**1700**in Groningen, the son of Johann Bernoulli and Dorothea Falkner.

In ** 1705 **, at the age of five, his family moved back to Basel, the ostensible reason being for his mother to look after her ailing father (although her father actually lived for several years longer).
His father ended up taking over Jakob's old chair.

In **1713 **
he entered Basel University to study Philosophy and Logic, in line with his father's wishes. He obtained his baccalaureate in **1715**.

In 1716, at the age of 16, he started to study medicine at Basel University.

**1718**
He studied medicine at Heidelberg, and at Strasbourg the year after.

In ** 1720 **
he returned to Basel to complete his doctorate in medicine. He wrote his doctoral thesis on the mechanics of breathing, and was awarded the title in **1721**.
Unable to get a job in Basel (he had applied for vacancies of Professor of Anatomy and Botany and Professor of Logic), in **1723** he undertook a study trip to Venice under the City physikus Pietro Antonio Michelotti(he seems to have been unable to fulfill an original aim to study with G.B.Morgagni in Padua because of illness). While in Venice he became acquainted with the card game of Faro. (wanted to go to Genoa originally)

### Mathematical Exercises

He had worked on mathematics in Venice, which provided the basis for his
*Mathematical Exercises* which was published in 1724 (with assistance from Goldbach) and consisted of four parts

Describes the game of faro

On the flow of water from a hole in a container (discussing also some incorrect theories of Newton)

Riccati Equation

ax

^{n}dx + u^{2}dx = b ducould be integrated through Separation of Variables for the values

c takes on all integral valueslunulae, figures bounded by two circular arcs

### St Petersburg

He went to Petersburg as Professor of Mathematics at the Academy in **1725** (after the death of Peter 1 in the same year), accompanied by his brother Nicolaus. Unfortunately, Nicolaus died 8 months after arriving in Petersburg.

Initially, the academy was accommodated in P. P. Shafirov's house on Gorodskoy Island. In 1728, it moved to the Kunstkammer and the nearby Tsarina Praskovya Fedorovna's Palace on Vasilievsky Island where the Zoological Institute is situated today

Leonhard Euler joined him in **1727**, opening up six years of fruitful mathematical collaboration.
Jakob Hermann had already been there since 1724 but left in 1731.

He determined the shape adopted by a perfectly flexible thread acted upon by two force components, one vertical and one parallel to a given direction. This allowed the derivation of an entire series of curves such as the catenary, velaria and lintearia.

He showed that the movement of strings of musical instruments are composed of an infinite number of harmonic oscillations all superimposed.

Together Bernoulli and Euler investigated the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. To investigate this, Daniel experimented by puncturing the wall of a pipe with a small open ended straw and noted that the height to which the fluid rose up the straw was related to fluid's pressure in the pipe. Soon physicians all over Europe were measuring patients' blood pressure by sticking point-ended glass tubes directly into their arteries. It was not until 1896 that an Italian doctor discovered the method which is used today.

Euler–Bernoulli beam equation

In **1728**, he produced a strictly mechanical theory of muscle contraction (compare Johann's theory of muscle contraction). In the same year he gave the location of the blind spot on the retina.

He left St. Petersburg in **1733**, after an apparently unhappy time (home-sickness etc).

### Hydrodynamica

This work was published in **1738** in Strasbourg, although it had been been completed by **1733**. He had left a draft version with a printer in Petersburg before he left. Hydrodynamics seemes to be a word of his own invention.

He introduced the idea of potential energy and gave a correct analysis of water flowing from a hole in a container, based on the principle of conservation of energy.

Chapter 9 contains a theory of the Screw of Archimedes. and a theory of windmill sails.

Chapter 10 gave a 'kinetic theory of gases' allowing a discussion of the gas laws, and gave (in a primitive form) an equation of state discovered later by Van de Waal. It discussed the pressure conditions in the atmosphere, giving a formula foe relating pressure to altitude. Gave a formula for the flow velocity of air streaming from a small opening.

Chapter 13 A primitive form of Bernoulli Equation is given although 'Bernoulli's equation' itself was given by Euler.

Chapter 13 Force of reaction of a jet of fluid and its reaction on a facing plate. The force of a jet of water on an inclined plane. Discussed applications of jet reactions to the propulsion of ships.

He analysed v α p but Lagrange integral of Euler.
A bad relationship had developed with his father seemingly from the time when they shared first prize from the Paris Academy in **1734**. Now
Johann published his own book *Hydraulica*, claiming many of Daniel's results for himself.

### Basel

He returned to Basel in **1734** and took up the post of Professor of Anatomy and Botany at the University.
In **1743**, he transferred to Physiology. Finally in **1750**, he became Professor of Natural Philosophy (Physics) at Basel, succeeding Benedict Stähelin.

vibrating systems. defined simple modes

**1732** higher modes of oscillation
**1737** investigated mechanical work done by heart

In 1738, he popularized the 'Petersburg Paradox' named because Bernoulli published it in the Commentarii of the Petersburg Academy.

1739 initiated study of music instruments

After B and E emphasizes this and then says all possible initial circumstances are represented as

hence all subsequent motion would be

Euler's paper of 1753 attacked this latter formula.

By 1760 he had discovered Coulomb's law of electrostatics - the law of attraction of static electric charges

He showed the shape of the curve called the lemniscate

(x ^{2} + y^{2} )^{2} = a^{2} (x^{2} - y^{2} )

In the 1760s he discussed medical statistics - the effect of innoculation on mortality resulting from smallpox in the various age groups. He advocated inoculation but d'Alembert criticied the rigor of his methods..

He also continued to produce work on the theory of oscillations and in a paper he gave a beautiful account of the oscillation of air in organ pipes.

1726, Zwei Jahre sp?ter wies er das erste Mal auf die oftmals gew?nschte Zerlegung einer zusammengesetzten Bewegung in Translations- und Rotations-Bewegungen hin. Der Aufbau ?hnelt Lagranges M?chanique Analytique, da alle Ergebnisse als Konsequenz eines einzigen Prinzips erscheinen, in diesem Fall der Energieerhaltung.

A paper followed over the theory of the tides, for which he received a prize from the French Academy, together with Euler und Colin Maclaurin. This paper contained everything that had been known about this topic between the publication of Isaac Newton's *Principia* and the researches of Laplace.

Bernoulli wrote a great number of articles over various mechanical questions, especially on problems connected with swinging strings and the solutions given by Brook Taylor and d’Alembert. He was the first to try and formulate a kinetic theory of gases and tried to explain the Boyle Mariotte Law, named after Robert Boyle and Edme Mariotte.

Essai d'une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l'inoculation pour la prévenir theoretaical analysis of the risks attending innoculation for smallpox

### Grand Prix of the Paris Academy

He won the Paris Academy Prize on the following occasions

**1725**for inventing an hour glass that could be used at sea. This is something he had done while in Venice.**1734**application of his ideas to Astronomy (inclination of planetary orbits to ecliptic), and was judged to be equal first with Johann, his father.-
**1737**joint winner with Poleni. The theme was the best shape for a ship's anchor. There were 3 sections and Johann II won another section. **1740**jointly with Euler and Mclaurin. on Newton's theory of the tides linkings its cause to the attraction of the Moon and Sun.**1743**magnetism - reducing errors made by compass Boussole**1746**magnetism. Three prizes won by Euler, Du Tour and, jointly, Daniel and Johann II Bernoulli**1747**method to determine time at sea when horizon is not visible (had been presented earlier, in 1745)**1751**origin and nature of ocean currents. double prize won by Daniel alone**1753**effects of forces on ships e.g rudder, but large portion dedicated to the number of men required to row a ship (using considerations of the energy that a human body can produce)**1757**proposals for reducing the pitching and tossing of a ship in high seas