Resumen

GIOVANNINI, Eduardo N. "Una mancha en el sol de Euclides": Hilbert y la teoría euclídea de las proporciones. Tópicos [online]. 2015, n.30. ISSN 1666-485X.

The paper examines one the most important contributions to the foundations of elementary Euclidean geometry achieved by David Hilbert in his book Foundations of Geometry (1899), namely the reconstruction of the Euclidean theory of proportion and similar triangles. It is argued that this reconstruction was not only motived by Hilbert's identification of implicit assumptions in Euclid's theory, but also it was essentially linked to the concern for the 'purity of methods'. Moreover, it is claimed that in this specific case, Hilbert's requirement of the purity of method has a general or foundational dimension, that is, it is not established with regard to the proof of a particular theorem, but rather it is referred to the very axiomatic construction of the theory.

Palabras clave : Hilbert, Euclid, proportions, axiomatic method, continuity.

        · resumen en Español     · texto en Español     · Español ( pdf )