The pyramidal shadow and kinds of derivative shadow
Simple derivative shadows classed as pyramidal, columnar and dilatable
Leonardo defines the pyramidal shadow cast by a cylindrical body, which grows narrower than the body the farther from it the derivative shadow is cut. He then classifies the simple derivative shadow into three rectilinear forms: the finite pyramidal, and two infinite ones, the columnar and the dilatable. These arise, respectively, when the shadowing body is smaller than, equal to, or larger than the light source, and the composite derivative shadows are noted to be columnar and dilatable in turn.
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The pyramidal shadow of a cylindrical body
The pyramidal shadow generated by a parallel (cylindrical) body grows narrower than the shadowing body in proportion as the simple derivative shadow is cut at a greater distance from that body. The two cylinder diagrams at right show the tapering triangular shadow.
Three forms of the simple derivative shadow
The simple derivative shadow is of two sorts: one finite in length, the pyramidal, and two infinite, the columnar and the dilatable, all of rectilinear sides. The pyramidal arises from a shadowing body smaller than the light, the columnar from one equal to it, and the dilatable from one larger; the composite derivative shadows are likewise columnar and dilatable.
