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### Single Idea 6297

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 2. Geometry]

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 Science of Pattern Recognition' [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.