Making a cube from a quadrilateral prism

Cubing the quadrilateral prism

To make a cube of the prism b, Leonardo divides it by the diagonal and puts the half at a, then with the fifth transmutes it into the square m.

The angle of proportionality

The square m is placed in the angle of proportionality, on whose sides is first set the diagonal cut of a cube upon its squaring (a c), where m goes at site d. He then makes the diagonal cut b of the cube he seeks, a rectangle whose minor sides are the cube's edges and whose major sides give the cube's lateral diagonal.

One cube from two cubes of different size

To make a single cube from two given cubes of different size, Leonardo lengthens the smaller cube to the height of the larger along line a c, placing it at c o b d; he carries the larger cube's height a c down to a b, sets the compass foot at b and draws the curve a n where it cuts the prism.

Parallelepipedo, con:

Rettangolo e quadrato equivalente, con:

Angolo della proporzionalità, con:

Due cubi, maggiore e minore, con:

Trasformazione del cubo minore in parallelepipedo, con:

Trasformazione del parallelepipedo a base rettangolare nell'equivalente a base quadrata, con:

Parallelepiped, with:

Rectangle and equivalent square, with:

Angle of proportionality, with:

Two cubes, larger and smaller, with:

Transformation of the smaller cube into a parallelepiped, with:

Transformation of the rectangular-based parallelepiped into the equivalent square-based one, with:

Making a cube from a quadrilateral prism

On this page

Cubing the quadrilateral prism

The angle of proportionality

One cube from two cubes of different size