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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas

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The fourteenth century marked the high point in
optical experimentation and in the conceptual devel-
opment of mechanics during the late Middle Ages. The
fifteenth and sixteenth centuries served mainly as pe-
riods of transition, where the underlying ideas were
diffused throughout Europe, entered into combination
with those of other cultures, and provided the proxi-
mate setting for the emergence of classical science.


Much of this interplay took place in Italy, although
France and Spain also figured in it to a limited extent.

1. Italy and Renaissance Influences. The tradition
perhaps most opposed to Scholasticism was that of
humanism, with its interest in classical antiquity, its
emphasis on the arts, and its general preference for
Plato over Aristotle. Writers such as Marsilio Ficino
and Erasmus ridiculed, respectively, the Paduan
Schoolmen and the “calculatory sophisms” of their
Parisian counterparts. Their overriding interest in
philology, moreover, led humanists to make much of
original texts, and, even in the case of Aristotle, to
confer unprecedented force on arguments from the
authority of the classical author. Yet they did make
available, in Greek and in accurate translation, the
mathematical and mechanical treatises of Euclid,
Archimedes, Apollonius, Pappus, Diophantus, and
Ptolemy—works that perforce had a salutary effect in
preparing for the new scientific mentality.

The writings of particular authors also contributed
in different ways to the coming revolution. Nicholas
of Cusa is important for his use of mathematical ideas
in elaborating his metaphysics, which prepared for the
transition, in Koyré's apt expression, “from the closed
world to the infinite universe.” He also placed great
emphasis on measurement, and preserved elements of
the medieval experimental tradition in his treatise on
“Experiments with Scales” (De staticis experi-
)—this despite the fact that most of his experi-
ments are purely fictitious and not one mentions a
numerical result. Leonardo da Vinci is perhaps over-
rated for his contributions to science, since his was
more the mentality of the engineer; his notebooks are
neither systematic nor lucid expositions of physical
concepts. Yet he too supplied an important ingredient,
wrestling as he did with practical problems of me-
chanics with great genius and technical ability. He
brought alive again the tradition of Jordanus Nemo-
rarius and Albert of Saxony, and his speculations on
kinematics and dynamics, if inconclusive, reveal how
difficult and elusive were the conceptual foundations
of mechanics for its early practitioners. Giordano
Bruno may also be mentioned as a supporter and suc-
cessor of Nicholas of Cusa; his works abound in Neo-
Platonism and mysticism, and show a heavy reliance
on Renaissance magic and the Hermetic-Cabalist tra-
dition. Of little importance for mechanics, his ideas
are significant mainly for the support they gave to
Copernicanism and to the concept of an infinite uni-

Of more direct influence, on the other hand, was
work done at the University of Padua under Averroist
and terminist influences. Aristotelianism flourished
there long after it had gone into eclipse at Oxford and
Paris, not so much in subordination to theology as it
was among Thomists, but rather under the patronage
of the Arab Averroës or of Alexander of Aphrodisias,
a Greek commentator on Aristotle. The Averroists
were Neo-Platonic in their interpretation of Aristotle,
whereas the Alexandrists placed emphasis instead on
his original text. Again, at Padua the arts faculty was
complemented not by the theology faculty but by the
inedical faculty; in this more secularized atmosphere
the scientific writings of Aristotle could be studied
closely in relation to medical problems and with much
aid from Arab commentators.

The result was the formation of a new body of ideas
within the Aristotelian framework that fostered, rather
than impeded, the scientific revival soon to be pio-
neered by the Paduan professor, Galileo Galilei.
Among these ideas some were methodological. They


derived from extended discussions of what Galileo
would refer to as the “method of analysis” (metodo
) and the “method of synthesis” (metodo com-
). Writers such as Jacopo Zabarella systema-
tized these results, showing how they could be applied
to detailed problems in physical science, thereby
bringing to perfection the methodology outlined by
Grosseteste, which has already been discussed.

More than a century before Zabarella, Paul of Venice
(Paolo Nicoletti), who had studied at Oxford in the late
fourteenth century, returned to Padua and propagated
Mertonian ideas among his students. A number of these
wrote commentaries on Heytesbury that were pub-
lished and widely disseminated throughout Europe.
Noteworthy is the commentary of Gaetano da Thiene,
who illustrated much of Heytesbury's abstract reason-
ing on uniform and difform motions with examples
drawn from nature and from artifacts that might be
constructed from materials close at hand. As far as is
known this fifteenth-century group performed no ex-
periments or measurements, but they took a step closer
to their realization by showing how “calculatory”
techniques were relevant in physical and medical in-

2. Paris and the Spanish Universities. The Paduan
school exerted considerable influence throughout
northern Italy; it also stimulated a renewed interest
in Mertonian ideas at the University of Paris at the
beginning of the sixteenth century. The group in which
this renewal took place centered around John Major
(or Jean Mair), the Scottish nominalist, who numbered
among his students John Dullaert of Ghent, Alvaro
Thomaz, and Juan de Celaya. Dullaert edited many
of the works of Paul of Venice, while he and the others
were generally familiar with the “calculatory” writings
of Paul's students. Major's group was eclectic in its
philosophy, and saw no inconsistency in making a
fusion of nominalist and realist currents, the former
embracing Oxonian and Parisian terminist thought and
the latter including Thomist and Scotist as well as
Averroist views. The Spaniard Gaspar Lax and the
Portuguese Alvaro Thomaz supplied the mathematical
expertise necessary to understand Bradwardine's,
Swineshead's, and Oresme's more technical writings.
Several good physics texts came out of this group;
especially noteworthy is that of Juan de Celaya, who
inserted lengthy excerpts from the Mertonians and
Paduans, seemingly as organized and systematized by
Thomaz, into his exposition of Aristotle's Physics
(1517). Celaya treated both dynamical and kinematical
questions, as by then had become the custom, and thus
transmitted much of the late medieval development
in mechanics (statics excluded) to sixteenth-century

Celaya was but one of many Spanish professors at
Paris in this period; these attracted large numbers of
Spanish students, who later returned to Spain and were
influential in modeling Spanish universities such as
Alcalá and Salamanca after the University of Paris. An
edition of Swinehead's Liber calculationum was edited
by Juan Martinez Silíceo and published at Salamanca
in 1520; this was followed by a number of texts written
(some poorly) in the “calculatory” tradition. Theolo-
gians who were attempting to build their lectures
around Thomist, Scotist, and nominalist concepts soon
complained over their students' lack of adequate prep-
aration in logic and natural philosophy. It was such
a situation that led Domingo de Soto, a Dominican
theologian and political theorist who had studied under
Celaya at Paris as a layman, to prepare a series of
textbooks for use at the University of Salamanca.
Among these were a commentary and a “questionary”
on Aristotle's Physics; the latter, appearing in its first
complete edition in 1551, was a much simplified and
abridged version of the type of physics text that was
used at Paris in the first decades of the sixteenth cen-
tury. It reflected the same concern for both realist and
“calculatory” interests, but with changes of emphasis
dictated by Soto's pedagogical aims.

One innovation in Soto's work has claimed the at-
tention of historians of science. In furnishing examples
of motions that are “uniformly difform” (i.e., uniformly
accelerated) with respect to time, Soto explicitly men-
tions that freely falling bodies accelerate uniformly as
they fall and that projectiles (presumably thrown up-
ward) undergo a uniform deceleration; thus he saw the
distance in both cases to be a function of the time of
travel. He includes numerical examples that show he
applied the Mertonian “mean-speed theorem” to the
case of free fall, and on this basis, at the present state
of knowledge, he is the first to have adumbrated the
correct law of falling bodies. As far as is known, Soto
performed no measurements, although he did discuss
what later thinkers have called “thought experiments,”
particularly relating to the vacuum. An extensive sur-
vey of all physics books known to be in use in France
and Spain at the time has failed to uncover similar
instance of this type, and one can only speculate as
to the source of Soto's examples.

3. Italy Again: Galileo. With Soto, the conceptual
development of medieval mechanics reached its term.
What was needed was an explicit concern with meas-
urement and experimentation to complement the
mathematical reasoning that had been developed along
“calculatory” and Archimedean lines. This final devel-
opment took place in northern Italy, again mainly at
Padua, while Galileo was teaching there. The stage was
set by works of considerable mathematical sophis-


tication, under the inspiration of Archimedes, by six-
teenth-century authors such as Geronimo Cardano,
Nicolo Tartaglia, and Giovanni Battista Benedetti. Also
the technical arts had gradually been perfected, and
materials were at hand from which instruments and
experimental apparatus could be constructed.

The person of Galileo provided the catalyst and the
genius to coordinate these elements and educe from
them a new kind of synthesis that would reach perfec-
tion with Isaac Newton. Galileo received his early
university training at Pisa around 1584, where his
student notebooks (Juvenilia) reveal an acquaintance
with many Schoolmen, including Soto, an edition of
whose Physics appeared at Venice in 1582. Galileo used
their terminology in an early treatise On Motion (De
), and only gradually departed from it. His teacher
at Pisa, Francesco Buonamici, himself a classical Aris-
totelian, seemingly gave a muddled account of the
medieval tradition, and it is difficult to know how well
Galileo understood what was presented. Actually this
matters little; what is important is that the ideas that
contributed to the developing science of mechanics
were at hand for himself or another to use. Classical
science did not spring perfect and complete, as Athena
from the head of Zeus, from the mind of Galileo or
any of his contemporaries. When it did arrive, it was
a revolution, and no one can deny this, but it was a
revolution preceded by a strenuous effort of thought.
The genesis of that thought makes an absorbing, if little
known, chapter in the history of ideas.