Thinning a Square Slab and Its Growth in Area

Slab, with:

first - a b

Transformation from slab to cylinder, with:

second - d - c

From cylinder to slab, with:

Re-dimensioning of the same, with:

fourth - h g

From a square slab thinned according to a given thickness, the increase of its squared area is asked. The first above is the given square slab. The mark a b is the given thickness, to which the slab must be thinned and remain square; c is this first slab converted into its square d. e is the same square d reduced into the slab of the given thinness f, which comes to remain a slab longer than it is wide. g is this longer slab, which is reduced into the square h, and it is of the same given thinness and is square. And this is what we were seeking.

In the margin beneath the figures.

the height of o n being [obtained] with the sixth of the first, and because the face n is the one that represents the width of the base of the shortened pyramid and does not remain square, I will square it with the first of the first and I will have made the solid, from which I will draw the greatest pyramid that fits in it, and so I will have my intent, making m the base of the pyramid.

Tavola, con:

Trasformazione da tavola a cilindro, con:

Da cilindro a tavola, con:

Ridimensionamento della stessa, con:

Nel margine sotto le figure.

Slab, with:

Transformation from slab to cylinder, with:

From cylinder to slab, with:

Re-dimensioning of the same, with:

In the margin beneath the figures.

Thinning a Square Slab and Its Growth in Area

On this page

Thinning a square slab yet keeping it square

Squaring the base of a shortened pyramid