Mean speed theorem
In the 14th-century, the Oxford Calculators of Merton College and French collaborators such as Nicole Oresme proved the mean speed theorem, also known as the Merton Rule of uniform acceleration, or the Merton mean speed theorem. It essentially says 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. Oresme essentially 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 trapezoid. Clay tablets used in Babylonian astronomy (350–50 BC) present trapezoid procedures for computing Jupiter's position and motion and anticipate the theorem by 14 centuries.
The medieval scientists demonstrated this theorem — the foundation of "The Law of Falling Bodies" — long before Galileo, who is generally credited with it. The mathematical physicist and historian of science Clifford Truesdell, wrote:
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