Let a cube be transformed into a four-sided cylinder [rectangular prism] according to a given length.

e – o – r m – f g c a – [h] – d b. Given the cube a b c d, let it be lengthened along the line e d. To satisfy the proposition I will set the foot of the compass at d and draw the curve e f. Then I will produce the line d f from the origin of the line d e; and from the angle b I will produce the line b g, parallel to the line d f. This done, in order to make the faces of this parallelepiped b g d f rectangular, I will take the triangle b h d from its place and carry it over to g m f, and so I will have made the parallelepiped h d m f, which, squared along the face m o f r, will be equal to the cube a b c d; and because that face does not remain square, having on one side the width equal to the width of the cube and on the other the width m f, I will make it of equal sides by the fifth [figure] below.

n – m. Here you see n, squared with the fifth, is equal to m, that is equal to the face m o f r above, and it is of the given length e d, which I set down here in the margin.

m a n – c b. a b, or if you like a c, will be the diagonal of a cube of half the volume of the cube n m b c.

n a – m. These two lines are two diagonals, of which n m is the diagonal of a cube half the volume of the cube of which this square is one of its sides.

The accidental centre, once it has touched the centre of the world, immediately flees from it, and the centre of natural gravity enters into its place, and the motion of the one and of the other will be at a right angle.

n – h o g – c b a e f. The space h o will be similar to the excess that the space e b has over the space f e.

The weight that here descends always makes its descent at a right angle over its roller.

m c b a [n] – f d. When the falcon b d is moved the small span b c, its far end f will make the whole motion n f m by itself; and in the time that its load is given to it, if it is moved from c to a, it will make the whole motion m f a by itself, up to the place where it discharges; and the motion a c ought to be one braccio, and such a motion ought to be made with a single lever, as is here shown.

a n – b c. The whole weight c rests upon a b. And if n a is equal to a b, then the force from c to n will be equal to that which ..