CHAPTER XII — Critical Commentary & Notes¶
On the Orders and Spacing (Intercolumniations / Tetrants) of Round Columns in Buildings, and How the Architect Must Adapt Symmetry to the Site and Load (Vitruvius Book V).
Historical & Mathematical Commentary¶
Vitruvius III.3 (Intercolumniations) and V.6.7 (Tempering *Symmetria* by *Eurythmia* and *Usus*): Pacioli pairs Vitruvius’s classification of intercolumniations (Pycnostyle \(1\frac{1}{2}D\), Systyle \(2D\), Eustyle \(2\frac{1}{4}D\), Diastyle \(3D\), Araeostyle \(>3D\)) with the famous passage from Book V Chapter 6 on theaters, explaining why human-scale functional elements (steps, balustrades, passages) cannot simply be scaled down linearly in smaller buildings.
Constantin Winterberg’s Commentary (1889 Edition)¶
Winterberg Footnotes 1–2 (Arch. Cap. XII, p. 318): (1) Pacioli writes tygraphi for Vitruvius’s triglyphi (triglyphs). (2) In the 1509 print, read tecto (‘roof’) instead of lecto (‘bed’). (Winterberg Fussnoten 1–2 (Arch. Cap. XII, S. 318): 1) Tygraphen = Triglyphen. 2) Text l. tecto st. lecto.)
Philological and Folio Apparatus¶
1509 Paganini Witness Folios: 0077 (f. 31r–f. 31r)
Winterberg 1889 Italian Source:
winterberg/02_architectura_italian/012_cap_XII.txtWinterberg 1889 German Source:
winterberg/04_architectura_german/012_cap_XII.txtMarginal Woodcut Diagrams: 0 figure(s) extracted from the 1509 Venice witness.