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

Primary Text: Read Verbatim Treatise Track (pp. 419–428) · Overview: Analytical Summary · Cross-Corpus Loci: Master Concordance

Historical & Cross-Corpus Commentary

Connection to Rational & Projective Trigonometry (Wildberger)

Russell’s §407 observation that rational algebraic functions of cross-ratios characterize collinear order and quadric polarity prior to transcendental logarithms directly anticipates modern algebraic/projective metrical formulations (cf. N. J. Wildberger’s Divine Proportions and Universal Hyperbolic Geometry).

Explicit Self-Correction of 1897 EFG §§37 & 42

Compare EFG §37, where Russell argued projective coordinates could convey no genuinely metrical truth; in §406–407 Russell explains why logicism dissolves that objection.