825.00 Greek Scribing of Right-Angle Modularity in a Plane

825.01 It was easy for the Greeks to use their fixed dividers to identify two points on the plane marked by the divider’s two ends: A and B, respectively. Employing their straightedge, they could inscribe the line between these two points, the line/IB. Using one end of the dividers as the pivot point at one end of the line, A, a circle can be described around the original line terminal: circle A. Using point B as a center, a circle can be described around it, which we will call circle B. These two circles intersect one another at two points on either side of the line AB. We will call the intersection points C and C.

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Fig. 825.01.

825.02 By construction, they demonstrated that points C and C were both equidistant from points A and B. In this process, they have also defined two equilateral triangles ABC and ABC, with a congruent edge along the line AB and with points C and C equidistant on either side from points A and B, respectively.