Critical Notes — Chapter XLVII: Metrical Geometry (§§ 388–404)

Primary Text: Read Verbatim Treatise Track (pp. 404–418) · Overview: Analytical Summary · Cross-Corpus Loci: Master Concordance

Historical & Cross-Corpus Commentary

Hoenen’s Direct Rebuttal in De Noetica Geometriae (Caput IV, §§2–3 & §7)

This chapter is the primary Russellian text engaged in geometor/hoenen:

  1. Caput IV, §2, nn. 3–5 (pp. 107–111) quotes §390 (pp. 405–406) verbatim (‘strikes every intelligent child as a juggle… leopard can change its spots’) and replies that Russell mistakes fictitious empty receptacle-space (spatium imaginarium) for real extended being (ens extensum), of which continuous mobility and homogeneous site-individuation (materia intelligibilis) are essential propria.

  2. Caput IV, §3 (pp. 111–116) applauds Russell’s thermometer refutation of Poincaré/Helmholtz physical rigidity, then converts Russell’s §391 congruence postulate into an intuitive static demonstration from the homogeneity of extension.

  3. Caput IV, §7, n. 28 (pp. 139–142) quotes §389 (p. 404) on I.1 circle intersection, arguing that while formal scientia must list continuity explicitly, architectonic intellectus principiorum legitimately grasps circle-intersection from planar continuity.

Heath’s Commentary on Euclid Book I (C.N. 4 & Prop. 4)

In geometor/euclid, Sir Thomas L. Heath (Vol. I, p. 227 & p. 249) cites PoM p. 405 (§§389–390) and Russell’s 1902 Britannica article when concluding that Euclid used superposition reluctantly and that modern axiomatics rightly postulates I.4 with Hilbert.