(i) to determine the brachistochrone, and
(ii) to find a curve such that if any line drawn from a fixed point O cut it in P and Q then OP^n+OQ^n would be constant.
Leibnitz solved the first of these questions after an interval of rather more than six months, and then suggested that they be sent as a challenge to Newton and others. Newton received the problems on Jan. 29, 1697, and the next day gave the complete solutions to both, at the same time generalising the second question. An almost exactly similar case occurred in 1716 when Newton was asked to find the orthogonal trajectory of a family of curves. In five hours Newton solved the problem in the form in which it was propounded to him, and laid down the principles for finding trajectories i.e integral calculus
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