The bounce is the resurgence of a finished motion.

Here it is asked why it is necessary that the angle of incidence be equal to the angle of rebound.

Since, as I have said in the cases of the motions of heavy bodies, the impetus is of greater power than the percussion, we shall place the simple impetus on the line s c and the simple percussion on the line n p, and we shall prove how it is more powerful, by means of the impetus, to move the moving body from s to c than, by the percussion, to make an equal motion from p to n. Now the bounce grows the more, or diminishes, the nearer to or farther from the point s the moving body is set in motion. Therefore the moving body that sets out at an equal distance from s and from n will partake equally of the power of the impetus and of the percussion, so that of necessity it will not rebound entirely to n nor to c. But because at the beginning of the motion it partook of n as much as of s, it will rebound between n and c, whence the angles a b will be equal to one another, and the upper angles will be equal among themselves and to the lower ones aforesaid: which concludes what it was promised to prove.

The angle made by the rebounding motion of heavy bodies is equal to the angle made by the incident motion.

What is proposed is proved, because the moving body driven by the power of the impetus moves more and with greater power than the moving body driven by the power of the percussion. And to put the case precisely, we shall say that the line a b is the simple power of the impetus, and that the perpendicular line i m is the simple power of the percussion. Now, because the percussion extends only in the generation of bounces, or rebounding motions, and the impetus extends in incident motions, if the motion of the moving body i is followed from i to m, there will arise the rebounding motion m K; which, since that incident motion has no share in the line of the impetus a b, springs up again along the same perpendicular line down which it descended, between two right angles which are always equal. But if the said moving body is moved along the line e m, which is situated midway between the power of the impetus and of the percussion, its motion partakes as much of the one as of the other: and as regards the share of the percussion, that moving body rises up as far as the place f; and as regards the share of the impetus, that moving body moves away from the line of the percussion through the whole space r f. Hence it is concluded that of necessity the moving body rebounds to the place f, where it is found to be as far from the line of the impetus a b as from the line of the percussion i m, and therefore the angle is equal.

Percussion is only the impediment of motion. Impetus is properly the motion itself.

Why the incident and rebounding motions are born between equal angles.

The incident line is that along which the motion of the moving body is generated from the beginning of its motion to the place of its percussion.

Rebounding motion.

Motion is born from 2 different causes, of which the first is called impetus, the 2nd is called percussion. The motion born of the impetus is that which leads the moving body to the place of the percussion. The motion born of the percussion is that which is generated from the struck place between 2 right angles. Now we shall say, in the figure above, that when a moving body moves from a to b, that moving body is moved as far as b by the simple power of the impetus alone; and if that moving body is moved from c to d, that moving body will rebound by rebounding motion from d to n: which motion from d to n is born of the simple power of the percussion.

Now, having defined the 2 natures of the motions, we shall come, by means of such definitions, to prove why the angle of the rebounding motion is necessitated to be equal to the angle of the incident motion.

Let a moving body be moved equally distant from the line of the simple impetus and from the line of the simple percussion, whose beginning of motion is at the point m; and let the said moving body finish its incident motion at the point d. I say that, since that motion is made between 2 equal angles, namely between s and o, its rebounding motion partakes as much of the power of the percussion as it does of the power of the impetus; and therefore, since that rebounding motion is not born of the simple percussion alone, that moving body cannot rebound to the place o; and again, since that motion is not born of the simple impetus, that moving body cannot rebound to b, but rebounds midway between the one and the other power at an equal distance, because it partakes equally of the one and the other. Hence necessity leads that moving body to a place such that it is equally remote from the one and the other power.

Among the motions of heavy bodies, that is called incident motion which is made by the moving body between its mover and the place of its percussion.