[FOM] Query concerning E. H. Neville's Prolegomena to Analytical Geometry (Marion, Mathieu)

Adam Trybus adam.trybus at gmail.com
Thu Jun 6 14:08:32 EDT 2019

> I recently chanced upon Eric Harold Neville?s Prolegomena to Analytical
> Geometry (Cambridge University Press, 1922). In the Preface, he alludes to
> Russell?s Principles of Mathematics as well as to Principia Mathematica in
> order to motivate his particular take on the topic, but I could see what
> the rest of it owed specifically to ideas from Russell. My knowledge of
> both the history of mathematics and of foundations of mathematics is
> limited, so I wonder: would anyone know if the book had any impact?

Russell wrote two books touching on geometry An Essay on the Foundations of
Geometry and Principles of Mathematics. PM Part IV was to contain chapters
on geometry but it, famously, was never published. The Essay was generally
not considered a serious contribution to the topic, even by Russell
himself. PoM had some impact (e.g. Whitehead in his 'The Axioms of
Descriptive Geometry' credits Russell with coming up with a version of an
axiom system for this geometry). Also, Henry Forder in his Foundations of
Euclidean Geometry mentions Russell but not PoM specifically. Apart from
that I am not sure. I came across a reference to PoM here and there
(Lukasiewicz, maybe Couturat I think?) but it was not in relation to

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