From a Square Slab to a Pyramid of Equal Volume
Reducing slab to cylinder to cube to the required pyramid
The page opens mid-argument, finishing a comparison of two cylinders: once each body wears its whole cylinder, the smaller base of the ninth is subtracted from the base of the tenth to strip off the excess, so the tenth equals the ninth, and discarding two-thirds of the cylinder leaves a pyramid base equal to the given cube and height. Leonardo then poses a fresh problem: from a square slab, make a square-based pyramid of given height and find the width of its base. The recipe reduces the slab to its cylinder, the cylinder to its cube, and the cube to the wanted pyramid, each step citing a numbered proposition. A tall pyramid on a slab is sketched at right.
On this page
Equalizing two cylinders by subtracting bases
Continuing an earlier construction, once each body is clothed in its whole cylinder, the smaller base of the ninth is subtracted from the base of the tenth to remove the tenth's excess, leaving the tenth equal to the ninth. Discarding two-thirds of the cylinder yields a pyramid base equal to the given cube and to the given height.
From a square slab to a pyramid
From a square slab, a square-based pyramid of given height is required, and the width of its base is asked. The slab's thickness is reduced to its natural cylinder by the sixth of the second, the cylinder to its cube by the first of the second, and that cube to the requested pyramid with the aid of the tenth.