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Single Idea 14155

[from 'The Principles of Mathematics' by Bertrand Russell, in 6. Mathematics / A. Nature of Mathematics / 2. Geometry ]

Full Idea

Two points will define the line that joins them ('descriptive' geometry), the distance between them ('metrical' geometry), and the whole of the extended line ('projective' geometry).

Gist of Idea

Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective)

Source

report of Bertrand Russell (The Principles of Mathematics [1903], §362) by PG - Db (ideas)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.382


A Reaction

[a summary of Russell's §362] Projective Geometry clearly has the highest generality, and the modern view seems to make it the master subject of geometry.

Related Idea

Idea 14157 Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]