CHAPTER LX — Critical Commentary & Notes

On Four-Sided (Quadrilateral) Lateral Columns and the Five Species of Quadrilaterals (Plates XLVII–XLVIII).

Historical & Mathematical Commentary

• Arabic-Latin Geometric Terminology (*Elmuaym* and *:term:`Elmuariffe <elmuariffe>`*): In Adelard of Bath’s, Gerard of Cremona’s, and Campanus’s Latin editions of Euclid Euclid I.Def.22, the Arabic terms al-mu’ayyan (rhombus) and al-munharif (trapezium / irregular quadrilateral) were transliterated as helmuaym, simile helmuaym (rhomboid), and helmuariphe (:term:`elmuariffe <elmuariffe>`). Pacioli preserves both the Greek/Italian terms (rombo, romboide, irregulari) and the Campanian Arabic-Latin terms (elmuaym, :term:`elmuariffe <elmuariffe>`), illustrating each with lettered marginal woodcuts A, B, C, D, E on Folios 0053–0054.

• Paganini 1509 Plates Referenced:

  • Plate XLVII (0285.rst, Quadrilateral Prism, solid) and Plate XLVIII (0287.rst, Quadrilateral Prism, skeletal).

Constantin Winterberg’s Commentary (1889 Edition)

• Winterberg Footnotes 1–2 (Cap. LX, p. 253): (1) Compare the marginal prism diagrams on p. 107 (Paganini Folio 0052, 0052.g1.png–0052.g3.png). (2) In the 1509 TOC (p. 168), elmuhaym and elmuariffe denote the rhombus and rhomboid/trapezium. (Winterberg Fussnoten 1–2 (Cap. LX, S. 253, Inh. S. 168): 1) vgl. Fig. pag. 107. *) Rhombus und Rhomboide.)

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0052, 0053 (f. 18v–f. 19r)

• Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/060_cap_LX.txt

• Winterberg 1889 German Source: winterberg/03_divina_proportione_german/060_cap_LX.txt

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