CHAPTER V — Critical Commentary & Notes

On the Length (Height), Thickness, Entasis, and Base (Spira) of the Round Column.

Historical & Mathematical Commentary

  • Vitruvius’s Attic Base (Vitruvius III.5.2): Pacioli's step-by-step arithmetic for the Attic column base (Plate 0213) follows Vitruvius III.5.2–3: total base height \(= \frac{1}{2}D\); plinth width \(= 1\frac{1}{2}D\); plinth height \(= \frac{1}{3}\) of base height (\(= \frac{1}{6}D\)), leaving \(\frac{2}{3}\) of base height (\(= \frac{1}{3}D\)), of which \(\frac{1}{4}\) is the upper torus and the remaining \(\frac{3}{4}\) is split equally (\(\frac{3}{8}\) each) between the lower torus and the scotia (trochilus) with its fillets.

Constantin Winterberg’s Commentary (1889 Edition)

  • Winterberg Footnotes 1–3 (Arch. Cap. V, pp. 305–306): (1) Compare the column plate at the end of the treatise (Paganini Folio 0213, 0213.g1.png). (2) Instead of the nonsensical reading ‘immedietate’ in the 1509 print, read ‘immediate’ (‘immediately’). (3) Compare Chapter LIX of the preceding treatise (Compendio) on the circular base and shaft. (Winterberg Fussnoten 1–3 (Arch. Cap. V, S. 305–306): 1) Vgl. die betreffende Figur am Ende des Tractats. 2) Statt des keinen Sinn gebenden Ausdrucks „immedietate“ wohl „immediate“ zu lesen. 3) cfr. Cap. LIX des vorigen Tractats.)

Philological and Folio Apparatus

  • 1509 Paganini Witness Folios: 0071 (f. 28r–f. 28r)

  • Winterberg 1889 Italian Source: winterberg/02_architectura_italian/005_cap_V.txt

  • Winterberg 1889 German Source: winterberg/04_architectura_german/005_cap_V.txt

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