A square slab of given thickness made from a pyramid
Problems 13 and 14, staged in four figures: pyramid, pyramid-in-cylinder, cylinder-to-slab, squared slab
Two numbered problems (13 and 14) turn a pyramid into a square slab (tavola), staged across four small figures labelled first, second, third and fourth. In problem 13 the slab's thickness is given and its width sought: the pyramid becomes a cylinder at a third of its height, then a slab of the given thickness, which is finally squared. Problem 14 reverses this, giving the width and seeking the thickness, and offers an alternative squaring when the slab's face falls short of or exceeds the required width. Successive propositions of the first and second books are cited at each step.
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Problem 13: square slab of given thickness, find width
A square slab of given thickness is required from the pyramid and its width sought. Leonardo makes the cylinder at a third of the pyramid's height, forms the slab to the given thickness, and because it does not stay square he squares it by the fifth of the first, satisfying the question.
Problem 14: square slab of given width, find thickness
Reducing the pyramid to its natural cylinder, he makes the slab to the given width as before, then squares it by the sixth of the second. Alternatively, when the face falls short of or exceeds the given width, he returns the slab's face into the cylinder's base and extends that base to the given face-length.