CHAPTER XXXIX — Critical Commentary & Notes¶
How the Tetracedron Is Formed in the Octocedron.
Historical & Mathematical Commentary¶
Commensurability in Length (:math:`2:3`): Notice the remarkable rational consequence of composing Campanus XV.4 (\(s_{\text{cube}} = \frac{\sqrt{2}}{3}s_{\text{octa}}\)) with Campanus XV.2 (\(s_{\text{tetra}} = \sqrt{2}\,s_{\text{cube}}\)): the \(\sqrt{2}\) factors cancel completely, leaving \(s_{\text{tetra}} = \frac{2}{3}s_{\text{octa}}\)!
Constantin Winterberg’s Commentary (1889 Edition)¶
Winterberg Footnote 1 (Cap. XXXIX, p. 230): Namely, the midpoints (scil. Mittelpunkte) of the edges of the octahedron. (Winterberg Fussnote 1 (Cap. XXXIX, S. 230): scil. Mittelpunkte.)
Philological and Folio Apparatus¶
1509 Paganini Witness Folios: 0042 (f. 13v–f. 13v)
Winterberg 1889 Italian Source:
winterberg/01_divina_proportione_italian/039_cap_XXXIX.txtWinterberg 1889 German Source:
winterberg/03_divina_proportione_german/039_cap_XXXIX.txtMarginal Woodcut Diagrams: 0 figure(s) extracted from the 1509 Venice witness.