Developments in kinematics and dynamics in England between 1328 and 1350 exercised a deep influence on late medieval physics and natural philosophy in Western Europe, which flourished in the fourteenth and subsequent centuries.

Thomas Bradwardine’ Bradwardine, Thomas
Treatise on Proportions
Treatise on Proportions (Bradwardine) of 1328 proposing his dynamic law of movement began a period of intense speculation in natural philosophy at Merton College, Oxford. Speculation in natural philosophy, or physics, was still associated closely in the late medieval period with classical scientists as well as their Greek and Arabic commentators whose works gradually appeared in the Latin West after the twelfth century. [kw]Flowering of Late Medieval Physics (1328-1350)
[kw]Physics, Flowering of Late Medieval (1328-1350)
Physics
Europe (general);1328-1350: Flowering of Late Medieval Physics[2740]
Science and technology;1328-1350: Flowering of Late Medieval Physics[2740]
Bradwardine, Thomas
Heytesbury, William
Swineshead, Richard
Dumbleton, John
Buridan, Jean
Oresme, Nicholas
Albert of Saxony

Of first importance was Aristotle Aristotle , whose Physica (335-323 b.c.e.; Physics, 1812), widely known and commented on in antiquity and the later medieval period, would serve as a fundamental text for students well into the seventeenth century. According to Aristotle, all things were composed of matter and form. From his postulates that the form of a substance determines its essence, that each substance has a natural inclination that dominates all the changes or movements it experiences, and that every motion presupposes a mover, Aristotle propounded a dynamic law of movement postulating that the velocity of a moving body is directly proportional to the moving force and inversely proportional to the resistance of the medium traversed. Aristotle’s law implied that in a vacuum movement would take place instantaneously since the density, hence the resistance, of the medium would be zero. The impossibility of an instantaneous movement led Aristotle, in turn, to deny the existence of a vacuum.

In the sixth century, John Philoponus John Philoponus , in attempting to demonstrate that movement in a vacuum was possible, criticized Aristotle’s dynamic law. In place of Aristotle’s assertion that velocity was indirectly proportional to the resistance, he proposed that velocity was proportional to the motive force (referred to by late medieval scholars as “impetus”) minus the resistance. Accordingly, movement in a vacuum was possible because the absence of a resisting medium merely reduced arithmetically the time needed to move through a given space. Philoponus’s views were transmitted to the West indirectly through Averroës Averroës ’s commentary on Aristotle’s Physica, which rejected criticism of Aristotle’s law made by Avempace (a twelfth century Arabian scholar living in Spain) who repeated the views of Philoponus.

The Ptolemaic universe as explained by Johann Müller (Regiomantus), a wood engraving in Epitome … Johannes de Monte Regio (1543).

(Frederick Ungar Publishing Co.)

Not until Bradwardine’s Treatise on Proportions was an attempt made to reformulate Aristotle’s law in precise mathematical language. Bradwardine followed Aristotle and Averroës in characterizing the relationship between force and resistance, the parameters determining velocity, as a kind of proportion or ratio. In so doing, he rejected Avempace’s and Aquinas’s postulations of a law of simple arithmetical difference. Moreover, Bradwardine went beyond earlier treatments of the Aristotelian dynamic law of movement by giving it a mathematical expression that adequately reflected the observed results in cases in which the motive force is equal to or less than the resistance. In such critical cases, the simple Aristotelian proportion yielded erroneous conclusions. While Aristotle’s law would predict some value greater than zero when force and resistance are equal, the velocity would in fact be zero. Even though Bradwardine used the medieval language of proportions, he expressed results more or less equivalent to the exponential function used today to define velocity.

Averroës and his school at Córdoba in the thirteenth century played a key role in transmitting the works of Aristotle and other Greek and Arab scientists to the West.

(Library of Congress)

The importance of this application of mathematical reasoning to problems of dynamics must not be underestimated. Bradwardine was followed at Merton College by such distinguished natural philosophers as William Heytesbury, Heytesbury, William Richard Swineshead, Swineshead, Richard and John Dumbleton Dumbleton, John , scholars who made significant contributions to medieval kinematics. Furthermore, interest spread to Paris, where it stimulated the work of Jean Buridan Buridan, Jean , of his pupil Nicholas Oresme, Oresme, Nicholas and of Albert of Saxony Albert of Saxony . All these scholars helped to impart to late medieval physics a characteristic form perceptible in the key physical problems discussed, such as the laws of falling bodies, the principle of inertia, and the question of the center of gravity, as well as in the extensive use of the logical-mathematical methods of analysis and measurement. The brilliant Oresme, who was a precursor of Descartes in the development of analytical geometry, in emphasizing the daily rotation of the earth introduced a basic alteration of Ptolemaic cosmology. The scientific ferment also spread to the universities of Italy. The ardent fifteenth century German Humanist Nicholas of Cusa Nicholas of Cusa , in doubting the geocentric theory and in proposing that the Earth moved in rhythm with the heavens, helped to form the tradition against which the physics of Galileo developed as well as the doctrines of relativity in space and motion supported later by Bruno.

Science in the late Middle Ages had its last great exponent in Johann Müller, Müller, Johann or Regiomontanus, and his school at Nuremberg in the latter half of the fifteenth century. His work in mathematics became the basis of trigonometry in western Europe as previously it was developed in the Arab world, and his scientific astronomical observations and charts were used by Columbus.

The significance of the intellectual events described here for the study of the history of science lies in the fact that until the beginning of the twentieth century it was universally taken for granted that the history of modern mechanics began with Galileo, at the beginning of the seventeenth century. However, beginning at the turn of the twentieth century, the outstanding French historian and philosopher of science, Pierre Duhem, himself a physicist of first rank, uncovered the largely forgotten work of the Oxford and Parisian scholars here described. He then proposed the view that the scientific revolution, at least in mechanics, really began in the fourteenth century. This view ascribes to Galileo a much less dominant role than usually accepted. Duhem’s thesis has been vigorously opposed by other scholars, and the dispute continues.

• Clagett, Marshall. Giovanni Marliani and Late Medieval Physics. Reprint. New York: AMS Press, 1967. This study deals with the problems of heat reaction and includes a discussion of Marliani’s reaction to kinematic and dynamic developments at Oxford and Paris.
• Clagett, Marshall. The Science of Mechanics in the Middle Ages. Madison: University of Wisconsin Press, 1959. A fundamentally important work to the student of medieval mechanics that discusses the Aristotelian tradition and aspects of late medieval dynamics. The last section dealing with “The Fate and Scope of Medieval Mechanics” summarizes both the spread of the English and French physics, and the overall accomplishments of medieval mechanics, a study originally aided by concepts from scholastic philosophy.
• Clagett, Marshall, and Ernest Moody. The Medieval Science of Weights. Madison: University of Wisconsin Press, 1952. A comprehensive survey of medieval statics, containing numerous texts and translations in addition to commentaries.
• Crombie, A. C. Augustine to Galileo: The History of Science A.D. 400-1650. 1952. Rev. ed., Medieval and Early Modern Science. London: Heinemann, 1962. This work is an excellent introduction to medieval science as a whole, but it should be supplemented by more technical literature.
• Dijksterhuis, E. J. The Mechanization of the World Picture. London: Oxford University Press, 1961. A work especially helpful in explaining the terms “intension” and “remission.”
• Golino, C. Q., ed. Galileo and His Precursors. Berkeley: University of California Press, 1966. See especially the chapter “Galileo Reappraised,” by Ernest Moody.
• Molland, A. G. “The Geometrical Background to the ’Merton School’: An Exploration into the Application of Mathematics to Natural Philosophy in the Fourteenth Century.” British Journal for the History of Science 4 (1968): 108-125. Outlines important features in the introduction of mathematical methods of analysis to fourteenth century natural philosophy.
• Murdoch, John E. “The Medieval Science of Proportions: Elements of the Interaction with Greek Foundations and the Development of New Mathematical Techniques.” In Scientific Change, edited by A. C. Crombie. London: Heinemann, 1963. An important article dealing with the medieval language of proportions.
• Shank, Michael H. The Scientific Enterprise in Antiquity and the Middle Ages. Chicago: University of Chicago Press, 2000. This anthology of essays in the history of science includes articles on Bradwardine and medieval mechanical knowledge.
• Sylla, Edith D. “Thomas Bradwardine’s De Continuo and the Structure of Fourteenth-Century Learning.” In Texts and Contexts in Ancient and Medieval Science. New York: Brill, 1997. An examination of scientific scholarship and education using Bradwardine’s work as a case study.