Rome: Giacomo Mazzochi, 1516.
Extremely rare first edition of this influential and controversial work, an important step towards the arithmetization of the theory of proportion.
In the Eudoxian theory of proportion, treated in Book V of Euclid’s Elements, proportion is a relation between magnitudes of the same kind, and is not identified with a numerical value. Thus, the ratio of the diagonal of a square to a side is a valid concept in the Euclidean theory of proportion, although it is not identified with a number as this number would (in modern terms) be irrational. The evolution from proportion to numerical ratio began with Umar al-Khayyam in the 12th century and was continued by Nicole Oresme in the 14th. The most decisive progress in the modern era was made by Clavius in his great commentary on Euclid (first published in 1574). Clavius there criticized and completed the Euclidean theory of proportion, and took the first steps toward its arithmetization. According to Rommevaux (p. 72), Clavius’s critique was ‘certainly inspired’ by the present work of Ridolfi, which treats proportions as quantities, so that proportions are just the same as proportions of quantities.
Ridolfi’s work was attacked by Jean Fernel in his De proportionibus libri duo (1528), who argued that treating proportions as quantities was inconsistent with Euclid, Book V, and that it fails to see when these proportions of proportions are irrational (although understanding this had been one of the major achievements of Oresme). History found in Ridolfi’s favour, however, when the arithmetization of the theory of proportion was completed in the next century.
S. Rommevaux, Clavius: Une Clé pour Euclide au XVI Siècle, 2006. W. R. Laird & S. Roux (eds.), Mechanics and Natural Philosophy before the Scientific Revolution, 2008 (see pp. 103-105). Smith, Rara Arithmetica, addenda, p. 11; Riccardi I 387; STC Italian, Vol. 3, p. 35. OCLC lists copies at Brown, Columbia, Madison Wisconsin, Michigan and Tübingen; not in COPAC.
4to, ll , several marginal woodcut diagrams. Nineteenth-century boards (spine a little worn), housed in a brown morocco-backed folding box.