187.
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 part of the base of the t. And c is the terminal point of the derived shadow and the chief beginning of the highest light.
[Footnote: The diagram on Pl. IV, No. 5 belongs to this passage; but it must be noted that the text explains only the figure on the right-hand side.]
FOURTH BOOK ON LIGHT AND SHADE.
On the shape of the cast shadows (188-191).
188.
The form of the shadow cast by any body of uniform density can never be the same as that of the body producing it. [Footnote: Comp. the drawing on PI. XXVIII, No. 5.]
189.
No cast shadow can produce the true image of the body which casts it on a vertical plane unless the centre of the light is equally distant from all the edges of that body.
190.
If a window a b admits the sunlight into a room, the sunlight will magnify the size of the window and diminish the shadow of a man in such a way as that when the man makes that dim shadow of himself, approach to that which defines the real size of the window, he will see the shadows where they come into contact, dim and confused from the strength of the light, shutting off and not allowing the solar rays to pass; the effect of the shadow of the man cast by this contact will be exactly that figured above.