In 1730 he became professor of physics, and in 1733 he succeeded Daniel Bernoulli in the chair of mathematics.

Nicolas Bernoulli (1687-1759), cousin of the three preceding, and son of Nicolas Bernoulli, one of the senators of Basel, was born in that city on the 10th of October 1687.

Six months were allowed by Bernoulli for the solution of the problem, and in the event of none being sent to him he promised to publish his own.

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In 1740 Maclaurin divided with Leonhard Euler and Daniel Bernoulli the prize offered by the French Academy of Sciences for an essay on tides.

The same name is also given to the first positive pedal of any central conic. When the conic is a rectangular hyperbola, the curve is the lemniscate of Bernoulli previously described.

Daniel Bernoulli (1700-1782), the second son of Jean Bernoulli, was born on the 29th of January 1700, at Groningen.

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.

When generalizing the theory of pendulums of Jacob Bernoulli (1654-1705) he discovered a principle of dynamics so simple and general that it reduced the laws of the motions of bodies to that of their equilibrium.

The approximate theory of pipes due to Bernoulli assumes a loop at the open end, but the condition for a loop at the open end, that of no pressure variation, cannot be exactly fulfilled.

Jacques Bernoulli wrote elegant verses in Latin, German and French; but although these were held in high estimation in his own time, it is on his mathematical works that his fame now rests.