...the said circles are not actually completed original: "non cōplentur actu." The author explains that drawing full circles would clutter the diagram. because, if completed in fact, they would take away the evident visibility of the square established beneath them.

Conclusion

In this fourth conclusion, Campanus Campanus of Novara (c. 1220–1296) was an important medieval mathematician whose commentary on Euclid’s Elements was a standard textbook for centuries. seems to hold that if two straight lines straight lines lineae rectae touch each other and, from their contact, a right angle right angle rectus angulus is formed in any of these four ways, namely:

Three geometric diagrams showing different configurations of two lines meeting at a right angle. The first diagram on the left is labeled with points A, B, and C, forming an inverted 'L' shape where A-B is horizontal and B-C is vertical.

Afterward, let the stationary leg of the compass compass circinus be fixed at the contact point of those lines; then let the other, moving leg be drawn from the end original: "caput," literally "head." of one line to the end of the other, specifically toward the circumference. For example, let the first straight line be a-b and the other be c-b, from whose contact at point b a right angle is formed. Afterward, let the leg of the compass be fixed at the contact point of these lines, b. Let the other moving leg of the compass be drawn from the end of line a toward the outer part of the contact of those lines, only as far as point c, which ends the second line b-c. Nor should the circle itself be actually completed otherwise, but rather it should be understood as complete for a reason to be stated below. And thus, the first circle is nearly established—namely a-f-c, whose center is b, and within that circle are two semi-diameters semi-diameters semidiametri, the first of which is a-b and the second b-c. Then, with the compass unchanged from its previous setting, let one stationary leg be placed at point a, which is the center of the second circle; while the other leg of the compass...