The science of shadows: simple, compound, and their crossings
Definitions of simple and compound shadow, and how intersecting shadows behave under one or two lights.
Both leaves are given over to Leonardo's science of shadows, worked in mirror-script beside many ray diagrams in which paired light-sources cast crossing shadows. He defines a simple shadow as one that sees no light and a compound shadow as one lit by one or more sources, and argues that where simple derivative shadows intersect they redouble in quantity but never in darkness, since the deepest darkness cannot be made deeper. Where a second light falls between the eye and the bodies, the crossing shadows become compound and evenly dark. A worked case labels the intersections n and m from lights a and b, noting that a compound shadow darkens in proportion as fewer lights see it.
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Simple shadow and compound shadow, defined
A simple shadow, Leonardo writes, is one that sees no luminous source; a compound shadow is one lit by one or more sources. By the first two propositions the intersections i K redouble in quantity but not in darkness, whereas in the third case the intersections g h redouble in both.
Two lights, two shadows, and the darkness at their crossing
The intersection n is made by shadows t b and s b cast by the light b, while m is made by shadows s a and t a cast by the light a. Uncover both lights and the shadows n and m form together, plus two simple shadows r c that see neither source; a compound shadow gains darkness in proportion as fewer lights see it.
Ray diagrams of intersecting shadows from paired lights
The right-hand leaf is dominated by geometric ray tracings in which lines from two light-sources pass a body and cross, their intersection points marked with letters. These projections make visible the propositions on how derivative shadows multiply and where their darkness gathers.