FOM: geometrical reasoning

[Stephen G Simpson]

Jacques Dubucs writes:
 > there is an increasingly fashionable tendancy to consider again
 > geometric reasoning by means of diagrams or figures as somehow
 > irreducible to logical inference. 

I wasn't aware of this trend.  Could you please summarize some of the
arguments here on FOM?

Doesn't the work of Euclid, Hilbert, Szmielew, ... in foundations of
geometry put this idea to rest once and for all, by showing that
geometrical reasoning can be formalized within the predicate calculus?
Do the naysayers have any serious arguments?

-- Steve