Oxford Calculators
The key "calculators", writing in the second quarter of the 14th century, were Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton.
[1] Using the slightly earlier works of Walter Burley, Gerard of Brussels, and Nicole Oresme, these individuals expanded upon the concepts of 'latitudes' and what real world applications they could apply them to.
[3] Historian David C. Lindberg and professor Michael H. Shank in their 2013 book, Cambridge History of Science, Volume 2: Medieval Science, wrote:[4] Like Bradwardine's theorem, the methods and results of the other Oxford Calculators spread to the continent over the next generation, appearing most notably at the University of Paris in the works of Albert of Saxony, Nichole Oreseme, and Marsilius of Inghen.Lawrence M. Principe wrote[5]:A group known as the Oxford Calculators had begun applying mathematics to motion in the 1300s; in fact, Galileo begins his exposition of kinematics in the Two New Sciences with a theorem they enunciated.
[6] This, and developing Al-Battani's work on trigonometry is what led to the formulating of the mean speed theorem (though it was later credited to Galileo) which is also known as "The Law of Falling Bodies".
In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since.
Almost immediately, Giovanni di Casale and Nicole Oresme found how to represent the results by geometrical graphs, introducing the connection between geometry and the physical world that became a second characteristic habit of Western thought ...In Tractatus de proportionibus (1328), Bradwardine extended the theory of proportions of Eudoxus to anticipate the concept of exponential growth, later developed by the Bernoulli and Euler, with compound interest as a special case.
Mathematician and mathematical historian Carl Benjamin Boyer writes, "Bradwardine developed the Boethian theory of double or triple or, more generally, what we would call 'n-tuple' proportion".
A group known as the Oxford Calculators had begun applying mathematics to motion in the 1300s; in fact, Galileo begins his exposition of kinematics in the Two New Sciences with a theorem they enunciated.
But Galileo went much further by linking mathematical abstraction tightly with experimental observation.Lindberg and Shank also wrote:In Book VII of Physics, Aristotle had treated in general the relation between powers, moved bodies, distance, and time, but his suggestions there were sufficiently ambiguous to give rise to considerable discussion and disagreement among his medieval commentators.
The most successful theory, as well as the most mathematically sophisticated, was proposed by Thomas Bradwardine in his Treatise on the Ratios of Speeds in Motions.
[4] Before Bradwardine decided to use his own theory of compounded ratios in his own rule he considered and rejected four other opinions on the relationship between powers, resistances, and speeds.
[4] By applying medieval ratio theory to a controversial topic in Aristotle's Physics, Brawardine was able to make a simple, definite, and sophisticated mathematical rule for the relationship between speeds, powers, and resistances.
[4] Bradwardine's Rule was quickly accepted in the fourteenth century, first among his contemporaries at Oxford, where Richard Swineshead and John Dumbleton used it for solving sophisms, the logical and physical puzzles that were just beginning to assume and important place in the undergraduate arts curriculum.
Instead, he proposed a new theory that, in modern terms, would be written as (V ∝ log F/R), which was widely accepted until the late sixteenth century.
The sixteenth-century polymath Girolamo Cardano placed him in the top-ten intellects of all time, alongside Archimedes, Aristotle, and Euclid.
One of his main pieces of work, Summa logicae et philosophiae naturalis, focused on explaining the natural world in a coherent and realistic manner, unlike some of his colleagues, claiming that they were making light of serious endeavors.
