CHAPTER XXXVII — Critical Commentary & Notes

How the Octocedron Is Placed in the Cube.

Historical & Mathematical Commentary

• Duality of Cube and Octahedron: Campanus XV.3 (Cap. XXXVII) and XV.4 (Cap. XXXVIII) establish the reciprocal duality between the cube (6 faces, 8 vertices, 12 edges) and the octahedron (8 faces, 6 vertices, 12 edges): the centers of the 6 faces of the cube are the 6 vertices of the inscribed octahedron, with \(s_{\text{octa}} = \frac{\sqrt{2}}{2} s_{\text{cube}}\).

Philological and Folio Apparatus

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

• Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/037_cap_XXXVII.txt

• Winterberg 1889 German Source: winterberg/03_divina_proportione_german/037_cap_XXXVII.txt

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