CHAPTER X — Critical Commentary & Notes

On Round and Lateral Pyramids in Architecture, and Praise of Leonardo da Vinci’s Incomparable Drawings.

Historical & Mathematical Commentary

• Weight (*Al Peso*) and Volume (*Ala Mesura*): Because the stonemasons of Sansepolcro needed to calculate the dead weight (peso) of stone spires, obelisks, and pyramidal roofs resting upon columns and walls, Pacioli points out that for homogeneous stone, Euclid’s \(\frac{1}{3}\) volume ratio (Euclid XII.7, Euclid XII.10) is simultaneously a weight ratio: a stone pyramid or cone weighs exactly one-third as much as a solid stone prism or cylinder of the same base and height!

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0076 (f. 30v–f. 30v)

• Winterberg 1889 Italian Source: winterberg/02_architectura_italian/010_cap_X.txt

• Winterberg 1889 German Source: winterberg/04_architectura_german/010_cap_X.txt

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