THE PRINCIPLES OF MATHEMATICS

Vol. I — 1903 First Edition: Preface, Part I (Chapter I), and Part VI (Space, Chapters XLIV–LII)

THE PRINCIPLES OF MATHEMATICS
BY BERTRAND RUSSELL, M.A.
LATE FELLOW OF TRINITY COLLEGE, CAMBRIDGE
VOL. I
CAMBRIDGE: AT THE UNIVERSITY PRESS — 1903

Editorial Scope & Public-Domain Provenance

This Book Codex presents the unabridged, verbatim 1903 Cambridge University Press first edition of the foundational and geometrical portions of The Principles of Mathematics: the 1903 Preface (pp. v–ix), Part I, Chapter I (Definition of Pure Mathematics, §§ 1–10, pp. 3–9), and the complete Part VI: Space (Chapters XLIV–LII, §§ 351–436, pp. 371–461)—comprising 96 numbered sections in full, including Chapter XLVII (§§ 389–391, pp. 404–407) where Russell formulates his celebrated critique of Euclid’s circle-intersection assumption (I.1) and method of superposition (I.4) directly answered by Fr. Petrus Hoenen, S.J. in De Noetica Geometriae (Caput IV) and cited by Sir Thomas L. Heath in The Thirteen Books of Euclid's Elements (Vol. I, pp. 225–227, 249).

Note

Russell’s later Introduction to the 1937 George Allen & Unwin second edition remains under copyright in several jurisdictions and is strictly excluded from this edition.

Analytical Table of Contents

Preface (1903)

Front Matter (1903 First Edition) · pp. v–ix

English (1903) · Summary · Notes

Chapter I: Definition of Pure Mathematics (§§ 1–10)

Part I — The Indefinables of Mathematics · pp. 3–9

English (1903) · Summary · Notes

Chapter XLIV: Dimensions and Complex Numbers (§§ 351–360)

Part VI — Space · pp. 371–380

English (1903) · Summary · Notes

Chapter XLV: Projective Geometry (§§ 361–373)

Part VI — Space · pp. 381–392

English (1903) · Summary · Notes

Chapter XLVI: Descriptive Geometry (§§ 374–387)

Part VI — Space · pp. 393–403

English (1903) · Summary · Notes

Chapter XLVII: Metrical Geometry (§§ 388–404)

Part VI — Space · pp. 404–418

English (1903) · Summary · Notes

Chapter XLVIII: Relation of Metrical to Projective and Descriptive Geometry (§§ 405–411)

Part VI — Space · pp. 419–428

English (1903) · Summary · Notes

Chapter XLIX: Definitions of Various Spaces (§§ 412–415)

Part VI — Space · pp. 429–436

English (1903) · Summary · Notes

Chapter L: The Continuity of Space (§§ 416–422)

Part VI — Space · pp. 437–444

English (1903) · Summary · Notes

Chapter LI: Logical Arguments Against Points (§§ 423–431)

Part VI — Space · pp. 445–453

English (1903) · Summary · Notes

Chapter LII: Kant’s Theory of Space (§§ 432–436)

Part VI — Space · pp. 454–461

English (1903) · Summary · Notes