4. Paris and the Growth of Dynamics. As in the
thirteenth century an interest in science with emphasis
on the mathematical began at Oxford, to be followed
by a similar interest with emphasis on the physical at
Paris, so in the fourteenth century an analogous pattern
appeared. The works of the English Calculatores were
read and understood on the Continent shortly after the
mid-fourteenth century by such thinkers as John of
Holland at the University of Prague and Albert of
Saxony at the University of Paris. Under less pro-
nounced nominalist influence than the Mertonians, and
generally convinced of the reality of motion, the Con-
tinental philosophers again took up the problems of
the causes and effects of local motion. Particularly at
Paris, in a setting where both Aristotelian and terminist
views were tolerated, “calculatory” techniques were
applied to natural and violent motions and new ad-
vances were made in both terrestrial and celestial
dynamics.
The first concept of significance to emerge from this
was that of impetus, which has been seen by historians
of medieval science, such as Duhem, as a forerunner
of the modern concept of inertia. The idea of impetus
was not completely new on the fourteenth-century
scene; the term had been used in biblical and Roman
literature in the general sense of a thrust toward some
goal, and John Philoponus, a Greek commentator on
Aristotle, had written in the sixth century of an “in-
corporeal kinetic force” impressed on a projectile as
the cause of its motion. Again Arabs such as Avicenna
and Abū'l-Barakāt had used equivalent Arabic termi-
nology to express the same idea, and thirteenth-century
Scholastics took note of impetus as a possible explana-
tion (which they rejected) of violent motion. What was
new about the fourteenth-century development was the
technical significance given to the concept in contexts
that more closely approximate later discussions of
inertial and gravitational motion.
The first to speak of impetus in such a context seems
to have been the Italian Scotist Franciscus de Marchia.
While discussing the causality of the Sacraments in a
commentary on the Sentences (1323), Franciscus em-
ployed impetus to explain how both projectiles and
the Sacraments produced effects through a certain
power resident within them; in the former case, the
projector leaves a force in the projectile that is the
principal continuer of its motion, although it also
leaves a force in the medium that helps the motion
along. The principal mover is the “force left behind”
(virtus derelicta) in the projectile—not a permanent
quality, but something temporary (“for a time”), like
heat induced in a body by fire, and this even apart
from external retarding influences. The nature of the
movement is determined by the
virtus: in one case it
can maintain an upward motion, in another a sideways
motion, and in yet another a circular motion. The last
case allowed Franciscus to explain the motion of the
celestial spheres in terms of an impetus impressed in
them by their “intelligences”—an important innova-
tion in that it bridged the Peripatetic gap between the
earthly and the heavenly, and prepared for a mechanics
that could embrace both terrestrial and celestial phe-
nomena.
A more systematic elaborator of the impetus concept
was John Buridan, rector of the University of Paris and
founder of a school there that soon rivaled in impor-
tance the school of Bradwardine at Oxford. Buridan,
perhaps independently of Franciscus de Marchia, saw
the necessity of some type of motive force within the
projectile; he regarded it as a permanent quality, how-
ever, and gave it a rudimentary quantification in terms
of the primary matter of the projectile and the velocity
imparted to it. Although he offered no formal discus-
sion of its mathematical properties, Buridan thought
that the impetus would vary directly as the velocity
imparted and as the quantity of matter put in motion;
in this respect, at least, his concept was similar to
Galileo's impeto and to Newton's “quantity of motion.”
The permanence of the impetus, in Buridan's view, was
such that it was really distinct from the motion pro-
duced and would last indefinitely (ad infinitum) if not
diminished by contrary influences. Buridan also ex-
plained the movement of the heavens by the imposition
of impetus on them by God at the time of the world's
creation. Again, and in this he was anticipated by
Abū'l-Barakāt, Buridan used his impetus concept to
explain the acceleration of falling bodies: continued
acceleration results because the gravity of the body
impresses more and more impetus.
Despite some similarities between impetus and in-
ertia, critical historians such as A. Maier have warned
against too facile an identification. Buridan's concept,
for example, was proposed as a further development
of Aristotle's theory of motion, wherein the distinction
between natural and violent (compulsory) still ob-
tained. A much greater conceptual revolution was
required before this distinction would be abandoned
and the principle of inertia, in its classical under-
standing, would become accepted among physicists.
Buridan's students, Albert of Saxony and Marsilius
of Inghen, popularized his theory and continued to
speak of impetus as an “accidental and extrinsic force,”
thereby preserving the Aristotelian notions of nature
and violence. Albert is important for his statements
regarding the free fall of bodies, wherein he speculates
that the velocity of fall could increase in direct pro-
portion to the distance of fall or to the time of fall,
without seemingly recognizing that the alternatives are
mutually exclusive. (This confusion was to continue in
later authors such as Leonardo da Vinci and the young
Galileo.) Albert himself seems to have favored distance
as the independent variable, and thus cannot be re-
garded as a precursor of the correct “law of falling
bodies.”
Perhaps the most original thinker of the Paris school
was Nicole Oresme. Examples of his novel approach
are his explanation of the motion of the heavens using
the metaphor of a mechanical clock, and his specula-
tions concerning the possible existence of a plurality
of worlds. An ardent opponent of astrology, he devel-
oped Bradwardine's doctrine on ratios to include irra-
tional fractional exponents relating pairs of whole-
number ratios, and proceeded to argue that the ratio
of any two unknown celestial ratios is probably irra-
tional. This probability, in his view, rendered all astro-
logical prediction fallacious in principle. Oresme held
that impetus is not permanent, but is self-expending
in its very production of motion; he apparently associ-
ated impetus with acceleration, moreover, and not with
sustaining a uniform velocity. In discussing falling
bodies, he seems to suggest that the speed of fall is
directly proportional to the time (and not the distance)
of fall, but he did not apply the Mertonian mean-speed
theorem to this case, although he knew the theorem
and in fact gave the first geometrical proof for it.
Further he conceived the imaginary situation of the
earth's being pierced all the way through; a falling
body would then acquire an impétuosité that would
carry it beyond the center, and thereafter would oscil-
late in gradually decreasing amplitudes until it came
to rest. A final and extremely important contribution
was Oresme's use of a two-dimensional figure to plot
a distribution of the intensity of a quality in a subject
or of velocity variation with time (Figure 4). Possibly
this method of graphical representation was antici-
pated by the Italian Franciscan Giovanni di Casali, but
Oresme perfected it considerably, and on this account
is commonly regarded as a precursor of Descartes'
analytic geometry.
