Primitive and Derivative Shadow; Which Is Darker
From the Treatise on Painting: cast shadow as physics, and how a bright or dark ground changes it
This page from the Fifth Part of the Treatise on Painting defines primitive shadow (that joined to the surface of a shadowy body) and derivative shadow (that which travels through the air and, meeting resistance, prints the shape of its base). A series of short propositions state that the primitive shadow always forms the base of the derivative, that the boundaries of derivative shadow are straight lines, and that derivative shadow grows fainter the farther it lies from the primitive. A further rule observes that a shadow looks darker surrounded by bright whiteness and fainter against a dark field. The chapter [554] then argues, with a small pen diagram lettered a and b c d e, that the primitive shadow is always the darker of the two unless corrupted by reflected light.
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Primitive versus derivative shadow defined
Primitive shadow is that joined to the surface of the shadowy body; derivative shadow departs from the body and travels through the air, halting where it strikes and taking the shape of its own base. The primitive shadow always serves as the base of the derivative, and the boundaries of derivative shadows are straight lines.
A shadow darkens against a bright ground
That shadow will appear darker which is surrounded by more brilliant whiteness; conversely it is less evident where it is produced against a darker field. The darkness of the derivative shadow also diminishes the more remote it becomes from the primitive.
Which is darker, primitive or derivative shadow
The primitive shadow is always darker than the derivative, provided it is not corrupted by a reflected light that becomes the ground of the derivative's impact. With b c d e as the shadowy body and a as the light, the primitive shadow b e c stays darker than the derivative b e c h i unless the reflected illumination f h and i g falls upon it.