Solid geometry: cube, sphere, cone and polyhedra

Roots of squares built on a lettered cube

The cube is lettered b n c m a: bc is the side (root) of the square nmbc; ac is the root of a square double that one; and ab is the root of a square equal to the two together. It sets out the duplicate-ratio relations of squares raised on the cube's edge and diagonals.

Cone, cylinder and sphere: surfaces and revolutions

A cone whose base diameter equals its slant side has a lateral surface double its base, and is generated by revolving the straight side of a semicircle. The circumference of a circle equals that of two of its greatest inscribed circles and its area equals four of them, while cylinder and sphere are handled by unrolling their 'skin.'

Forming a sphere from screwed lead strips

Strips of lead are drawn through a die, and many parallel strips are screwed together to build a cube; turned on a lathe this becomes a sphere, then resolved into circles which, straightened, give parallels of width. It is a mechanical, hands-on route to the very solids studied geometrically alongside.

A note: spectacles to see the moon enlarged

Turned upside down among the diagrams is the line 'Make spectacles for seeing the moon large.' It records the idea of a lens or eyeglasses to magnify the moon, an optical instrument aimed at an astronomical target.

Presso il margine inferiore. Cubo colle lettere:

Sopra il cubo figura di:

Figura di semisfera con:

Foglio capovolto. Dall'alto:

Piramide a base quadrata, con:

Poliedro colle lettere biffate:

Da destra verso sinistra.

Due cerchi entro un cerchio:

Semicerchio colle lettere:

A destra.

Cubo e sfera formati da piastre avvitate:

Proiezione di semisfera su un piano, con:

A sinistra. Pentagono iscritto e circoscritto, con:

Triangolo circoscritto, con:

Near the lower margin. Cube with the letters:

Above the cube, figure of:

Figure of a hemisphere, with:

Sheet upside down. From the top:

Pyramid with a square base, with:

Polyhedron with the crossed-out letters:

From right to left.

Two circles within a circle:

Semicircle with the letters:

On the right.

Cube and sphere formed from screwed plates:

Projection of a hemisphere onto a plane, with:

On the left. Inscribed and circumscribed pentagon, with:

Circumscribed triangle, with:

Solid geometry: cube, sphere, cone and polyhedra

On this page

Roots of squares built on a lettered cube

Cone, cylinder and sphere: surfaces and revolutions

Forming a sphere from screwed lead strips

A note: spectacles to see the moon enlarged