Surfaces of the cylinder, a theatre curtain cord, and the oblique beam

Equal surfaces and the unrolled cylinder

If two surfaces are in continuous contact, neither exceeding the other, they are equal. The complete revolution of the cylinder rolled upon a flat surface describes a surface equal to its lateral surface.

Wet cord shortens, wet cloth lengthens

A brief pen note over the red-chalk figure records that a wet cord shortens while wet cloth lengthens.

Cord a b for lowering the theatre curtain

A lettered figure shows a b, a pull-cord, which serves for letting down the curtain that conceals the comedy (the stage play).

Relations of cylinder, inscribed cone and sphere

When the cylinder's axis equals its diameter, the lateral surface is quadruple the face-circle. Further relations tie the inscribed cone's surface to the two faces and half the lateral surface, and the lateral surface to the largest inscribed sphere, ending with the greatest circle being quadruple the sphere's surface.

Oblique beam moves its upper end in a curve

With the sheet turned 90 degrees, a beam-and-support figure states that every oblique beam a b with fixed lower front a moves its upper front b along the curve b n d, while the support b c moves along the curve b m e.

In alto a sanguigna:

A penna sopra la figura a sanguigna:

Figura colle lettere:

A sinistra piccola figura di triangolo equilatero:

In alto a destra, girato il foglio di 90°, figura di trave e sostentacolo con:

At the top, in red chalk:

In pen over the red-chalk figure:

Figure with the letters:

On the left, a small figure of an equilateral triangle:

At the top right, the sheet turned 90 degrees, figure of a beam and support with: