You will find that the proportion of the diameter of the derived
shadow to that of the primary shadow will be the same as that
between the darkness of the primary shadow and that of the derived
shadow.
[Footnote 6: Compare No. 177.] Let _a b_ be the diameter of the
primary shadow and _c d_ that of the derived shadow, I say that _a
b_ going, as you see, three times into _d c_, the shadow _d c_ will
be three times as light as the shadow _a b_. [Footnote 8: Compare
No. 177.]
If the size of the illuminating body is larger than that of the
illuminated body an intersection of shadow will occur, beyond which
the shadows will run off in two opposite directions as if they were
caused by two separate lights.
On the relative intensity of derived shadows (175-179).
175.