 Oresme was a determined opponent of astrology, which he attacked on religious and scientific grounds. In De proportionibus proportionum Oresme first examined raising rational numbers to rational powers before extending his work to include irrational powers. The results of both operations he termed irrational ratios, although he considered the first type commensurable with rational numbers, and the latter not. His motivation for this study was a suggestion of Thomas Bradwardine that the relationship between forces \((F)\), resistances \((R)\), and velocities \((V)\) is exponential (Grant 1966, 24–40; Clagett 1974, 224). In modern terms: