825.10 Right Triangle

825.11 They then used a straightedge to connect points C and C with a line that they said bisected line AB perpendicularly, being generated by equidistance from either point on either side. Thus the Greeks arrived at their right triangle; in fact, their four right triangles. We will designate as point!) the intersection of the lines CC and AB. This gave the Greeks four angles around a common point. The four right triangles ADC, BDC, ADC, and BDC have hypotenuses and legs that are, as is apparent from even the most casual inspection, of three different lengths. The leg Z)B, for instance, is by equidistance construction exactly one-half of AB, since/IB was the radius of the two original circles whose circumferences ran through one another’s centers. By divider inspections, DB is less than CD and CD is less than CB. The length of the line CD is unknown in respect to the original lines AB, BD, or AC, lines that represented the original opening of the dividers. They have established, however, with satisfaction of the rules of their game, that 360 degrees of circular unity at D could be divided into four equal 90-degree angles entirely and evenly surrounding point/).