III. Six Books on Light and Shade: 174.
174.
THE FARTHER THE DERIVED SHADOW IS PROLONGED THE LIGHTER IT BECOMES.
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.
78 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. 79
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.