In 1696 Johann Bernoulli posed a puzzle to European mathematicians: derive a curve for motion of a frictionless bead falling between a higher and a lower point in the least possible time. He named the curve the " brachistochrone ", (from brachystos, "shortest", and chronos, "time") Isaac Newton, Gottfried Wilhelm Leibniz and others contributed solutions, and in 1718 Johann Bernoulli published an analysis based on the solution created by his brother James Bernoulli. All of these works, especially the approach taken by the Bernoullis, involved reasoning about small deviations in the path taken by the falling bead. Thus this became the first application of the variational technique, albeit as a special-case rather than an general principle.