The Science of Shadow: Foreshortening and Derivative Shadows
A light shows brightest against darkness; a derivative shadow doubles at each intersection
This folio continues Notebook C's investigation of light and shadow. An upper figure of a light casting shadows onto three bodies is used to argue that foreshortening changes only the apparent size of a shadow, not its intrinsic brightness or darkness. A lower figure with a single obstacle between luminous rays develops a graduated scale in which the derivative shadow grows twice, three times, and four times darker as successive intersections add more shadow to it.
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A light appears most splendid against the darkest surround
That luminous body will appear most splendid which is surrounded by the darkest shadows. The contrast of the enclosing darkness heightens the apparent brightness of the light.
Foreshortening shrinks a shadow's size but not its intensity
Though foreshortening makes the width and length of a shadow and its light narrower and shorter, it neither diminishes nor increases their brightness and darkness. The shadow's function is still to shade and the light's to illuminate the opposite body, according to how each appears to it.
The derivative shadow doubles in darkness at each intersection
Beyond the intersection g-z is seen only from the shadow a-m; y-z takes shadow m-n by intersection and a-m directly, so has twice the shadow of g-z; x-f, seeing o-b by intersection and o-n-m-a directly, is 4 times darker than z-g. Here a-b is the primitive shadow, b-c the primitive light, d the intersection, f-g the derivative shadow, f-e the derivative light.