Transmutation of solids: cylinders, cubes, and pyramids
Naming reduced cylinders and 'tables', defining the cube (dado), and reducing pyramids to equivalents.
Leonardo describes a 'geometry' of transmuting solid bodies of metal, which can be stretched and shortened as their students require. He classifies reductions of a cylinder as still 'cylinders' when taller than a cube and as 'tables' (tavole) when lower, and defines the cube, called a 'dado', as a body of six equal faces, twelve equal edges, eight three-sided corners and twenty-four right angles. A further note explains how to handle pyramids by substituting cylinders, cubes or tables of the same height and width, since a third of such a body equals the pyramid. A small figure shows a pyramid set within a cube.
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Naming reduced solids and defining the cube
A geometry that extends into the transmutation of metallic bodies, which can be extended and shortened as needed. Reductions of a cylinder taller than a cube keep the name of cylinder; those lower than a cube are called 'tables' (tavole). The cube, a body of six equal faces, twelve equal edges and twenty-four right angles, is the body called among us a die (dado).
Reducing pyramids to equivalent cylinders, cubes or tables
To work pyramids by increasing or decreasing them, Leonardo advises working with cylinders, cubes or tables of the same heights and widths as the pyramids. A third of such a body remains in the pyramid, and by this rule the work is done with brevity.