Tables and Cylinders: Transforming Solids of Equal Volume
Defining low and tall square solids, then converting cubes, tables and cylinders into one another
The verso continues Leonardo's calculus of solids, opening with a definition: square bodies lower than a cube he calls 'tables,' those taller than a cube 'cylinders.' A dense field of small parallelepipeds drawn in perspective illustrates a series of volume-preserving transformations — shortening a square-fronted cylinder to a given lowness while showing how it thickens, turning a cube into a table, and making a cylinder from a table's square to a given thickness. Short captions state each problem and record that the required height or length has been found.
On this page
Definition of 'tables' and 'cylinders'
Leonardo fixes his terms: all square bodies lower than a cube he will call 'tables,' and those that exceed the cube he will call 'cylinders.' The whole page then applies these two categories to solids of equal content.
Shortening a square-fronted cylinder
One problem shortens a cylinder of square front to a given lowness, and the accompanying parallelepipeds show how the solid thickens as it is lowered so as to keep its volume.
Making a table out of a cube
A caption beside a lowered, widened box records the completed transformation: 'And I have made a table out of the cube,' one of several conversions among cube, table and cylinder demonstrated here.