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### Single Idea 14157

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry]

Full Idea

In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed.

Gist of Idea

Modern geometries only accept various parts of the Euclid propositions

Source

comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.404

Related Idea

Idea 14155
Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) **[Russell, by PG]**