Bibliography & Cited Sources

Primary Russell Editions, 19th-Century Geometrical Sources, and GEOMETOR Critical Apparatus

This bibliography catalogues 24 foundational treatises, memoirs, and critical editions referenced across the 1897 and 1903 Book Codexes and cross-corpus notes. Every inline :cite: role links directly to its corresponding entry below.

Bertrand A. W. Russell — An Essay on the Foundations of Geometry (1897)

  • Citation Key: russell:1897

  • Publication / Locus: Cambridge: At the University Press

  • Context: First edition (xvi + 201 pp.); revised expansion of Russell’s 1895 Trinity Fellowship dissertation. Public domain (Project Gutenberg #52091).

Bertrand Russell — The Principles of Mathematics, Vol. I (1903)

  • Citation Key: russell:1903

  • Publication / Locus: Cambridge: At the University Press

  • Context: First edition (xxix + 534 pp.), containing Part I (The Indefinables of Mathematics) and Part VI (Space, Chs. XLIV–LII, §§351–436, pp. 371–461).

Bertrand Russell — Sur les axiomes de la géométrie (1899)

  • Citation Key: russell:1899:axioms

  • Publication / Locus: Revue de Métaphysique et de Morale 7, pp. 684–707

  • Context: Russell’s French exchange with Henri Poincaré marking his transition from the 1897 Essay toward Peano–Pieri axiomatics.

Bertrand Russell — Geometry, Non-Euclidean (1902)

  • Citation Key: russell:1902:britannica

  • Publication / Locus: Encyclopaedia Britannica, 10th ed., Vol. XXVIII (Vol. IV of New Volumes), pp. 664–674

  • Context: Cited by T. L. Heath in Euclid’s Elements Vol. I, p. 227 on motion in geometry as transference of attention.

Bertrand Russell — Le réalisme analytique (1911)

  • Citation Key: russell:1911:rmm

  • Publication / Locus: Bulletin de la Société française de Philosophie / Revue de Métaphysique et de Morale

  • Context: Cited by P. Hoenen in De Noetica Geometriae Caput III, §2.6.B on Cantorian point-set continua.

Alfred North Whitehead & Bertrand Russell — Principia Mathematica, Vol. I (1910)

  • Citation Key: whitehead-russell:1910

  • Publication / Locus: Cambridge: At the University Press (*2.01, p. 100)

  • Context: Formal symbolic execution of the logicist program announced in PoM (1903); analyzed by Hoenen in Caput V, §4.2.B.

Petrus H. J. Hoenen, S.J. — De Noetica Geometriae: Origine Theoriae Cognitionis (1954)

  • Citation Key: hoenen:1954

  • Publication / Locus: Analecta Gregoriana Vol. LXIII, Rome: Pontificia Universitas Gregoriana

  • Context: Thomistic epistemological treatise engaging Russell’s PoM §§389–391 in Caput IV (§§2–3, §7) and Russell’s continuum/logicism in Caput III & V.

Euclid (trans. Sir Thomas L. Heath) — The Thirteen Books of Euclid’s Elements (1908)

  • Citation Key: euclid:elements:i-1

  • Publication / Locus: Vol. I, Book I, Prop. 1 (pp. 241–243)

  • Context: Equilateral triangle construction critiqued in PoM §389 for assuming two-circle intersection without an explicit continuity postulate.

Euclid (trans. Sir Thomas L. Heath) — The Thirteen Books of Euclid’s Elements (1908)

  • Citation Key: euclid:elements:i-4

  • Publication / Locus: Vol. I, Book I, Prop. 4 & C.N. 4 (pp. 224–228, 247–250)

  • Context: Side-Angle-Side congruence by superposition; locus of Russell’s PoM §§390–391 critique, Heath’s p. 249 commentary, and Hoenen’s Caput IV §§2–3 defense.

Pappus of Alexandria — Synagoge (Collection), Book VII (c. 340 AD)

  • Citation Key: pappus:collection:vii

  • Publication / Locus: Props. 129–145 (Cross-Ratio & Harmonic Fourth)

  • Context: Ancient projective lemmas underlying Desargues, Chasles, von Staudt, and Russell’s projective chapters (geometor/pappus).

Immanuel Kant — Kritik der reinen Vernunft (Critique of Pure Reason, 2nd ed.) (1787)

  • Citation Key: kant:1787:krv

  • Publication / Locus: Transcendental Aesthetic (B37–B49) & Transcendental Methodology (B740–B766)

  • Context: Target of Russell’s critical reconstruction in EFG Ch. II (§§51–58) and logicist refutation in PoM Ch. LII (§§432–436).

Karl Georg Christian von Staudt — Geometrie der Lage (and Beiträge zur Geometrie der Lage, 1856–1860) (1847)

  • Citation Key: staudt:1847

  • Publication / Locus: Nürnberg: Friedrich Korn

  • Context: Purely synthetic foundation of harmonic conjugates via the complete quadrilateral construction without metrical cross-ratios.

Arthur Cayley — A Sixth Memoir upon Quantics (1859)

  • Citation Key: cayley:1859

  • Publication / Locus: Philosophical Transactions of the Royal Society of London 149, pp. 61–90

  • Context: Introduced the projective theory of distance relative to the Absolute conic/quadric.

Felix Klein — Über die sogenannte Nicht-Euklidische Geometrie (and Vorlesungen über Nicht-Euklidische Geometrie, 1893) (1871)

  • Citation Key: klein:1871

  • Publication / Locus: Mathematische Annalen 4 (pp. 573–625) & 6 (pp. 112–145)

  • Context: Unified hyperbolic, elliptic, and parabolic geometries under Cayley’s projective metric.

Bernhard Riemann — Über die Hypothesen, welche der Geometrie zu Grunde liegen (1854 (pub. 1867))

  • Citation Key: riemann:1854

  • Publication / Locus: Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 13

  • Context: Introduced n-dimensional manifolds, the quadratic differential metric ds², and spaces of constant curvature.

Hermann von Helmholtz — Über die Thatsachen, die der Geometrie zum Grunde liegen (1868)

  • Citation Key: helmholtz:1868

  • Publication / Locus: Nachrichten von der Kgl. Gesellschaft der Wissenschaften zu Göttingen, pp. 193–221

  • Context: Formulated the free-mobility and rigid-body derivation of constant-curvature metrics.

Moritz Pasch — Vorlesungen über neuere Geometrie (1882)

  • Citation Key: pasch:1882

  • Publication / Locus: Leipzig: B. G. Teubner

  • Context: Axiomatized descriptive geometry, linear betweenness, planar separation (Pasch’s axiom), and ideal elements.

Giuseppe Peano — I principii di geometria logicamente esposti (and Sui fondamenti della geometria, 1894) (1889)

  • Citation Key: peano:1889

  • Publication / Locus: Turin: Fratelli Bocca / Rivista di Matematica 4, pp. 51–90

  • Context: Symbolic axiomatization of descriptive and metrical geometry studied in PoM Chs. XLVI–XLVII.

Mario Pieri — I principii della geometria di posizione composti in sistema logico deduttivo (1898)

  • Citation Key: pieri:1898

  • Publication / Locus: Memorie della Reale Accademia delle Scienze di Torino (2) 48, pp. 1–62

  • Context: Hypothetico-deductive axiomatization of projective geometry adopted by Russell throughout PoM Ch. XLV.

David Hilbert — Grundlagen der Geometrie (1899)

  • Citation Key: hilbert:1899

  • Publication / Locus: Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, Leipzig: Teubner

  • Context: Modern axiomatic reconstruction of Euclidean geometry cited by Russell (PoM §§375, 390–391), Heath, and Hoenen.

Rudolf Hermann Lotze — Metaphysik: Drei Bücher der Ontologie, Kosmologie und Psychologie (1879)

  • Citation Key: lotze:1879

  • Publication / Locus: Leipzig: S. Hirzel (Book II, Ch. II, §§108–137)

  • Context: Source of the anti-metageometrical and anti-relational arguments examined in EFG §§85–96 and PoM §§424–428.

Benno Erdmann — Die Axiome der Geometrie: Eine philosophische Untersuchung der Riemann-Helmholtz’schen Raumtheorie (1877)

  • Citation Key: erdmann:1877

  • Publication / Locus: Leipzig: Johann Ambrosius Barth

  • Context: Empiricist treatise on Riemann–Helmholtz geometry critiqued in EFG §§74–84.

Alfred North Whitehead — A Treatise on Universal Algebra, with Applications, Vol. I (1898)

  • Citation Key: whitehead:1898

  • Publication / Locus: Cambridge: At the University Press

  • Context: Source for Russell’s discussion of complex numbers, Grassmann’s Ausdehnungslehre, and projective metrics in PoM Chs. XLIV & XLVIII.

G. H. Hardy — Mathematical Proof (1929)

  • Citation Key: hardy:1929

  • Publication / Locus: Mind 38 (149), pp. 1–25

  • Context: Cited by Hoenen (Caput V, §3.2.A n. 8) regarding Russell’s logistic proof of 2 + 2 = 4 vs. mathematical intuition.