Electronic edition published by Cultural Heritage Langauge Technologies (with permission from Charles Scribners and Sons) and funded by the National Science Foundation International Digital Libraries Program. This text has been proofread to a low degree of accuracy. It was converted to electronic form using data entry.
JORDANUS DE NEMORE (fl. ca. 1220), mechanics,
mathematics.
from a corruption of “de numeris” or “de numero”
from Jordanus' arithmetic manuscripts.3
Identification of Jordanus de Nemore with Jordanus
de Saxonia (or Jordanus of Saxony), the master
general of the Dominican order from 1222 to 1237,
has been made on the basis of a statement by Nicholas
Trivet (in a chronicle called Annales sex regum
Angliae) that Jordanus of Saxony was an outstanding
scientist who is said to have written a book on weights
and a treatise entitled De lineis datis.4 Although a
late manuscript of a work definitely written by
Jordanus de Nemore is actually ascribed to “Jordanus
de Alemannia” (Jordanus of Germany, and therefore
possibly Jordanus of Saxony), no mathematical or
scientific works can be assigned to Jordanus of
Saxony, whose literary output was seemingly confined
to religion and grammar. At no time, moreover, was
Jordanus of Saxony called Jordanus de Nemore or
Nemorarius. Finally, if Jordanus de Nemore lectured
at the University of Toulouse, as one manuscript
indicates,5 this could have occurred no earlier than
1229, the year of its foundation. As master general of
the Dominican order during the years 1229-1237, the
year of his death, Jordanus of Saxony could hardly
have found time to lecture at a university. For all
these reasons it seems implausible to suppose that
Jordanus of Saxony is identical with Jordanus de
Nemore.
It was in mechanics that Jordanus left his greatest
legacy to science. The medieval Latin “science of
weights” (scientia de ponderibus), or statics, is virtually
synonymous with his name, a state of affairs that has
posed difficult problems of authorship. So strongly
was the name of Master Jordanus identified with the
science of weights that manuscripts of commentaries
on his work, or works, were frequently attributed
to the master himself. Since the commentaries were
in the style of Jordanus, original works by him are
not easily distinguished. At present only one treatise,
the Elementa Jordani super demonstrationem ponderum,
may be definitely assigned to Jordanus. Whether he
inherited the skeletal frame of the Elementa in the
form of its seven postulates and the enunciations of
its nine theorems, for which he then supplied proofs,
is in dispute.6 Indisputable, however, is the great
significance of the treatise. Here, under the concept
of “positional gravity” (gravitas secundum situm), we
find the introduction of component forces into statics.
The concept is expressed in the fourth and fifth
postulates, where it is assumed that “weight is
heavier positionally, when, at a given position, its
path of descent is less oblique” and that “a more
oblique descent is one in which, for a given distance,
there is a smaller component of the vertical.”7 In a
constrained system the effective weight of a suspended
body is proportional to the directness of its descent,
directness or obliquity of descent being measured by
the projection of any segment of the body's arcal path
onto the vertical drawn through the fulcrum of the
lever or balance. It is implied that the displacement
which measures the positional gravity of a weight can
be infinitely small. Thus, by means of a principle of
virtual displacement (since actual movement cannot
occur in a system in equilibrium, positional gravity can
be measured only by “virtual” displacements)
Jordanus introduced infinitesimal considerations into
statics.
These concepts are illustrated in Proposition 2,
where Jordanus demonstrates that “when the beam of
a balance of equal arms is in horizontal position, then
if equal weights are suspended from its extremities, it
will not leave the horizontal position; and if it should
be moved from the horizontal position, it will revert
to it.”8 If the balance is depressed on the side of
B
(see Figure 1),
FIGURE 1
Jordanus argues that it will return to a
horizontal position because weight c at C will be
positionally heavier than weight b at B, a state of
affairs which follows from the fact that if any two
equal arcs are measured downward from C and B,
they will project unequal intercepts onto diameter
FRZMAKYE. If the equal arcs are CD and BG,
Jordanus can demonstrate (by appeal to his Philotegni,
or De triangulis, as it was also called) that the intercept
of arc CD--ZM--is greater than the intercept of arc
BG--KY--and the “positionally” heavier c
will cause
C to descend to a horizontal position. The concept of
positional heaviness, although erroneous when applied
to arcal paths, may have derived ultimately from
application of an idea in the pseudo-Aristotelian