CHAPTER XV — Critical Commentary & Notes

On Its Sixth Inexpressible Effect

Historical and Philological Commentary

  1. Euclid Euclid XIII.6 and Euclid X.73: Proposition 6 of Book XIII proves that if a rational straight line is cut in extreme and mean ratio, each of the segments is an irrational straight line called an apotome ($\dot{\alpha}\pi\omicron\tau\omicron\mu\acute{\eta}$, defined in Euclid X.73, Campanus X.79). Pacioli calls this the “inexpressible” or “innominable” (innominabile) effect because neither segment can ever be named by a rational number when the whole is rational.

Philological and Folio Apparatus

  • 1509 Paganini Witness Folios: 0027 (f. 6r–f. 6r)

  • Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/015_cap_XV.txt

  • Winterberg 1889 German Source: winterberg/03_divina_proportione_german/015_cap_XV.txt

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