Lunes and biangles: quadrature figures, with a French address

French address to Leonardo, painter to the King, at Amboise

A French address instructs the King's stable comptroller to have items delivered to Mr Leonardo the Florentine, painter to the King, for the affairs of the said lord, repeatedly naming Amboise. It records Leonardo's standing as painter to the King of France.

The least number of portions of a circle is three

The smallest number of portions that can be drawn from a circle is three, because the smallest rectilinear surface inscribed in a circle is the triangle, the next the square; the inscribed surface grows without limit as the number of its sides grows infinitely.

Lunes double one another

Two lunes are shown to be double one another, proved because the three circles involved are double one another. Companion figures repeat the relation of doubled lunes.

Halving series of nested circles

A group of circles nested one within another carries a descending halving series 64, 32, 16, 8, 4, 2 with labels a, c, b, expressing the proportional areas of the successive circles.

Facciata destra, colonna destra. Piccolo settore di cerchio:

Sedici bisangoli mezzi vacui entro un cerchio:

Cerchio e otto semicorone circolari entro un cerchio:

Due cerchi in un cerchio, e cerchio con:

Numeri in colonna biffati tranne l'ultimo:

A sinistra. Due lunule in un cerchio:

Figura analoga alla precedente:

Operazioni aritmetiche:

Facciata sinistra. Dall'alto. Otto bisangoli vacui in un cerchio iscritto nel quadrato con:

Stella bisangolare entro un cerchio, con:

Bisangolo quadripartito:

Cerchio con otto falcate a fiamma e due figure di falcate:

Triangolo iscritto in un cerchio:

Gruppo di cerchi interni l'uno all'altro, con:

A sinistra della figura:

Sopra la figura precedente, figura analoga:

Presso il margine, cerchio con bisangoli vacui e triangoli curvi:

Right face, right column. Small sector of a circle:

Sixteen half-empty biangles within a circle:

Circle and eight circular semi-crowns within a circle:

Two circles in a circle, and circle with:

Numbers in a column, struck through except the last:

At left. Two lunes in a circle:

Figure analogous to the preceding:

Arithmetic operations:

Left face. From the top. Eight empty biangles in a circle inscribed in the square, with:

Biangular star within a circle, with:

Quadripartite biangle:

Circle with eight flame-like curved rays and two figures of curved rays:

Triangle inscribed in a circle:

Group of circles nested one within another, with:

At left of the figure:

Above the preceding figure, an analogous figure:

Near the margin, circle with empty biangles and curved triangles:

Lunes and biangles: quadrature figures, with a French address

On this page

French address to Leonardo, painter to the King, at Amboise

The least number of portions of a circle is three

Lunes double one another

Halving series of nested circles