More squaring of lunes, with a sluice-gate and a maxim

A lune equal to a square, and the imperfect sector

a b c is worth the lune d e f, and the two portions a c are worth the two portions d f. Take a c from a b c and the square b remains; take d f from d e f and e remains unsquarable, since the concavity and convexity of the lune have similar curvature but unequal length. What remains is a dotted triangle, or an imperfect sector, made equal by removing the two dotted triangles from rectangle b.

Sickles in circles of continuous proportion 1, 2, 4

a b d is worth a b c; taking a from each leaves the sickle b d equal to the sickle b c, so that d is worth c and a is worth both b c and b d. The circles here are in continuous proportion 1, 2, 4, and so it can continue to infinity.

Equal parts removed from two semicircles leave square = lune

This circle is divided into two semicircles from which equal things are removed, the remainder promised equal. Removing a b c d from the upper semicircle leaves the square n; removing e f g h from the lower leaves the lune m, equal to the square n.

A transverse sluice-gate one braccio wide

Material is drawn out from a toward b and set back from b toward a, while the transverse sluice-gate is moved from n toward m and back. The gate is one braccio wide, clear, and its 'male' member is a quarter-braccio high and wide.

The greatest deception of men lies in their opinions

In the fourth column, apart from the geometry, stands a single maxim: the greatest deception of men is in their own opinions. It reads as a stand-alone sententia among the diagrams.

Dalla destra, prima colonna. Terza figura colle lettere:

Quarta figura:

Cerchio entro cerchio, colle lettere:

Seconda colonna.

Cerchio e lumla entro cerchio colle lettere:

Due figure curvilinee:

Porzione di cerchio divisa in quattro parti:

A destra della precedente, cerchio con:

Semicerchio e quadrante di cerchio divisi in falcate:

Cerchio e lunola entro un cerchio, con:

Terza colonna. Cerchio entro cerchio, con:

Cerchio colle lettere:

Cerchio colle lettere:

Cerchio colle lettere:

Bisangolo diviso con doppia curva, due cerchi il secondo dei quali con:

Quarta colonna.

Cerchio colle lettere:

Cerchio colle lettere:

Cerchio colle lettere:

Cerchio con 8 falcate disposte in croce:

Cerchio colle lettere:

Cerchio colle lettere:

Quinta colonna. Cerchio colle lettere:

Cerchio colle lettere:

Cerchio con due bisangoli:

From the right, first column. Third figure with the letters:

Fourth figure:

Circle within a circle, with the letters:

Second column.

Circle and lune within a circle, with the letters:

Two curvilinear figures:

Portion of a circle divided into four parts:

To the right of the preceding, a circle with:

Semicircle and quadrant of a circle divided into sickles:

Circle and lune within a circle, with:

Third column. Circle within a circle, with:

Circle with the letters:

Circle with the letters:

Circle with the letters:

Biangle divided by a double curve; two circles, the second with:

Fourth column.

Circle with the letters:

Circle with the letters:

Circle with the letters:

Circle with 8 sickles arranged in a cross:

Circle with the letters:

Circle with the letters:

Fifth column. Circle with the letters:

Circle with the letters:

Circle with two biangles:

On this page

A lune equal to a square, and the imperfect sector

Sickles in circles of continuous proportion 1, 2, 4

Equal parts removed from two semicircles leave square = lune

A transverse sluice-gate one braccio wide

The greatest deception of men lies in their opinions