BRACHISTOCHRONE (from the Gr.
In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems - (1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P 1, P 2, then AP 1 m +AP 2 m will be constant.
In 1697 John Bernoulli proposed the famous problem of the brachistochrone (see Mechanics), and it was proved by Leibnitz, Newton and several others that the cycloid was the required curve.
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