more on this theme | more from this thinker | more from this text
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 Ref
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]