Quadrature of lunes and equal-area curved figures

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© Veneranda Biblioteca Ambrosiana, Milan

From the top and the right, a figure with letters:

c d. On the second sheet and fourth face of this it is proved that c d are of equal curvature and of equal value.

Two figures with letters:

n m - a b. Make the portions a b equal to n m.

Central column, a figure with:

c g - f o - b a - 2. Here are 8 triangles of equal value. It follows that, a being of equal sides, that is from angle to angle, and c likewise, and c being equal to d, and c equal to a, a is squarable in itself, being equal to c f; and it follows that d too is squarable by similitude: squarable, but not in itself, because the portion that can be drawn from it does not fill the 2 lateral voids.

Figures with letters:

a - b. a b is equal but ...

A semicircle divided into sectors, with letters:

a b. a b gives and receives one same value with the portions.

A figure like the preceding, with letters:

a - b, e - c - f. a b is equal to c, because, e f being taken away, a c remains equal.

Below, a similar figure:

b c a. a is equal to b c.

Three figures with letters:

a b c. a b c are equal.

At the left:

To give a parallelogram equal to a portion.

A figure of a semicircle with letters:

b c d - e f g h. The greater portion a b c d is worth the two lesser portions e f g h. It follows that the remainder of the parallelogram is equal to the remainder of the semicircle, which was set equal to the parallelogram.

At the centre, the sheet turned upside down. A figure with letters:

a b - q r - d c - s. a b c is known because a is between two similar and equal peripheries. Again b c is known, being between 2 similar and equal peripheries. Then I have added d to a b c, and have made the rectilinear triangle d c.

A figure with letters:

f e - o p - g h - t. Here is set the whole surface aforesaid above. But it is all rectilinear and of the same value, for c is worth a, having the same base and the same height as a. f g is worth b c, having likewise the same base and height as b c. The line o p is similar to the line q r. The triangle o p t is worth the triangle q r s.

On the margin:

42 / 25 / 67.

Reader's Edition — described with AI from the e-Leo transcription.

Dall'alto e da destra: figura colle lettere:

Due figure colle lettere:

Colonna centrale, figura con:

Figure colle lettere:

Semicerchio diviso in settori colle lettere:

Figura simile alla precedente colle lettere:

In basso, figura simile:

Tre figure colle lettere:

A sinistra:

Figura di semicerchio colle lettere:

Al centro, capovolto il foglio. Figura colle lettere:

Figura colle lettere:

Sul margine: