Derivative shadow springs from the body, not the angle; its three kinds
The two joined shadowy pyramids, and how the cut on the wall reveals the size of the light
Continuing an argument on the science of shadows, Leonardo rejects the claim that a derivative shadow ends at the angle where its sides meet, showing instead that its birth produces the figure of two shadowy pyramids joined at their angles. He argues that shadow is an accident created by the interposed opaque body, not by an angle, so it is generated only by the shadow-casting body. A new chapter (591) states that derivative shadows are of three kinds, according to whether their cut on the wall is greater, smaller, or equal to their base. Two small pen diagrams of tapering shadow-cones accompany the text.
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The figure of two shadowy pyramids joined at their angles
Leonardo denies that the shadow ends at the angle where its sides meet: as the derivative shadow arises, there manifestly appears the figure of two shadowy pyramids joined at their angles. This is contrary to the rule that a thing is fully terminated when no part exceeds its boundaries.
Shadow is caused by the opaque body, not by an angle
Against the adversary who says the second pyramid is caused by the angle, Leonardo invokes the definition that shadow is an accident created by opaque bodies interposed between the site of the shadow and the luminous body. Hence shadow is generated only by the shadow-casting body, not by the angle of the derivative shadow.
Three kinds of derivative shadow (591)
Derivative shadows are of three kinds: the cut on the wall where the shadow strikes may be greater, smaller, or equal to its base. A greater cut signals that the illuminating light is smaller than the body; a smaller cut, that the light is greater; an equal cut, that light and body are equal.