A nice paper on the Brachistochrone which dwelves a little more on J. Bernoulli's approach is: http://www.math.umt.edu/tmme/vol5no2and3/tmme_vol5nos2and3_a1_pp

A nice paper on the Brachistochrone which dwelves a little more on J. Bernoulli's approach is: http://www.math.umt.edu/tmme/vol5no2and3/tmme_vol5nos2and3_a1_pp.169_184.pdf http://www.math.umt.edu/tmme/vol5no2and3/tmme_vol5nos2and3_a...