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.