The motion of a shadow is always more rapid than that of the body
which produces it if the light is stationary. To prove this let _a_
be the luminous body, and _b_ the body casting the shadow, and _d_
the shadow. Then I say that in the time while the solid body moves
from _b_ to _c_, the shadow _d_ will move to _e_; and this
proportion in the rapidity of the movements made in the same space
of time, is equal to that in the length of the space moved over.
Thus, given the proportion of the space moved over by the body _b_
to _c_, to that moved over by the shadow _d_ to _e_, the proportion
in the rapidity of their movements will be the same.
But if the luminous body is also in movement with a velocity equal
to that of the solid body, then the shadow and the body that casts
it will move with equal speed. And if the luminous body moves more
rapidly than the solid body, the motion of the shadow will be slower
than that of the body casting it.
But if the luminous body moves more slowly than the solid body, then
the shadow will move more rapidly than that body.