i p and g and k neither side is lighted by more than one single light: that is i p is invisible to h g and k will never be lighted by g ; hence p q will be twice as light as the two visible portions that are in shadow.
[Footnote: 5—6. This passage is so obscure that it would be rash to offer an explanation. Several words seem to have been omitted.]
On the relative depth of cast shadows (200-202).
200.
A spot is most in the shade when a large number of darkened rays fall upon it. The spot which receives the rays at the widest angle and by darkened rays will be most in the dark; a will be twice as dark as b, because it originates from twice as large a base at an equal distance. A spot is most illuminated when a large number of luminous rays fall upon it. d is the beginning of the shadow d f, and tinges c but a little; d e is half of the shadow d f and gives a deeper tone where it is cast at b than at f. And the whole shaded space e gives its tone to the spot a. [Footnote: The diagram here referred to is on Pl. XLI, No. 2.]
201.
A n will be darker than c r in proportion to the number of times that a b goes into c d.
202.
The shadow cast by an object on a plane will be smaller in proportion as that object is lighted by feebler rays. Let d e be the object and d c the plane surface; the number of times that *d