Jules Tannery on Teaching Elementary Geometry
To mathematicians, Jules Tannery needs no introduction. The point he makes here is argued in more
detail (and perhaps more forcefully) three decades later by
Tatjana Ehrenfest-Afanassjewa. It is, as
another French thinker (Gonseth) pointed out, that the beginning becomes the beginning only at the end.
In other words, geometry is not inherently deductive ab initio, but becomes so as a result of
what Afanassjewa calls the relentless striving for clarity.
Nevertheless, there is no denying the pleasure of following Euclid's path from Proposition to Proposition
in a mixture of problem-solving and discovering the working of a great mind. Incidentally, the second sentence
on page 272 below does not sound quite right, and might be checked against the original.