Making a Cylinder from a Square Slab
Stereometry: converting a square board into a cylinder of given thickness and finding its length
The page works the inverse problem: from the square slab a b c d, make a cylinder of a given thickness n and find the length of the resulting cylinder. A sequence of small figures at right — a labelled square, wedge-like slabs and a large arc — track the stages, while the main column gives the full procedure using 'the fifth of the first' and 'the seventh of the first.' Leonardo forms the cylinder m, transfers it below at b, marks the thickness b c on its face, and lowers the face until the cylinder lies spread out as a slab of the required dimensions.
On this page
From square slab a b c d to a cylinder of thickness n
The stated problem: from the square slab, make a cylinder of a given thickness n, and ask the length of the resulting cylinder. The construction forms cylinder m from the slab's thickness taken over the slab's length, using the fifth of the first, with the slab's thickness becoming o.
Lowering the cylinder's face into a slab
Cylinder m is placed below at b and the given thickness n marked on its face as b c; by the seventh of the first the face b is lowered by b c until it spreads into n m, leaving the cylinder in the form of a slab as long as a b c d, as wide as n m, and as thick as the given cylinder n.
Squaring and extending the slab n m o p
A note beneath the figure directs that the slab n m o p be first squared by the fifth of the first, then extended to the thickness given at n by the seventh of the first.