Studies in the quadrature of the circle and lunes

Lunes and the quadrature of the circle

Circles standing in quadruple proportion let the four portions be struck from the greatest circle, leaving a square; abcd are worth the greatest square of the greatest circle. Leonardo further states that the 8 lunes are worth the 4 greatest portions of the greatest circle.

Lunes cannot converge without intersecting

At the mark v, beside a circle carrying six perforated lunes, Leonardo notes that no more lunes can be given in nature converging to one same point without intersecting one another.

Interlace rosettes and a shell-spiral

The upper-left of the sheet carries knot-like interlace rosettes and a large shell-form spiral drawn among the geometric figures, decorative in character.

Facciata destra, in basso. Figura colle lettere:

Figura colle lettere:

Facciata sinistra, capovolgendo il foglio. Al centro, figura colle lettere:

A sinistra della precedente figura, cerchio con sei bisangoli traforati. Sotto la figura la lettera:

Angolo inferiore destro; quattro cerchi inclusi in un cerchio:

Nell'estremità dell'angolo inferiore:

In alto, a matita, quadrilatero con due lati opposti curvi e due rettilinei, internamente diviso da linee parallele in sette parti:

Right face, below. Figure with the letters:

Figure with the letters:

Left face, turning the sheet upside down. At the center, figure with the letters:

To the left of the preceding figure, a circle with six perforated lunes. Beneath the figure, the letter:

Lower right corner; four circles enclosed in a circle:

At the far edge of the lower corner:

Above, in pencil, a quadrilateral with two opposite curved sides and two straight ones, internally divided by parallel lines into seven parts:

Studies in the quadrature of the circle and lunes

On this page

Lunes and the quadrature of the circle

Lunes cannot converge without intersecting

Interlace rosettes and a shell-spiral