Transmuting triangles and squaring lunes, with cord statics

Reshaping a triangle while keeping its area

Paired problems on the upper margin: widen a triangle's base along a given line and diminish its axis (height) so the enlarged triangle keeps its first area; then narrow the base along a given line and find the increase of the axis that does not diminish the triangle's capacity.

Equal lune-pyramids in a circle

Leonardo asserts that all lune-pyramids of equal sides, 'uniformly non-uniform,' that spring from the circumference of a circle and end at its centre are equal, however different their lengths, because the space from centre to circumference is a parallel space crossed by equal straight lines.

Unequal sectors and their rectilinear triangles

In superimposed circle sectors lettered a n b, r e, d p, o m, Q, the figure a b is equal to c d because a b is 2/8 of the circle whose eighth part (c d) is a double circle; the sectors n m o and r o Q are equal, yet their rectilinear triangles are not, because p o q is smaller.

Supports beneath a divided beam

With the sheet turned upside-down, a beam divided into compartments is studied: if an odd number of supports carries a beam of equal divisions, the two end supports each bear half the weight of those in the middle, and supports of equal divisions carry at equal distances.

Rods suspended from pulleys

Rods hung from pulleys are set out with the ratios 2 1/2 and 13/5, part of the leaf's study of how loads distribute across suspension points.

Numeric operations across the sheet

Columns of arithmetical operations (16, 32, 32, 16, 128 ... 512, 256) run beside the balance schemes, recording the doublings and sums behind the mechanical ratios.

(a) Metà destra. Schema di bilancia con:

Idem sopra la piega mediana:

Andando a destra, schema con:

Schema a linee incrociate:

Idem con:

Schema triangolare:

Schema con:

Angolo inferiore destro, schema colle lettere:

Metà sinistra, dall'alto. Schema con:

Aste sospese a carrucole, con:

Schema con:

Idem con:

Operazioni aritmetiche e numeri:

Sulla piega mediana, schema con:

Angolo inferiore sinistro:

A foglio capovolto. Disegno di trave compartito e piccoli schemi di ripartizione:

In alto a destra. Due cerchi - rapporto 1:2- sovrapposti, colle lettere:

Piccolo settore colla lettera:

Lungo il margine superiore:

Sotto il precedente:

Sotto il precedente:

Angolo superiore sinistro:

Sul margine sinistro, settori di cerchio sovrapposti, con:

Dal margine destro. Piccola figura di porzione colle lettere:

Grande figura di porzione con:

Figura di porzione:

Composizione di triangoli colle lettere:

Tre piccoli triangoli colle lettere:

Cerchio con due ' piramidi falcate ' :

(a) Right half. Diagram of a balance with:

The same, above the central fold:

Moving to the right, a diagram with:

A diagram of crossed lines:

The same, with:

A triangular diagram:

A diagram with:

Lower right corner, a diagram with the letters:

Left half, from the top. A diagram with:

Rods suspended from pulleys, with:

A diagram with:

The same, with:

Arithmetical operations and numbers:

On the central fold, a diagram with:

Lower left corner:

With the sheet turned upside-down. Drawing of a beam divided into compartments and small diagrams of distribution:

Upper right. Two circles - ratio 1:2 - superimposed, with the letters:

A small sector with the letter:

Along the upper margin:

Below the previous:

Below the previous:

Upper left corner:

On the left margin, superimposed circle sectors, with:

From the right margin. A small figure of a portion with the letters:

A large figure of a portion with:

A figure of a portion:

A composition of triangles with the letters:

Three small triangles with the letters:

A circle with two 'lune-pyramids':