CHAPTER XXXIV — Critical Commentary & Notes

On the Inscriptions of the Five Regular Bodies in One Another, How Many There Are in All, and Why.

Historical & Mathematical Commentary

  • Book XV in the Campanus Tradition: While the Greek Elements Book XV (compiled in the circle of Isidore of Miletus, 6th century CE) contained only a handful of simple inscriptions (Tetrahedron in Cube, Octahedron in Tetrahedron, Octahedron in Cube, Cube in Octahedron, Dodecahedron in Icosahedron), Campanus of Novara (c. 1259) expanded Book XV into a systematic sequence of 13 propositions covering 12 polyhedral inscriptions (XV.1–12) plus the inscription of the sphere in all five regular solids (XV.13).

  • Structure of Chapters XXXV–XLVII: Pacioli devotes Cap. XXXV through Cap. XLVII to translating and explaining Campanus’s Book XV propositions one by one, accompanied by marginal woodcuts on Folios 0038–0041.

Philological and Folio Apparatus

  • 1509 Paganini Witness Folios: 0041 (f. 13r–f. 13r)

  • Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/034_cap_XXXIV.txt

  • Winterberg 1889 German Source: winterberg/03_divina_proportione_german/034_cap_XXXIV.txt

  • Marginal Woodcut Diagrams: 0 figure(s) extracted from the 1509 Venice witness.