Squaring of the Circle

Third

...as is clear in the figure divided into 11 equal parts, which is equivalent to a semicircular line or a semicircle semicircle semicirculus.

101

[A geometric diagram showing a horizontal line labeled 'k' on the left and 'L' on the right. The line passes through the centers of eleven overlapping circles, each numbered 1 through 11. The circles are arranged in a linear sequence where each circle's center lies on the circumference of the preceding one.]

It can also be proven in another way as follows: let a circle of any size be established. Then, without changing the compass compass circinus: a tool for drawing circles and measuring distances, let its movable leg be placed on the circumference circumference circunferentia of the circle. Let the other fixed leg be extended outside the circle; and there, with a new center center centrum now fixed, let the compass be rotated so that a second circle is marked, touching the previous circle only at the circumference. In the same way, let a third circle be placed touching the second, and a fourth touching the third. Finally, let a straight line straight line linea recta be drawn through their centers from end to end—namely, from point a to point b. It will thus happen that the line is cut into four equal parts original: "quatuor... equalia." Although the text specifies four parts, the subsequent heading and diagram illustrate a division into three parts. as happened above, in this manner:

[A geometric diagram showing a horizontal line labeled 'A' on the left and 'B' on the right. The line passes through the centers of three circles. The circles are tangent to one another, with their centers aligned along the horizontal axis.]