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1722

The work unfinished by Cotes on his death is published as

1724

Jacapo Riccati studies the *Riccati differential equation* in a paper. He gives solutions for certain special cases to the equation which was first studied by Jacob Bernoulli.

1724

Academy of Sciences is founded in St Petersburg.

1727

Euler is appointed to St Petersburg. He introduces the symbol *e* for the base of natural logarithms in a manuscript entitled *Meditation upon Experiments made recently on firing of Cannon*. The manuscript was not published until 1862.

1728

Grandi publishes *Flora geometrica* (*Geometrical Flowers*). He gives a geometrical definition of curves which resemble petals and leaves of flowers. For example the *rhodonea curves* are so called since they look like roses while the *clelie curve* is named after the Countess Clelia Borromeo to whom he dedicated his book.

1730

De Moivre gives further theorems concerning his trigonometric representation of complex numbers. He gives Stirling's formula.

1731

Clairaut publishes *Recherches sur les courbes à double coubure* on skew curves.

1733

De Moivre first describes the normal distribution curve, or law of errors, in *Approximatio ad summam terminorum binomii *(*a*+*b*)^{n}* in seriem expansi*. Gauss, in 1820, also investigated the normal distribution.

1733

In *Euclides ab Omni Naevo Vindicatus* Saccheri does important early work on non-euclidean geometry, although he considers it an attempt to prove the parallel postulate of Euclid.

1734

Berkeley publishes *The analyst: or a discourse addressed to an infidel mathematician*. He argues that although the calculus led to true results its foundations were no more secure than those of religion.

1735

Euler introduces the notation *f*(*x*).

1736

Euler solves the topographical problem known as the "Königsberg bridges problem". He proves mathematically that it is impossible to design a walk which crosses each of the seven bridges exactly once.

1736

Euler publishes *Mechanica* which is the first mechanics textbook which is based on differential equations.

1737

Simpson publishes his *Treatise on Fluxions* written as a textbook for his private students. In the book he uses infinite series to find the definite integrals of functions.

1738

Daniel Bernoulli publishes *Hydrodynamica* (*Hydrodynamics*). It gives for the first time the correct analysis of water flowing from a hole in a container and discusses pumps and other machines to raise water. He also gives, in Chapter 10, the basis of the kinetic theory of gases.

1739

D'Alembert publishes *Mémoire sur le calcul intégral* (*Memoir on Integral Calculus*).

1740

Simpson publishes *Treatise on the Nature and Laws of Chance*. Much of this probability treatise is based on the work of de Moivre.

1740

Maclaurin is awarded the Grand Prix of the Académie des Sciences for his work on gravitational theory to explain the tides.

List of mathematicians alive in 1720.

List of mathematicians alive in 1740.

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