GEOMETOR • bertrand-russell

Foundational Treatises on Geometry by Bertrand Russell (1872–1970)

Critical digital Book Codices, analytical reconstructions, vector geometric figures, and cross-corpus philosophical concordance for the two Cambridge University Press treatises on the foundations of geometry by Bertrand Russell—compiled as primary reference sources for Fr. Petrus Hoenen, S.J.’s De Noetica Geometriae (1954), Sir Thomas L. Heath’s The Thirteen Books of Euclid's Elements (1908), and Pappus of Alexandria’s projective lemmas in the GEOMETOR initiative.

Primary Codices (Opera Geometrica)

The Principles of Mathematics (1903, 1st Edition)

Vol. I — Preface (pp. v–ix), Part I: Chapter I (§§ 1–10, pp. 3–9), and Part VI: Space, Chapters XLIV–LII (§§ 351–436, pp. 371–461). Cambridge: At the University Press, 1903.

Russell’s landmark logicist treatise reducing pure mathematics to formal implication (p implies q) over logical constants and reconstructing projective, descriptive, and metrical geometry through the relational logic of Giuseppe Peano, Georg Cantor, and Mario Pieri. Includes all 96 numbered sections verbatim, featuring Chapter XLVII (§§ 389–391, pp. 404–407)—Russell’s celebrated critique of Euclid’s circle-intersection assumption (I.1), triangle superposition (I.4), the mercury thermometer paradox, and the three-part congruence postulate directly answered by Hoenen in De Noetica Geometriae Caput IV. (Strictly omits the copyrighted 1937 second-edition introduction.)

An Essay on the Foundations of Geometry (1897)

Complete Unabridged Treatise — Preface, Introduction, and Chapters I–IV (§§ 1–209, pp. 1–201), with 171 Author’s Footnotes and 9 Analytical Vector Figures. Cambridge: At the University Press, 1897.

Russell’s revised 1895 Trinity College Fellowship dissertation investigating nineteenth-century metageometry (Lobachevsky, Bolyai, Riemann, Helmholtz, Cayley, Klein, Lie) and deducing the a priori axioms of projective and metrical geometry from the neo-Kantian concept of a form of externality, culminating in the dialectical antinomies of the point and relational continuum in Chapter IV.

Cross-Corpus Apparatus & Essays