Critical Notes — Chapter XLV: Projective Geometry (§§ 361–373)

Primary Text: Read Verbatim Treatise Track (pp. 381–392) · Overview: Analytical Summary · Cross-Corpus Loci: Master Concordance

Historical & Cross-Corpus Commentary

Cross-Link to GEOMETOR Pappus Corpus

Russell’s §§365–373 provide the modern logicist culmination of the projective tradition originating in Pappus of Alexandria (Collection Book VII, modeled in geometor/pappus), where cross-ratio invariance and the four-line harmonic fourth were first proved metrically before von Staudt purified them of length.

Refinement of 1897 EFG §§111–121

In 1897 Ch. III Sec. A, Russell had not yet discovered Pieri’s 1898 proof deriving cyclic order purely from harmonic conjugates without assuming open segments.