Squaring of the Circle

Fourth

106

c 2

...[be] moved and placed in the center of the first circle, namely at point b. And let it be rotated accordingly, forming a circle circle circulus that intersects the first; and let it be intersected by that same circle in one place toward the circumference, specifically directly above the midpoint of line a-b. And let it be rotated to the point where a straight line straight line linea recta, if drawn, would form a right angle right angle angulus rectus with the radius radius semidiameter of the first circle, so that the second circle ends at a place where a straight line drawn from center a toward the lower part can fall perpendicularly perpendicularly ortogonaliter directly over the point ending the second line b-c. This line should be extended directly downward and called the third line, a-d.

From these two circles, it is clearly evident to the observer that three sides of a square square quadratum will have been established: the first side will be a-b, the second b-c, and the third the line a-d, which is also the radius of the second circle b-g-d.

Once these things have been carried out, let one stationary foot of the compass compass circinus be placed at the point or at the end original: "capite," literally "head." of the other radius of the first circle—the radius or second line which was called b-c above. Let the other moving foot of the compass be placed at the center of that same first circle, namely at point b. Let this third circle be rotated toward the circumference of the first, intersecting the first and being intersected by it in one place toward the outer part, specifically directly above the midpoint of line b-c. And let this third circle b-h-d be rotated up to point d. Afterward, let a straight line be drawn from that same point d to point c, which is the center of this third circle.

And thus, from four equal straight lines, an equilateral equilateral equilaterum and right-angled right-angled rectangulum square is established. For indeed, all such lines of the square are equal to each other, because any two straight lines in the same circu... The text breaks here; the catchword "lo" at the bottom of the original page completes the word "circulo," meaning "circle."