OF SIMPLE SHADOWS.

Why, at the intersections _a_, _b_ of the two compound shadows _e f_
and _m e_, is a simple shadow pfoduced as at _e h_ and _m g_, while
no such simple shadow is produced at the other two intersections _c
d_ made by the very same compound shadows?

ANSWER.

Compound shadow are a mixture of light and shade and simple shadows
are simply darkness. Hence, of the two lights _n_ and _o_, one falls
on the compound shadow from one side, and the other on the compound
shadow from the other side, but where they intersect no light falls,
as at _a b_; therefore it is a simple shadow. Where there is a
compound shadow one light or the other falls; and here a difficulty
arises for my adversary since he says that, where the compound
shadows intersect, both the lights which produce the shadows must of
necessity fall and therefore these shadows ought to be neutralised;
inasmuch as the two lights do not fall there, we say that the shadow
is a simple one and where only one of the two lights falls, we say
the shadow is compound, and where both the lights fall the shadow is
neutralised; for where both lights fall, no shadow of any kind is
produced, but only a light background limiting the shadow. Here I
shall say that what my adversary said was true: but he only mentions
such truths as are in his favour; and if we go on to the rest he
must conclude that my proposition is true. And that is: That if both
lights fell on the point of intersection, the shadows would be
neutralised. This I confess to be true if [neither of] the two
shadows fell in the same spot; because, where a shadow and a light
fall, a compound shadow is produced, and wherever two shadows or two
equal lights fall, the shadow cannot vary in any part of it, the
shadows and the lights both being equal. And this is proved in the
eighth [proposition] on proportion where it is said that if a given
quantity has a single unit of force and resistance, a double
quantity will have double force and double resistance.

DEFINITION.

The intersection _n_ is produced by the shadows caused by the light
_b_, because this light _b_ produces the shadow _x b_, and the
shadow _s b_, but the intersection _m_ is produced by the light _a_
which causes the shadow _s a_, and the shadow _x a_.

But if you uncover both the lights _a b_, then you get the two
shadows _n m_ both at once, and besides these, two other, simple
shadows are produced at _r o_ where neither of the two lights falls
at all. The grades of depth in compound shadows are fewer in
proportion as the lights falling on, and crossing them are less
numerous.