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594 MEDIEVAL ENGLAND
place to another as a process requiring the continuous action of
a motive agent, a
conception precisely opposite to the seven^
teenth/century conception of inertia. So long as the external
motive agent continued to operate, the Aristotelian theory held
that velocity would be directly proportional to the motive
power and inversely proportional to the resistance of the
medium; remove the external agent, and the motion would
stop. Many everyday phenomena supported these judgements,
5
but three did not. First, according to this Aristotelian law ,
there should be a finite
velocity with any finite values ofpower and resistance, yet in fact ifthe power is smaller than the resis^
tance it may fail to move the body at all. To escape this diffi'
culty, Bradwardine used a modification ofthe 'law* according
to which velocity was proportional to the excess of power over
resistance, and he tried to
express by means of an algebraic
function how change in
velocity was related, as a dependent
variable, to the
independent variables, power and resistance.
Bradwardine's use of mathematical functions seems to have
inspired the attempt made by the French physicist, Jean
Buridan, to deal with the other two phenomena that provided
difficulties for Aristotle's conception ofmotion, the motion of
a projectile after leaving the projector, and the acceleration ofa
freely falling body. What was the motive power that kept the
projectile going? This question had worried physicists since
Aristotle himself. Buridan introduced a quantitative notion
of impetus, analogous to Newton's momentum, imparted by the
projector; this impetus maintained the projectile's velocity and
enabled it to impart velocity to other bodies with which it col'
lided. The acceleration of freely falling bodies Buridan attri'
buted to successive increments of impetus added by gravity.
Work relevant to both problems was taken up again in Ox'
ford. William of in
^Ockham, accordance with his general
principles of inquiry, reduced motion to the fact that from inx
stant to instant a is body observed to change its
spatial relations
with other bodies. He rejected Buridan's impetus as an unx
necessary complication. Science, he declared in effect, should,
in the interests of economy, confine itself to the description of