# Chronology

### 1720 - 1740

#### 1722

- The work unfinished by Cotes on his death is published as
*Harmonia mensurarum*. It deals with integration of rational functions. It contains a thorough treatment of the calculus applied to logarithmic and circular functions.

#### 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. - 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. - 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.
- 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*).