CHAPTER LV — Critical Commentary & Notes

On the Way to Know How to Form Still More Bodies Beyond Those Mentioned, How Their Forms Proceed to Infinity, and Why Plato Assigned the Five Regular Bodies to the Five Simple Bodies of the Universe.

Historical & Mathematical Commentary

• Paganini 1509 Marginal Diagrams: Folio 0049 (f. 17r) contains two woodcut diagrams (0049.g1.png and 0049.g2.png) illustrating the subdivision of the regular pentagon into 5 central triangles and each triangle into 6 scalene right triangles (\(5 \times 6 = 30\) per pentagon, \(12 \times 30 = 360\) over the whole dodecahedron).

• Philosophical Authorities Cited:

  • Plato, Timaeus 53c–56c (the geometric atomism of the four elements and the cosmos).

  • Alcinous (Didaskalikos / Epitome doctrinae Platonicae, 13, translated into Latin by Marsilio Ficino and Pietro Balbi), source of the 12 signs / 360 triangles zodiacal correspondence (\(12 \times 5 \times 6 = 360\)).

  • Calcidius (4th-century Latin translator and commentator on the Timaeus), Macrobius (Commentarii in Somnium Scipionis), and Apuleius (De Platone et eius dogmate).

• Comparison with Earlier Draft Track: The earlier divina_en_2/55.txt draft compressed this major cosmological and Neoplatonic chapter into four short paragraphs and omitted the citations of Alcinous, Calcidius, Macrobius, and Apuleius as well as the \(12 \times 5 \times 6 = 360\) Zodiacal triangulation explained by diagrams 0049.g1.png and 0049.g2.png.

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0048, 0049 (f. 16v–f. 17r)

• Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/055_cap_LV.txt

• Winterberg 1889 German Source: winterberg/03_divina_proportione_german/055_cap_LV.txt

• Marginal Woodcut Diagrams: 1 figure(s) extracted from the 1509 Venice witness.