A new look at euclid’s second proposition

ConclusionsWe mention in closing that even the 20th-centuryAlgorithm CO pales by comparison withAlgorithm 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 fromA andB.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.

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