Doubling the cube, with cube-roots and a stamping press

A press for stamping candlesticks

An instrument a braccio long, made of one piece with the rest: b is the die (the impressed part), c the presser and d the driver, which must be a cube half a braccio on every side, of iron-shod oak with iron-plate faces.

Making candlesticks in stamped halves

Candlesticks are to be made half by half, or better quarter by quarter, then soldered together once enamelled. The foot is inlaid with bas-relief and filled with fixed enamel, the enamel finished on the lathe.

Solid rectangles after Pythagoras

Working the lines a c, a b, a e, a g and a f, the note builds the numbers 4, 8, 9 and 27, seeking to do for solid rectangles what Pythagoras did for the surfaces. Nearby, cubes on the sides 3, 4 and 5 give 27, 64 and 125.

Doubling the cube by its diagonal section

The squaring of the diagonal section of the sub-double cube equals a square that forms a side of the double cube. Squaring a b c d, the diagonal section of the given cube, yields the side of the doubled cube, while a n m o is shown as double the smaller cube.

Square roots laid out along a line

Along a line a b is taken as the root of 1, a c the root of 2, a d of 3, a e of 4, and so on to a K the root of 9. From these Leonardo tries to frame a rule for finding the cube roots of two cubes double one another.

Reducing many cubes to one

Wishing to make of many cubes a single one, he cuts a four-sided prism along its diagonal into a long parallelepiped and squares it, correcting acute or obtuse angles by rule so that no quantity is lost.

Facciata destra, in alto; macchina per ' stampire ':

Figura di centina colle lettere:

In alto, strumento analogo al primo, con:

In basso, figura con:

Figura di cinque piccoli cubi con:

Facciata sinistra. In alto, due figure con:

A sinistra:

Cubo dimezzato, con:

Altro cubo dimezzato, con:

Metà inferiore da destra a sinistra. Cubo e parallelepipedo accostati, con:

Tre cubi costruiti sui lati di un triangolo rettangolo, con:

Cubo segato diametralmente, con:

In basso, parallelepipedo formato da nove cubi, colle lettere:

Lo stesso segato diametricalmente, con:

Lo stesso ridotto a superficie rettangolare, con:

Figure di parallelepipedo e prisma a base triangolare:

Right side, at the top; machine for 'stamping':

Figure of a rib (centina) with the letters:

At the top, an instrument similar to the first, with:

Below, a figure with:

Figure of five small cubes with:

Left side. At the top, two figures with:

On the left:

Halved cube, with:

Another halved cube, with:

Lower half, from right to left. Cube and parallelepiped set together, with:

Three cubes built on the sides of a right triangle, with:

Cube cut diagonally, with:

Below, a parallelepiped formed of nine cubes, with the letters:

The same cut diagonally, with:

The same reduced to a rectangular surface, with:

Figures of a parallelepiped and a triangular prism: