Lunes, Triangles and Pyramids Compared

Quadrature of a three-arc lune

The quadrature of the lune a b, of three sides of similar but unequal curvature, is shown to be b c d: the whole portion a equals the two opposite halves c d, so adding equal b to each keeps the sums equal.

Lunes born of equal triangles are equal

The right-angled triangle a and the acute-angled triangle b are equal, having equal bases between two parallels; the lunes generated below them are likewise equal to each other and to their triangles, so the two lunes equal the two triangles.

From sesquialteral to double proportion

If from 6 he takes two and from 4 he takes 2, the remainders 4 and 2, which before stood in sesquialteral proportion, are now in double proportion.

Reducing a mixed-line lune to a known part

To make e d c equal to b c he lends a equal to d, removes the common part c to leave b equal to e a d, then draws the squarable part e from b, so what remains is made known and bounded by two straight sides and one curve.

Falcata colle lettere:

Falcata colla lettera:

Due doppie figure di triangoli e falcate, con:

Semicolonna centrale Grande figura di falcate, con:

Triangolo tagliato da quattro parallele, con:

Angolo inferiore destro. Due triangoli colle lettere:

Semicolonna sinistra.

Falcate divise, con:

Figura di falcate entro un triangolo, con:

Lune with the letters:

Lune with the letter:

Two double figures of triangles and lunes, with:

Central half-column. Large figure of lunes, with:

Triangle cut by four parallels, with:

Lower right corner. Two triangles with the letters:

Left half-column.

Divided lunes, with:

Figure of lunes within a triangle, with:

Lunes, Triangles and Pyramids Compared

On this page

Quadrature of a three-arc lune

Lunes born of equal triangles are equal

From sesquialteral to double proportion

Reducing a mixed-line lune to a known part