CHAPTER IX — Critical Commentary & Notes

What the Root of a Number and of Any Other Quantity Is

Historical and Philological Commentary

1. Terminology of Roots (*Radix discreta* vs. *Radix surda*): Pacioli provides a concise glossary for courtly readers unfamiliar with abacus algebra. The Latin/Italian term radice sorda (“deaf” or “mute” root, rendering the Arabic jadhr asamm, which in turn translated the Greek $\alpha\lambda\omicron\gamma\omicron\varsigma$, “without ratio” or “inexpressible”) denotes an irrational square root such as $\sqrt{10}$ or $\sqrt{125}$ (Euclid X.def.3).

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0026 (f. 5v–f. 5v)

• Winterberg 1889 Italian Source: winterberg/01_divina_proportione_italian/009_cap_IX.txt

• Winterberg 1889 German Source: winterberg/03_divina_proportione_german/009_cap_IX.txt

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