Converting a Quadrilateral Cylinder into a Cube
Finding the cube's height from a prism by its diameters and an arc
Here Leonardo reverses the operation, making a cube out of a given quadrilateral 'cylinder' (a rectangular prism) and asking the height of that cube. Let the prism be b c d e and the resulting cube f c n m: he draws the prism's diameters b e and d c, sets the compass at their intersection and describes the arc f s p so that its chord f p touches the corner at b and the arc's ends meet the two indefinite lines q e and o e. Where chord and arc reach f, one side of the cube is created between f c. A closing line poses the next problem, making a cylinder of given length from a cube. A semicircular arc with a set-square is drawn at the upper right.
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Diameters, intersection and the arc f s p
For prism b c d e transmuted into cube f c n m, draw the diameters b e and d c and place the compass foot at their intersection. Describe the arc f s p so that its chord f p touches the prism's corner at b and the ends of arc and chord touch the indefinite lines q e and o e; where they touch the line at f, one side of the cube is fixed between f c.
The next problem posed
A single line at the foot turns the operation around again, setting up the inverse case: of a cube make a cylinder of a given length, and it is asked what its thickness will be, the problem carried out on the following leaves.