Full Idea
As a branch of pure mathematics, geometry is strictly deductive, indifferent to the choice of its premises, and to the question of whether there strictly exist such entities. It just deals with series of more than one dimension.
Gist of Idea
Pure geometry is deductive, and neutral over what exists
Source
Bertrand Russell (The Principles of Mathematics [1903], §352)
Book Reference
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.372
A Reaction
This seems to be the culmination of the seventeenth century reduction of geometry to algebra. Russell admits that there is also the 'study of actual space'.