 We have already mentioned that the potential infinite occurs in Greek mathematics from the outset, most obviously in the natural number series and in the geometrical operations of addition and division of segments and other geometrical magnitudes. The Greek mathematicians, starting with Eudoxus, developed a technique for measuring plane and solid figures that avoided recourse to the infinite even where an infinite “limit” process would seem to be forced by the situation. This technique, known today as the method of exhaustion (the expression was coined in the 17th century by Gregory of Saint Vincent), is found in Euclid’s Elements, book XII, and then in some of the most spectacular results by Archimedes (3rd century BCE). The idea is to replace an infinite approximation by a double reductio ad absurdum. That means that one shows the equality in area or volume of two figures, say a circle \(C\) and an associated triangle \(T\), by noting that \(C \lt T, C \gt T\) or \(C = T\) and then showing that the assumptions \(C \lt T\) and \(C \gt T\) both lead to a contradiction. (Here ‘\(C\)’ and ‘\(T\)’ refer with systematic ambiguity to the figures and their areas/volumes.) Further discussion can be found in the