On the Ratios of Velocities in Motions

Thomas Bradwardine's treatise on the proportions of velocities in motion emerged from the sophisticated mathematical and philosophical environment of fourteenth-century Oxford, where scholars at Merton College were pioneering new approaches to understanding natural phenomena. Written in 1328, this work addresses fundamental questions about how forces, resistances, and velocities relate in physical motion, problems that had puzzled natural philosophers since Aristotle. Bradwardine, who would later become Archbishop of Canterbury, brought both theological conviction and mathematical rigor to bear on these questions, seeing in the mathematical structure of nature evidence of divine wisdom and order.

The treatise develops a mathematical law governing motion that relates the ratio of motive force to resistance with the velocity produced. Bradwardine argues that velocity increases in arithmetic proportion as the ratio of force to resistance increases in geometric proportion, expressed in what would later be called logarithmic terms. This represented a decisive break from Aristotelian physics, which held that velocity was simply proportional to force divided by resistance. Beyond its mathematical innovation, the work demonstrates Bradwardine's conviction that mathematical relationships reveal the rational structure God has built into creation. He sees the precise proportional relationships governing motion as manifestations of divine wisdom, arguing that understanding these mathematical harmonies brings the natural philosopher closer to understanding God's creative activity.

While Bradwardine's specific kinematic law was eventually superseded by later developments in physics, his approach proved influential in establishing mathematics as essential to natural philosophy and in demonstrating how rigorous analysis of the physical world could serve theological ends. His integration of mathematical precision with theological reflection helped shape the medieval synthesis that would later influence both Renaissance natural philosophy and early modern science. This work should be read by those interested in medieval approaches to natural philosophy, the historical relationship between mathematics and theology, and the development of scientific method within a Christian framework. It is not suitable for readers seeking purely technical physics or those uninterested in the mathematical dimensions of medieval thought.