A Cylinder of Given Length from a Cube
Constructing the cylinder's thickness with three perpendiculars and an arc
This proposition extends a cube m into a cylinder of a given length c d and asks how much the thickness is thereby narrowed. On the base line c d Leonardo raises three indefinite perpendiculars, c g and d K at the ends and n h in the middle, and forms the hypotenuse f i of the right angle f d i. Placing the compass on the middle perpendicular he draws the arc f r i and slides the ruler until the segment a c is exactly double the segment e n, at which point a c gives the cylinder's thickness. A semicircular arc with a right-angle set-square is drawn at the upper right.
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Raising three perpendiculars and the arc f r i
From cube m an extension is made to the given length c d. On c d three indefinite perpendiculars c g, d K and n h are raised; the hypotenuse f i of the right angle f d i is drawn, and the compass, set on the middle perpendicular at e and opened by e f, describes the arc f r i whose chord is that hypotenuse.
The doubling condition that yields the thickness
Leonardo tests whether the part a c of perpendicular g c is twice as long as the part e n of line h n. If not, he keeps shifting the ruler along K d, holding it fixed at f, until a c is double e n; the space a c is then the thickness of the cylinder into which the cube was extended.