Capacity of polygons and the surfaces of cylinder and sphere

The polygon with more sides has the greater capacity

Among polygonal figures of equal diameter, Leonardo states that the one with more sides will have the greater capacity.

Perimeters of circumscribed and inscribed polygons versus the circle

The perimeter of polygons circumscribing a circle is greater than the circle's, the more so the fewer their sides; conversely the perimeter of a polygon inscribed in the circle is smaller, the less so the fewer its sides.

Least and greatest capacity, and the mean between them

The triangle is the least in capacity of the polygonal figures and the circle the greatest. Leonardo asks to be given the mean capacity between the triangle and the circle.

The curved surface of the cylinder clothes a sphere

If a cylinder contains a square, its curved surface has the same proportion to its base as a sphere's surface has to its great circle; that curved surface, drawn from the cube, clothes a sphere whose great circle equals the cylinder's base.

The weight b does not bear wholly on the central line

A lettered figure (c b a - n - g - f e) carries the note that the weight b does not bear entirely upon the central line b–e.

Glossary of geometric terms

Beside small figures of a pentagon, triangle, square and rectangle Leonardo glosses geometric vocabulary: periphery as 'boundary', polygon as 'of many sides', and the Latin-inflected terms quadrangulus, helix ('curvature') and perimeter.

A destra dall'alto: Figura con:

Figura colle lettere:

Altra figura colle lettere:

A sinistra delle due figure precedenti:

Due figure di triangolo iscritto e circoscritto:

Due cerchi circoscritti a un rettangolo e a un triangolo:

Figure di sfera entro cilindro e cubo, di cilindro entro cubo:

Presso il margine destro.

Figura di pentagono:

Figura di triangolo:

Figura di quadrato:

Figura di rettangolo:

Upper right. Figure with:

Figure with letters:

Another figure with letters:

To the left of the two preceding figures:

Two figures of an inscribed and circumscribed triangle:

Two circles circumscribed about a rectangle and a triangle:

Figures of a sphere within a cylinder and cube, and of a cylinder within a cube:

Near the right margin.

Figure of a pentagon:

Figure of a triangle:

Figure of a square:

Figure of a rectangle: