Mean speed theorem

Source: Wikipedia, the free encyclopedia.
Not to be confused with
The Merton Rule
.

Oresme's geometric verification of the Oxford Calculators' Merton Rule of uniform acceleration, or mean speed theorem.
Oresme
had made centuries earlier.

The mean speed theorem, also known as the Merton rule of

Merton College, and was proved by Nicole Oresme. It states that a uniformly accelerated body (starting from rest, i.e. zero initial velocity) travels the same distance as a body with uniform speed whose speed is half the final velocity of the accelerated body.[2]

Details

Oresme provided a geometrical verification for the generalized Merton rule, which we would express today as (i.e., distance traveled is equal to one half of the sum of the initial and final velocities, multiplied by the elapsed time ), by finding the area of a

motion and anticipate the theorem by 14 centuries.[4]

The medieval scientists demonstrated this theorem—the foundation of "

Galileo, who is generally credited with it. Oresme's proof is also the first known example of the modelization of a physical problem as a mathematical function with a graphical representation, as well as of an early form of integration, thus laying the foundation of calculus. The mathematical physicist and historian of science Clifford Truesdell, wrote:[5]

The now published sources prove to us, beyond contention, that the main

uniformly accelerated motions, still attributed to Galileo by the physics texts, were discovered and proved by scholars of Merton college.... In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. The work was quickly diffused into France, Italy, and other parts of Europe. 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 ...

The theorem is a special case of the more general kinematics equations for uniform acceleration.

See also

Notes

  1. ^ Edward Grant A Source Book in Medieval Science (1974) Vol. 1, p. 252.
  2. ISBN 978-0-486-60509-8
    .
  3. ^ C. H. Edwards, Jr., The Historical Development of the Calculus (1979) pp. 88-89.
  4. S2CID 206644971
    .
  5. ^ Clifford Truesdell, Essays in The History of Mechanics, (Springer-Verlag, New York, 1968), p. 30

Further reading

  • Sylla, Edith (1982) "The Oxford Calculators", in Kretzmann, Kenny & Pinborg (edd.), The Cambridge History of Later Medieval Philosophy.
  • Longeway, John (2003) "William Heytesbury", in The Stanford Encyclopedia of Philosophy.
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