Table of squares, lunes, and figures equated by curvature

Table of the first ten square numbers

A column running down the right margin multiplies each whole number by itself: 1 by 1 is 1, 2 by 2 is 4, 3 by 3 is 9, and so on up to 10, which gives 100. It is a plain table of squares.

Counterweighted system of rods

A drawn arrangement of rods carries a weight a, described as being of gravity equal to the member that supports it, but noted to be an 'accidental' weight. A companion figure repeats the label a.

Squares on the sides of a right triangle

In the centre of the page three squares are built on the sides of a right-angled triangle, labelled c, d, a, b. The note states that the three sides each multiplied by themselves equal the three squares a b c, and that of these the square c equals a and b together.

Curvilinear 'squares' equal to straight figures

A triangle with three curvilinear squares carries the labels c, d, a, b, with the claim that the two squares a b are worth the third square c, the curvatures of opposite sides being equal and similar. Nearby, a rectangle and a lune show a straight parallel a equal to the curvilinear parallel b.

Straight versus revolving motion of strips

A wavy strip above a rectangle is labelled a, b under the heading 'straight motion', the sinuous parallel a being equal to the straight-sided parallel b. A strip of increasing height above a triangle, labelled m, q, r, illustrates revolving motion about the angle m.

Dall'alto lungo il margine destro:

Sistema di aste con contrappeso:

Figura simile alla precedente, con:

Centro della pagina, tre quadrati costruiti sui lati di un triangolo, con:

A sinistra, rettangolo e lunula, con:

Triangolo e tre quadrati curvilinei, con:

Figura simile sotto la precedente, con:

A sinistra, striscia curvilinea ondulata sopra un rettangolo, con:

Striscia ondulata di altezza crescente sopra un triangolo, con:

From the top, along the right margin:

System of rods with a counterweight:

A figure similar to the preceding, with:

Centre of the page, three squares built on the sides of a triangle, with:

On the left, a rectangle and a lune, with:

A triangle and three curvilinear squares, with:

A similar figure below the preceding, with:

On the left, a wavy curvilinear strip above a rectangle, with:

A wavy strip of increasing height above a triangle, with: