# Physics

## Causes Of Motion: Medieval Understandings

Medieval scholars put considerable effort into modifying Aristotelian dynamics and answering the problems posed by it. Because most terrestrial bodies were composed of many elements, their natural motion was explained by summing the total power of heavy and light elements. This led medieval scholars to consider the minority type of material as providing a kind of "internal resistance." Using this idea, motion in a hypothetical void or vacuum could be explained by qualities of both motive force and resistance that inhered in the object itself.

Probably the greatest puzzle facing medieval interpreters of Aristotle was the violent motion of projectiles. If the motion of every object required the analyst to specify a mover or cause for that motion, then what caused projectiles to continue in their trajectories after they lost contact with their original projector? Aristotle suggested that a surrounding medium was pushed by the original mover and so continued to push the projectile. For medieval scholars who admitted the possibility of a vacuum, however, this explanation was not tenable. In addition, if the medium was slight compared to the projectile (such as the air compared to a stone), then it was difficult to see how a corporeal mover could continue to be the cause of violent motion. Motivated by such concerns, in the sixth century John Philoponus suggested that the continued motion of a projectile was due to an incorporeal force that was impressed on the projectile itself by the original mover. The projectile would finish its motion when this impressed force wore off.

Some eight hundred years later, in the fourteenth century at the University of Paris, Jean Buridan renamed Philoponus's impressed force "impetus," and used the concept to interpret the motion of projectiles and falling bodies. Once impressed on a projectile, the impetus could bring about virtually constant motion unless it was interrupted or dissipated by a resistive medium, a notion that bears some resemblance to the conceptions of inertia developed later. Buridan also attempted to quantify impetus, by saying it was proportional to the moving object's speed and its quantity of matter. As an object engaged in free fall, the power of gravity imparted larger and larger amounts of impetus to the object, thereby increasing its velocity.

A number of scholars attempted to quantify a relation between the impressed force and the velocity of an object. Paramount among these was Thomas Bradwardine of Merton College. In comparison to a projectile, a falling object presented special problems. Aristotle suggested that the velocity of the object was proportional to the total impressed force (F) and inversely proportional to the resistance of an ambient medium (R). Bradwardine rejected this formulation and a number of other suggestions by Philoponus, Avempace, and Averroes that involved simple ratios or subtractions of F and R. Instead, he proposed a dynamics in which the velocity of a body increased arithmetically as the ratio F/R increased geometrically. This formulation proved to be influential well into the sixteenth century.