Full Idea
The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis.
Gist of Idea
The whole of Euclidean geometry derives from a basic equation and transformations
Source
David Hilbert (Axiomatic Thought [1918], [05])
Book Reference
'From Kant to Hilbert: sourcebook Vol. 2', ed/tr. Ewald,William [OUP 1996], p.1108
A Reaction
This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea...