Some Pioneers of Greek Geometry

Abstract

It is essentially in Greece, some seven centuries before Christ, that a deductive approach to geometry—based on ruler and compass constructions—starts to appear. The names of Thales and Pythagoras are certainly famous to this respect, as well as the three so-called “classical problems”: the trisection of the angle, the duplication of the cube and the squaring of the circle. Less popular but much more fundamental, the work of Eudoxus overcomes the problem of “incommensurable magnitudes” …that is, in contemporary terms, he introduces Dedekind cuts to handle the “continuity arguments”.