Rebound of a Moving Body After Percussion
Impetus, natural motion, and angles of rebound (f. 18r)
Leonardo studies how a moving body bounces after striking an object, arguing that a weaker percussion sends it farther and a stronger one nearer, and separating the part of the motion owed to impetus from the part that is natural. He works out that the rebound at s repeats the angle of incidence, so that angle d s c enters angle p s c thirteen times just as angle a s b enters angle b s p. A large fan of radiating lines at the top of the leaf lays out the trajectories and angles.
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Rebound distance depends on the force of percussion
Among bodies of equal shape, weight, impetus and distance striking equally resistant objects, the one struck by the lesser power rebounds farther, while the one struck by the greater power rebounds nearer. When a stronger percussion yields a smaller bounce, it is because the impetus outweighs the percussion in moving heavy bodies.
Natural motion versus motion given by the mover (p s and a s)
The motion p s is made without any power from its mover, since natural motion alone suffices for it, whereas the motion a s is made entirely by the power of the mover. The bounce that departs from b and, striking the object s, rebounds to d partakes of impetus by as many degrees as b is remote from a.
The angle of rebound divided thirteen times
Point b is remote from a by 1 degree and from p by 13 degrees; the opposite angle of the rebound d s c enters 13 times into the angle p s c, just as the angle a s b entered 13 times into the angle b s p.
