Primitive and derivative shadow: darkness set by proportion
How a shadow lightens with distance, and where luminous and shadowy angles meet
Three diagrams of a luminous body casting shadow from small opaque bodies accompany propositions on the primitive shadow (on the body) and the derivative shadow (cast beyond it). Leonardo states that the derivative shadow grows lighter the farther it moves from the primitive, and that the ratio of their diameters governs the ratio of their darkness, so that a derivative shadow whose diameter is three times the primitive's is three times lighter. A further figure shows that when the illuminating body exceeds the illuminated one, a shadowy intersection divides the shadow into two branches as if cast by two lights. The last block analyses how the thicker luminous angle overpowers a thinner shadowy angle at their meeting point h.
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The derivative shadow lightens with distance
The more the derivative shadow moves away from the primitive, the more it partakes of brightness. The ratio of the diameter of the derivative shadow to that of the primitive gives the ratio of their darkness: if a b enters three times into d c, the shadow d c is three times lighter than that of a b.
When the light exceeds the body: a divided shadow
If the size of the illuminating body exceeds that of the illuminated body, a shadowy intersection occurs, after which the divided shadows converge in two different concourses, as if they derived from two different lights.
The darkest part of a derivative shadow lies nearest its source
That part of the derivative shadow is darker which is nearest to its derivation. Where a thicker luminous angle joins a thinner shadowy one, the light overcomes and almost converts it to its own nature; conversely a thicker shadowy angle almost converts a thinner luminous one.
The meeting of shadowy and luminous pyramids at h
At h the angles of the shadowy pyramid m n h and the luminous pyramid o p h join. The shadowy is the smallest among b c d e f g h born from m n, while h is the largest among the luminous pyramids born at o p. The thicker luminous angle always keeps company with the smaller shadowy angle.