3. Use of Calculation. Mathematical analysis was
not entirely lacking from scientific investigation in the
thirteenth century. One unexpected source came at the
end of the century in the work of Arnald of Villanova,
who combined alchemical pursuits with those of phar-
macy and medicine. Arnald was interested in quanti-
fying the qualitative effects of compound medicines,
and refined and clarified a proposal of the Arabian
philosopher Alkindi (ninth century) that linked a geo-
metric increase in the number of parts of a quality
to an arithmetic increase in its sensed effect. The ex-
ponential function this implies has been seen by some
as a precursor of the function later used by Thomas
Bradwardine (d. 1349) in his dynamic analysis of local
motion (McVaugh, 1967).
A more noteworthy mathematical contribution was
found, however, in earlier work on mechanics, partic-
ularly in statics and kinematics, that definitely came
to fruition in the fourteenth century. Jordanus Nemo-
rarius and his school took up and developed (though
not from original sources) the mechanical teachings of
antiquity, exemplified by Aristotle's justification of the
lever principle, by Archimedes' axiomatic treatment
of the lever and the center of gravity, and by Hero's
study of simple machines. They formulated the concept
of “positional gravity” (gravitas secundum situm), with
its implied component forces, and used a principle
analogous to that of virtual displacements or of virtual
work to prove the law of the lever. Gerard of Brussels
was similarly heir to the kinematics of antiquity. In
his De motu he attempted to reduce various possible
curvilinear velocities of lines, surfaces, and solids to
the uniform rectilinear velocity of a moving point. In
the process he anticipated the “mean-speed theorem”
later used by the Mertonians, successfully equating the
varying rotational motion of a circle's radius with a
uniform translational motion of its midpoint.
Other conceptual work in the study of motive pow-
ers and resistances, made in the context of Aristotle's
rules for the comparison of motions, laid the ground-
work for the gradual substitution of the notion of force
(as exemplified by vis insita and vis impressa) for that
of cause, thereby preparing for later more sophisticated
analyses of gravitational and projectile motion.
