Turning a cylinder into a squared board of given thickness
Finding the width of a slab equal in volume to a cylinder
Here Leonardo poses the problem of converting a cylinder into a squared board (tavola) of a prescribed thickness and asks what its width must be. Taking cylinder a b c d and given thickness e c f d, he lays the cylinder on its face, unrolls its front g h L m by the 'seventh of the first', and forms the board front i o l p to that thickness, as long as the cylinder and as wide as L p. He then reduces the board q S r t to a square x y q u that contains the whole quantity of the cylinder, thereby fixing the true width with certainty. Three diagrams show the upright board, the board seen in perspective, and a square with an inscribed quadrant.
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Cylinder to a squared board of given thickness
The problem, marked with labels a b - e f - c d, is to make from a cylinder a squared board of a given thickness. What is asked is the width the board must have.
Unrolling the cylinder's front and squaring the board
Given cylinder a b c d and target thickness e c f d, Leonardo lays the cylinder on its face g h L m, marks the thickness L i m k, and by the seventh of the first book spreads the front into the board i o l p, as long as the cylinder and as wide as L p. Placing the board as q S r t, he reduces it by the fifth of the first to the square x y q u, which holds the whole quantity of the cylinder and yields the true width.