Abstract

There are few topics in plane geometry that have had as strange a career as that of the indirect proof. In Euclid's Elements it does not appear separated from the other method of proof. There is no comment indicating that it is a unique device. There are no reasons quoted for each of the steps taken, as is done so meticulously in the other proof. Moreover, this type of mathematical reasoning invented by Eudoxus in 375 b.c. had become so much a part of the methodology of the Greek geometers that Euclid uses it no less than 14 times in 35 proofs in Book I, and 16 times in 31 theorems in Book III of his Elements.

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