ROBERT PODKOŃSKI, The Calculus of Ratios (Calculationes) — the New Method in Natural Science at Oxford University in the First Half of the Fourteenth Century

SUMMARY

The Oxford Calculators’ School, active in the first half of the fourteenth century, is famous among historians of science for its introduction of mathematical tools of analysis into Aristotelian natural philosophy. A tool they developed and exploited was the calculationes, based on the Euclidean theory of ratios derived from the book V of his Elements. This introduction of mathematics into natural philosophy became possible thanks to William of Ockham’s concept of theoretical science. William rejected the Aristotelian prohibition of metabasis — that is, the prohibition of using arguments taken from one science (for example, mathematics) in order to prove statements of other science. For Ockham and his intellectual heirs at Oxford, mathematics was a handy tool of argumentation with regard to physical problems, especially to the so-called science of motion. For instance, William Heytesbury, one of most important Oxford Calculators, used the mathematical method of calculationes to prove the “mean speed theorem,” establishing the exact relation between uniform and uniformly accelerated or decelerated motions. His student, Richard Swineshead, analyzed motions that are characterized by uniformly changing acceleration or deceleration. A few Continental thinkers — like Nicole Oresme, Albert of Saxony and Marsilius of Inghen — adopted and developed Calculators’ theories. Yet they faced, it would seem, much stronger opposition from philosophers in their communities that accepted the Aristotelian prohibition of metabasis.