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. 186. Why the intersections at _n_ being composed of two compound derived shadows, forms a compound shadow and not a simple one, as happens with other intersections of compound shadows. This occurs, according to the 2nd [diagram] of this [prop.] which says:--The intersection of derived shadows when produced by the intersection of columnar shadows caused by a single light does not produce a simple shadow. And this is the corollary of the 1st [prop.] which says:--The intersection of simple derived shadows never results in a deeper shadow, because the deepest shadows all added together cannot be darker than one by itself. Since, if many deepest shadows increased in depth by their duplication, they could not be called the _deepest_ shadows, but only part-shadows. But if such intersections are illuminated by a second light placed between the eye and the intersecting bodies, then those shadows would become compound shadows and be uniformly dark just as much at the intersection as throughout the rest. In the 1st and 2nd above, the intersections _i k_ will not be doubled in depth as it is doubled in quantity. But in this 3rd, at the intersections _g n_ they will be double in depth and in quantity. 187. HOW AND WHEN THE SURROUNDINGS IN SHADOW MINGLE THEIR DERIVED SHADOW WITH THE LIGHT DERIVED FROM THE LUMINOUS BODY.