Transforming a cube into a rectangular prism
Solid-geometry constructions using the 'angle of proportions'
This sheet works through the transformation of a cube into an equivalent four-sided prism (parallelepiped) of a given length, a step toward doubling the cube. Leonardo describes extending a smaller cube into a long rectangular prism matching the height of a larger cube, then making its unequal sides equal with the aid of 'the fifth' proposition and joining the bodies at the 'angle of proportions,' invoking the second-to-last proposition of Elements Book I. The diagrams show stacked parallelepipeds, a hatched box, and three cubes set against the sides of a right triangle. The mirror-script Italian is fully transcribed.
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A cube turned into a four-sided prism of given length
Leonardo proposes making from a cube a four-sided prism of 4 equal sides of a given length. The proposed cube is labelled q p b S and the given height of the prism is a b.
Squaring the prism's unequal sides
Because the sides of the long prism are not equal, he makes them equal without losing any of its quantity: he sets it below at m and, with the aid of the fifth, makes it square as shown at n. He then joins prism c with cube a so that b arises, equal to a joined with c.
Three cubes on a right triangle at the angle of proportions
Three cubes are set to the sides of a right triangle. Leonardo directs: place the square c in the angle at c and you will find a, its correspondent.