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SCIENCE 595
changing relations between observable entities; *a plurality
should not be postulated without necessity', as he expressed
what came to be called Ockham's Razor; it was 'futile* to postu^
late causes like impetus. Ockham's parsimony in hypotheses was
here in some respects misplaced, for Buridan's impetus became
the ancestor of Galileo's impeto or memento; but Ockham's
general approach to scientific problems encouraged the view,
to be used by Galileo and Newton in their negative criticism
of contemporary physics, that the function ofa scientific theory
is in the first instance to correlate the observed data and not to
reveal the essences of things.
In keeping with this view some contemporaries ofOckhatn
developed some fruitful mathematical methods of describing
changing relations between phenomena and rates of change.
Bradwardine developed a kind of algebra in which letters of
the alphabet were used for variable quantities while the opera'
tions of adding, dividing, &c., were described in words. John
of Dumbleton described how to express relationship between
two^ quantities by means of graphs, in which the lengths of
vertical lines drawn at intervals perpendicular to a horizontal
'line represented, for example, velocity at successive intervals of
time. Dumbleton and two other Mertonian mathematicians,
William of Heytesbury and Richard Swineshead (the famous
"Calculator*), proved algebraically, some time before 1335,
the important rule, which may be called the Mertonian Rule,
that the space traversed in a given time by a body moving with
uniformly accelerated velocity was equal to the product ofthe
total time of moving multiplied by the mean ofthe initial and
final velocities. The French mathematician Nicole Oresme,
later in the fourteenth century, proved this geometrically, and
it gave Galileo the kinematic law of falling bodies, which he
himself regarded as his profoundest discovery.
4
In none of the other sciences cultivated in the west in the
middle ages did England achieve such profound and in'
fluential results as in the methodological and mathematical in'