Turning a pyramid into a slab of given length and width
Problems 15 and 16: finding a slab's thickness, then its width, from a pyramid of equal volume
Following a note that the converses of the preceding problems should also be worked out, two numbered cases (15 and 16) turn a pyramid into a flat slab (tavola). In the first, the slab's length and width are given and its thickness is sought, solved by reducing the pyramid to a cylinder and re-extending it to the slab's dimensions. In the second, the slab's length and thickness are given and its width is sought, by extending the cylinder to the given length and then lowering its face to the given thickness. A rectangle with a slab and two pyramid figures accompany the demonstrations.
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Problem 15: slab of given length and width, find thickness (a b, b c)
A slab of given length and width is to be made from the pyramid and its thickness sought. Leonardo reduces the pyramid to its cylinder and makes the slab's width a b; because the cylinder is not as long as the slab's length b c, he rebuilds the cylinder's face from the thickness of side b c and re-extends it to the slab's full given length.
Problem 16: slab of given length and thickness, find width
Here a slab of given thickness and length is required and its width is asked. He makes the cylinder of the pyramid, extends the cylinder to the slab's given length, then lowers its face to the slab's given thickness, and so obtains the needed width.