CHAPTER LXXI — Critical Commentary & Notes

What Is Understood by the Mathematical Terms Used in This Compendium—Namely Hypothesis, Hypotenuse, Corausto, Pyramidal Cone, Pentagonal Chord, Perpendicular, Cathetus, Diameter, Parallelogram, Diagonal, Center, and Sagitta—and Conclusion of Part I (December 14, 1498).

Historical & Mathematical Commentary

• Paganini 1509 Marginal Diagram: Folio 0059 (f. 22r) contains diagram 0059.g1.png illustrating the circular segment with its arco (arc/bow), corda (chord/bowstring), and saetta (sagitta/arrow).

• Dating of the Colophon (December 14, 1498): The colophon on Folio 0061 (f. 23r) reads “Finis a di 14. decembre in Milano nel nostro almo convento MCCCCXCVII. Sedente summo pontifice Alexandro VI. del suo pontificato anno VII.” Because Pope Alexander VI (Rodrigo Borgia) was elected on August 11, 1492, his seventh pontifical year (anno VII) ran from August 11, 1498 to August 10, 1499—and Cap. LXIX explicitly refers to the Franciscan General Chapter held in Milan in May–June 1498 (de l’anno presente). Thus MCCCCXCVII in the 1509 print dropped a final I for MCCCCXCVIII (December 14, 1498), the exact date recorded in the presentation manuscripts (Geneva MS l.e. 210 and Milan Biblioteca Ambrosiana MS 170 sup.).

Constantin Winterberg’s Commentary (1889 Edition)

• Winterberg Footnote 1 (Cap. LXXI, p. 274): Namely, regular polyhedra (scil. reguläre). (Winterberg Fussnote 1 (Cap. LXXI, S. 274): scil. reguläre.)

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0059, 0060, 0061 (f. 22r–f. 23r)

• Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/071_cap_LXXI.txt

• Winterberg 1889 German Source: winterberg/03_divina_proportione_german/071_cap_LXXI.txt

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