CHAPTER VI — Critical Commentary & Notes

On Its Worthy Commendation

Historical and Philological Commentary

1. Campanus of Novara on Book XIV, Proposition 10 (*:term:`Irrationale <irrationale>` Simphonia*): Pacioli translates and adapts a celebrated passage from Campanus of Novara’s 13th-century commentary on Book XIV, Proposition 10 of Euclid’s Elements (a corollary added by Campanus to Hypsicles’ Book XIV comparing the dodecahedron and icosahedron inscribed in the same sphere). Campanus marveled at the mirabilis :term:`potentia <potentia>` lineae secundum proportionem habentem medium duoque extrema divisae, writing: “Cui cum plurima admiranda conveniant, hoc praecipue… ex invariabili natura superiorum principiorum sibi adest, ut tam diversa solida, tum magnitudine, tum basium numero, tum etiam figura, :term:`irrationali <irrationale>` quadam symphonia rationabiliter conciliet” (“To which, though very many admirable properties belong, this above all is present to it from the invariable nature of higher principles: that it rationally reconciles solids so diverse in magnitude, in number of bases, and in figure, by a certain irrational symphony”).

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0023 (f. 4r–f. 4r)

• Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/006_cap_VI.txt

• Winterberg 1889 German Source: winterberg/03_divina_proportione_german/006_cap_VI.txt

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