To make a cube double or half another

Cutting the cube into half and quarter

The larger cube a is cut from the upper diagonal to the lower diagonal, leaving a long square b; that is cut equidistant to the base to give the part c, which is worked in the angle of proportions as on the reverse of the sheet.

Constructing a subduple square from a diagonal

Given the diagonal a b, its square is found by drawing the perpendicular n m at mid-length, cutting from it a part equal to half the diagonal (made with the quarter-circle), and drawing a to b to form triangle a m b, which is one fourth of the square of which a b is the diagonal.

Making a cube half the given cube

Cube a is divided in half by a cut from the upper to the lower diagonal; the half b is made a perfect square c with the fifth; half of b (d) is likewise squared to e. Because d is not proportioned to itself as c is to its b, the figure is completed with the angle of proportions.

Cubo tagliato diagonalmente, con:

Metà dello stesso, con:

Un quarto dello stesso, con:

Trasformazione e raddoppio dello stesso quarto.

Quadratura d'un rettangolo.

Formazione d'un quadrato subduplo, con:

Cubo diviso diagonalmente, con:

Faccia rettangolare ottenuta e sua quadratura, con:

Metà della faccia rettangolare e sua quadratura, con:

Cube cut diagonally, with:

Half of the same, with:

A quarter of the same, with:

Transformation and doubling of the same quarter.

Squaring of a rectangle.

Formation of a subduple square, with:

Cube divided diagonally, with:

Rectangular face obtained and its squaring, with:

Half of the rectangular face and its squaring, with:

To make a cube double or half another

On this page

Cutting the cube into half and quarter

Constructing a subduple square from a diagonal

Making a cube half the given cube