Quadrature of lunes: circles, squares, and hexagons

From a known, a known removed leaves a known

A square with curvilinear sectors labelled b a, c d carries the governing rule: if from a known you take a known, the remainder is known. Since both the hatched region and the whole square are known, subtracting the hatched leaves a squarable remainder, and the un-hatched part is worth half the square a b d c. The same maxim recurs along the median fold.

Octuple proportion between two circles of portions

A circle carrying 24 two-angles is set against a greater circle: forty-eight portions in the smaller answer to six in the greatest. The proportion is therefore octuple, so the greatest circle is octuple to the smallest, and dividing forty-eight by eight returns six. Like part answers to like part as like whole to like whole.

Hatched portions squaring the greatest circle

Above a sun-like circle Leonardo notes that eight of the hatched pieces are worth the four greatest portions of the greatest circle, so the remainder is squarable. Elsewhere twelve two-angles within a quadruple circle are judged worth the greatest square of the greatest circle. The figures test when curved slivers can be exchanged for straight-sided equivalents.

Squares of interlaced curvilinear motifs

The upper left of the sheet is filled with a grid of small squares bearing symmetric interlaced and knotted curvilinear designs. Though drawn as geometric quadrature exercises they read as decorative panels of applied ornament. Further faint pen labelling accompanies several of them.

A cooling drink of the Turks

Set to the right of the geometry is an unrelated household jotting. Sugar, rosewater, lemon and fresh water are strained through white cloth, and this, Leonardo writes, is the drink of the Turks in summer. It is a memorandum of a recipe rather than a study.

Metà destra, lungo il margine destro. Quadrato con settori curvilinei e le lettere:

Gruppo di cerchi ed esagoni colle lettere:

Gruppo di esagoni con:

Stella bisangolare entro corona circolare, con

Lungo la piega mediana.

Formazione di cerchi con 42 bisangoli:

Operazione aritmetica:

Facciata sinistra. Colonna destra. Quadrato curvilatero con bisangoli:

Foglio capovolto; 16 falcate doppie in una corona circolare:

Rigirato il foglio:

Cerchio con 24 bisangoli:

Colonna centrale.Archi di:

Cerchio con 12 bisangoli entro un cerchio quadruplo, con:

Entro il quadrato:

Cerchio e quadrato curvo:

Corona circolare con stella iscritti in un quadrato:

A destra del precedente:

In alto a sinistra, tra due figure:

Sopra un cerchio del tipo ' sole ' :

Angolo superiore sinistro, capovolto il foglio:

Right half, along the right margin. Square with curvilinear sectors and the letters:

Group of circles and hexagons with the letters:

Group of hexagons with:

Two-angled star within a circular ring, with:

Along the median fold.

Formation of circles with 42 two-angles:

Arithmetical operation:

Left face. Right column. Curved-sided square with two-angles:

Sheet inverted; 16 double crescents in a circular ring:

The sheet turned again:

Circle with 24 two-angles:

Central column. Arcs of:

Circle with 12 two-angles within a quadruple circle, with:

Within the square:

Circle and curved square:

Circular ring with star inscribed in a square:

To the right of the preceding:

Above, at left, between two figures:

Above a 'sun'-type circle:

Upper left corner, the sheet inverted:

On this page

From a known, a known removed leaves a known

Octuple proportion between two circles of portions

Hatched portions squaring the greatest circle

Squares of interlaced curvilinear motifs

A cooling drink of the Turks