TRANSCRIBER'S NOTE
The cover image was created by the transcriberand is placed in the public domain.
Obvious typographical errors and punctuation errors have beencorrected after careful comparison with other occurrences withinthe text and consultation of external sources.
More detail can be found at the end of the book.
THE
FOUNDATIONS OF GEOMETRY.
London: C. J. CLAY AND SONS,
CAMBRIDGE UNIVERSITY PRESS WAREHOUSE,
AVE MARIA LANE.
Glasgow: 263, ARGYLE STREET.
Leipzig: F. A. BROCKHAUS.
New York: THE MACMILLAN COMPANY.
Bombay: GEORGE BELL AND SONS.
AN ESSAY
ON THE
FOUNDATIONS OF GEOMETRY
BY
BERTRAND A. W. RUSSELL. M.A.
FELLOW OF TRINITY COLLEGE, CAMBRIDGE.
CAMBRIDGE:
AT THE UNIVERSITY PRESS.
1897
[All Rights reserved.]
Cambridge:
PRINTED BY J. AND C. F. CLAY,
AT THE UNIVERSITY PRESS.
PREFACE.
The present work is based on a dissertation submitted atthe Fellowship Examination of Trinity College, Cambridge,in the year 1895. Section B of the third chapter is inthe main a reprint, with some serious alterations, of an articlein Mind (New Series, No. 17). The substance of the book hasbeen given in the form of lectures at the Johns HopkinsUniversity, Baltimore, and at Bryn Mawr College, Pennsylvania.
My chief obligation is to Professor Klein. Throughout thefirst chapter, I have found his "Lectures on non-EuclideanGeometry" an invaluable guide; I have accepted from him thedivision of Metageometry into three periods, and have foundmy historical work much lightened by his references to previouswriters. In Logic, I have learnt most from Mr Bradley, andnext to him, from Sigwart and Dr Bosanquet. On severalimportant points, I have derived useful suggestions fromProfessor James's "Principles of Psychology."
My thanks are due to Mr G. F. Stout and Mr A. N.Whitehead for kindly reading my proofs, and helping me bymany useful criticisms. To Mr Whitehead I owe, also, theinestimable assistance of constant criticism and suggestionthroughout the course of construction, especially as regardsthe philosophical importance of projective Geometry.
Haslemere.
May, 1897.
TO
JOHN McTAGGART ELLIS McTAGGART
TO WHOSE DISCOURSE AND FRIENDSHIP IS OWING
THE EXISTENCE OF THIS BOOK.