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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.
1
87.
HOW AND WHEN THE SURROUNDINGS IN SHADOW MINGLE THEIR DERIVED
SHADOW
WITH THE LIGHT DERIVED FROM THE LUMINOUS BODY.
The derived shadow of the dark walls on each side of the bright
light of the window are what mingle their various degrees of shade
with the light derived from the window; and these various depths of
shade modify every portion of the light, except where it is
strongest, at c. To prove this let d a be the primary shadow
which is turned towards the point e, and darkens it by its derived
shadow; as may be seen by the triangle a e d, in which the
angle e faces the darkened base d a e; the point v faces the
dark shadow a s which is part of a d, and as the whole is
greater than a part, e which faces the whole base [of the
triangle], will be in deeper shadow than v which only faces part
of it. In consequence of the conclusion [shown] in the above
diagram, t will be less darkened than v, because the base of the
t is part of the base of the v; and in the same way it follows
that p is less in shadow than t, because the base of the p is
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