The cube and its transformation into a cylinder
Resolving a cube into twelve equal cylinders and building it back again
The converse of the preceding operation: a cube is resolved into twelve equal cylinders by dividing one of its sides into twelve, then the cylinders are squared and reassembled into the required cube. Leonardo notes that the rule works cleanly for the five regular solids because they have equal bases, but for bodies with unequal sides one must first make two or three kinds of cylinders. Two diagrams sit at the upper right: a segmented rod-like body and a cube ruled into a grid.
On this page
Resolving a cube into twelve equal cylinders
From a cube one makes a body of twelve equal cylinders by dividing one side of the cube into twelve parts. The face of a cylinder is then squared, and twelve like cylinders set in a straight line are recombined into the required cube.
The rule and the five regular solids
The method serves for the five regular solids because they are of equal base. For bodies of unequal sides it fails unless one first prepares two or three kinds of cylinders for the two or three kinds of base, then cubes and equalises their thickness.
Two solid diagrams at the head of the page
At the upper right are two drawings: a long segmented body resembling a bundle of cylinders, and a cube ruled into a grid of small squares, illustrating the subdivision described in the text.