Squaring of the Circle

Conclusion

[A diagram of a horizontal line extending from point A on the left to point B on the right. Four circles, numbered 1, 2, 3, and 4, are arranged side-by-side along the line. Each circle touches its neighbor at a single point (tangent), and the center of each circle lies on the line AB.]

Fourth conclusion.

¶ From four equal straight lines, construct an equilateral and right-angled square original: "quadratū equí laterum atq; rectangulum" — a square with equal sides and four 90-degree angles..

[A large decorative initial 'H' featuring a floral arrangement in a classical vase, surrounded by leaves.] This is indeed obvious, and nonetheless it can be demonstrated in this way: let two straight lines be made touching each other at their ends original: "in capite," literally "at the head.", so that from their contact a single right angle is formed. Then, let the first leg of the compass compass circinus be placed at the point of contact of those lines; and let the other leg be placed at the end of the other aforementioned lines. Let the circle not be drawn completely, but be understood as if it were complete. From here, let the leg of the compass (which has not been adjusted) be placed at the end of the other aforementioned lines toward the circumference circumference circunferentia, given that the two aforementioned lines are the two radii radii semidiametri of the previously mentioned circle. Let the other leg be placed in the center center centrum of the aforementioned circle and be drawn so as to form a circle that intersects the previous one—and itself through it—in one place, up to the point where a straight line, drawn appropriately, may form a right angle with the radius of the first circle, ending at the center of this second circle. After this, let the leg of the compass (again, not having changed its width) be placed at the end of the other radius of the first circle toward the circumference; let the other leg be placed in the center of that same first circle and be drawn up to the point where it ends... The text cuts off mid-word "terminatur" (ends) at the bottom of the page.