Full Idea
Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries.
Clarification
'Synthetic' relates to experience; 'analytic' is pure definitions
Gist of Idea
Euclid's geometry is synthetic, but Descartes produced an analytic version of it
Source
report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4
Book Reference
Resnik,Michael D.: 'Mathematics as a Science of Patterns' [OUP 1999], p.55
A Reaction
I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist.