Mixing Two Shadows: Perfect and Imperfect
How overlapping shadows from two bodies and two sources combine in depth
A single large diagram shows the crossed ray-pyramids of two shadowing bodies lit by two sources, producing overlapping shadows of varying depth. Leonardo reasons that the more the darkness of two rays of imperfect shadow differs, the more the shadow resulting from their mixture differs from its original state. He concludes that two perfect (full) shadows can never combine into a shadow of darker quality, but that two imperfect shadows can commingle into a perfect one.
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Two imperfect shadows can combine into a perfect one
It is impossible for the mixture of two perfect shadows to yield a shadow of darker quality, since a full shadow cannot deepen. But it is possible for the commingling of two imperfect shadows to result in a perfect shadow, as the overlapping penumbrae of the two bodies show.
Mixed shadows differ from their original state
By as much as the darkness of two rays of imperfect shadow differs, by so much will the shadow that results from their mixture differ from its first being. Leonardo thus grades the resulting shadow by the disparity of the two rays that meet in it.
Crossed ray-pyramids of two shadowing bodies
The diagram sets two round shadowing bodies between two luminous sources, drawing dense sheaves of straight rays whose pyramids cross to enclose a central overlapping shadow. The crossing traces where the two penumbrae mingle to form the deepest zone.