A new look at euclid's second proposition

We mention in closing that even the 20th-century Algorithm CO pales by comparison with Algorithm Euclid from the point of view of robustness with respect to singularities. Consider, for example, the case where point C happens to lie at a location equidistant from A and B. Algorithm Euclid executes in this case as easily as in any other because everything is well-defined. Without special flag-waving code, however, Algorithm CO could crash attempting to draw a circle with radius zero and then intersecting two circles, one of which has radius zero.