Double Shadow: Sun-Shadow Cast Within Air-Shadow
Derived shadow tracks its primitive; a body lit by both sun g and diffuse air e f yields a doubled shadow
A text page from the fifth part of the Treatise on Painting, with a small semicircular diagram (the vault of air) over a base line bearing objects m and n. It states that a derived shadow grows and shrinks with its primitive shadow and copies its body's outline only when the light shares that shape. Its central chapter proves how a shadow born of the sun can fall upon a shadow born of the diffuse air, producing a doubled shadow where a region sees neither sun g nor air e f. It closes by noting that shadow bounds are less perceptible under diffuse light and widen as the light grows.
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Derived shadow follows its primitive
The derived shadow grows and diminishes according to the increase or diminution of its primitive shadow. And it is never wholly like the shadowed body that generates it unless the light girding the body's bounds with its rays is of the same shape as the body.
A double shadow from sun and air
A shadow born of the sun can be cast upon a shadow born of the air. Let object m cast a shadow from the air e f into the space d c b, and object n, by the sun g, cast the shadow a b c; the remaining region d m e, which sees neither the air e f nor the sun, is a double shadow, generated by the two objects n and m.
Sharpness of shadow bounds under diffuse versus point light
The bounds of a derived shadow are less perceptible under universal (diffuse) lights than under particular ones. And the bounds of derived shadows dilate around the shadowed body all the more as the light that generates them is larger.