Squaring the circle by transmutation of surfaces

Propositions on similar and equal parts

First, similar parts are not always equal to one another, but are similar in figure and equal in quantity. Second, similar unequal parts keep the same proportion as their wholes. Third, whoever restores to a quantity the part taken away returns it to its whole.

a is the quadrature of the circle less two portions

With labelled points a, b, n, m, he states that a b above is worth a b below, and that a is the quadrature of the circle less the two portions n m, so that a is worth b.

Transmuting surface O p into q q

The surface O p is taken from its place and transmuted into q q; there remains n m outside the quadrature q r S, and n is worth p.

Completing six-eighths of the circular ring

The lower triangle o p is carried above into f b, to which c is added, completing six-eighths of the circular parallel; the two remaining eighths are left curvilinear, and the missing part e is supplied by moving portion a, which is proved equal to e.

Quadruple circles and equal surfaces

Two circles quadruple one to the other are compared: removing the n portion of the larger circle, the o portion of the fourth, and four portions of the smaller circle leaves the curvilinear and rectilinear surfaces e S g n equal among themselves.

A worked multiplication

A short numerical working in the lower left sets down 40 and 20 against 800 and 60, giving 48000.

Dall'alto.

Lungo il margine destro. Due cerchi concentrici, con:

Figura analoga, con:

Grande figura centrale, con:

Sesta riga dall'alto.

Margine sinistro.

Angolo inferiore destro.

Operazioni aritmetiche:

From the top.

Along the right margin. Two concentric circles, with:

A similar figure, with:

Large central figure, with:

Sixth line from the top.

Left margin.

Lower right corner.

Arithmetic operations: