Calculations in Oxford – Wikipedia

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From Wikipedia, Liberade Libera.

Richard Swineshead, Calculator , 1520
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I Oxford Calculates They were a group of fourteenth century thinkers – almost all enrolled in the Oxford Merton College – which was why “Merton’s school” were nicknamed. They adopted a strong logical-mathematical approach, applying it to philosophical problems. The most important “calculators” whose treaties date back to the first half of the fourteenth century – were Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton. They were based on previous works by Walter Burley and Gerardo di Brussels.

The progress made by these thinkers were initially of a purely mathematical nature, but later they became relevant also in the field of mechanics. They mainly made use of Aristotelian logic and physics. They also studied and attempted to quantify every single observable physical entity, such as heat, strength, color, density and light. Aristotle was convinced that only the length and motion could be quantifiable. Oxford’s calculators referred precisely to his thought showing its unreliability, being able to calculate physical properties such as temperature and power. [first] They developed the work of Al-Battani on the trigonometry and their best known contribution was the average speed theorem [2] – although attributed subsequently to Galileo – and better known as “the Law of fall of the serious”. [3] Despite the attempt to quantify the observable entities, their main interests were stored more in philosophy and logic than in the natural world. They used the numbers to refute philosophically and to demonstrate the “why” and not only the “how” something works in a certain way. [4]

Oxford’s calculators distinguished kinematics from dynamics, attributing greater importance to the first and investigating instantaneous speed. First of all they formulated the average speed theorem: a body that moves at constant speed travels in the same time span the same distance of an accelerated body if the speed it reached corresponds to the half of the final of the accelerated body.

The mathematical and historical physique of Science Clifford Truesdell, wrote: [5]

“The sources published now show us indisputably as the main kinematic properties of the uniformly accelerated motorcycle – still attributed to Galileo by physics texts – were actually discovered and demonstrated by the students of the Merton school … The characteristics of Greek physics were replaced Basically – at least as regards the motorcycle – from the numerical quantities that have since dominated western science. Their scientific contribution spread rapidly in France, Italy and other parts of Europe. Almost simultaneously, Giovanni da Casale and Nicole Oresme discovered how to represent the results of their research with the help of geometric graphics, thus introducing the connection between geometry and the physical world, which became the second peculiarity of western thought … ”

In the Treaty of proportions (1328) Bradwardine expanded Eudosso’s proportions theory, anticipating the concept of exponential growth – later developed by Bernoulli and Euler – and considering the composed interest as a special case. The arguments relating to the average speed theorem (above) require the modern limit concept, so Bradwardine had to refer to the conjectures of its time.

The mathematician and historian of the mathematics Carl Benjamin Boyer wrote: “Bradwardine developed the Boezian theory of the double or triple proportion or, more generally, what we would call ‘n-sima’ proportion. [6]

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Boyer also argued that “some foundations of trigonometry were contained in Bradwardine’s works”. However “Bradwardine and his Oxford colleagues have not taken any step forward towards modern science”. [7] The missing essential tool was the algebra.

  1. ^ Agutter, Paul S.; Wheatley, Denys N. (2008) “Thinking About Life”
  2. ^ Steven Weinberg, Explain the world. The discovery of modern science , Milan, Mondadori, 2016, p. 154, ISBN 978-88-04-66000-2.
  3. ^ Gavroglu, Kostas; Renn, Jurgen (2007) “Positioning the History of Science”
  4. ^ Paul S. Agutter, and Denys N. Wheetley (A Cura DI), Thinking About Life , Springr, 2008, isbn 978-1-4020-8865-0.
  5. ^ Clifford Truesdell, Essays in The History of Mechanics , (Springer-Verlag, New York, 1968)
  6. ^ Carl B. Boyer, Uta C. Merzbach, A History of Mathematics .
  7. ^ Norman F. Cantor, In the Wake of the Plague: The Black Death and the World it Made , 2001, p.  122 .
  • Sylla, Edith (1999) “Oxford Calculators”, in The Cambridge Dictionary of Philosophy .
  • Gavroglu, Kostas; Renn, Jurgen (2007) “Positioning the History of Science”.
  • Agutter, Paul S.; Wheatley, Denys N. (2008) “Thinking About Life”.
  • M. Clagett, “The science of mechanics in the Middle Ages”, Milan, 1972, Feltrinelli.
  • A. Crombie, “From S. Agostino to Galileo. History of science from the 5th to the 17th century”, Milan, 1970, Feltrinelli.
  • E. Dijksterhuis, “The mechanism and image of the world”, Milan, 1971, Feltrinelli.

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