The circumference is divided into four equal parts.
In its lower part, a horizontal tangent line is drawn.
Next, we are going to carry out the rectification of a semicircle, by the METHOD OF THE POLYGONS.
With center in the superior part of the circumference, an arc with the same radius is drawn, cutting it in the point R.
Now with center at point S, from its bottom, and radius up to point R, an arc is drawn that will cut to the horizontal line, at point N.
From the same center, another arc with radius is drawn up to point T, cutting the same line at point A.
We verify that the measurement of the segment A N, is equal to the semiperimeter, of the circumference, of pi by the radius.
To this semiperimeter, the radius of the circumference is added.
We find the proportional mean of these two segments.
we draw the bisector of segment M, N.
with center at this midpoint, and radius to N, we draw a semicircle.
From point A, a perpendicular is drawn that will cut this arch, at point B.
Segment A, B, is the measurement on the side of the square, equivalent to the given circumference.
We check that they have the same areas.
Knowing that the area of a circle is pi by the radius squared.