. by this portion of the whole motive virtue CH which the body B resists. Therefore, the motive force of A would be diminished by as much. Conversely, the repercussion which would be exerted by the body B moving at a velocity EF against the body A stable and movable, or indifferent to movement, would be measured by the portion IM or LO of the whole motive virtue IF. Obviously, in a mutual collision of the bodies A and B the same opposite percussions occur. Therefore, the ratio of the partial percussion of A to the repercussion of B is equal to the ratio of the velocities CD/EF. The ratio of one of them, for example the partial percussion of A against the movable body B at rest, to their sum is equal to the ratio of the velocity CD to the sum of the two velocities. Q.E.D.