Bernoulli, Johann

▪ Swiss mathematician
born Aug. 6 [July 27, old style], 1667, Basel, Switz.
died Jan. 1, 1748, Basel
 major member of the Bernoulli family of Swiss mathematicians. He investigated the then new mathematical calculus, which he applied to the measurement of curves, to differential equations, and to mechanical problems.

      The son of a pharmacist, Johann studied medicine and obtained his doctor's degree in Basel in 1694, with a thesis on muscular contraction. However, he turned to mathematics despite his father's opposition. In 1691–92 he wrote two texts, not published until later, on differential and integral calculus. In 1692 he taught calculus to the mathematician Guillaume-François-Antoine de L'Hospital, who agreed to pay him for mathematical discoveries. From 1695 to 1705 he taught mathematics at Groningen, Neth., and, on the death of his elder brother, Jakob, assumed a professorship at Basel.

      Johann exceeded his brother in the number of contributions he made to mathematics. He applied calculus to the determination of lengths and areas of curves, such as the isochrone, along which a body will fall at constant speed, and the tautochrone, which was found to be important in clock construction. He also made contributions to the theory of differential equations, the mathematics of ship sails, and optics. Johann sent to L'Hospital in Paris a method or rule for solving problems involving limits that would apparently be expressed by the ratio of zero to zero, now called L'Hospital's rule on indeterminate forms because it was included in L'Hospital's influential textbook of 1696, Analyse des infiniment petits (“Analysis of the Infinitely Small”).

      The Bernoulli brothers often worked on the same problems, but not without friction. Their most bitter dispute concerned finding the equation for the path followed by a particle from one point to another in the shortest time, if the particle is acted upon by gravity alone, a problem originally discussed by Galileo. In 1697 Jakob offered a reward for its solution. Accepting the challenge, Johann proposed the cycloid, the path of a point on a moving wheel, pointing out at the same time the relation this curve bears to the path described by a ray of light passing through strata of variable density. A protracted, bitter dispute then arose when Jakob challenged the solution and proposed his own. The dispute marked the origin of a new discipline, the calculus of variations.

      Ardent in his friendships and keen in his resentments, Johann zealously defended the cause of G.W. Leibniz in the dispute with Isaac Newton over who had originated calculus. His text in integral calculus appeared in 1742 and his differential calculus shortly afterward. During his last years he worked mainly on the principles of mechanics. His works were published in Opera Johannis Bernoullii, 4 vol. (1742).

* * *

Universalium. 2010.

Look at other dictionaries:

  • Bernoulli , Johann I — Bernoulli , Johann (or Jean) I (1667–1748) Swiss mathematician Johann I was the brother of Jakob I Bernoulli and was born in Basel, Switzerland. As in the case of several of the Bernoulli family Johann I s father did not encourage him to make a… …   Scientists

  • Bernoulli — Johann I …   Scientists

  • Johann Bernoulli — (* 27. Julijul./ 6. August 1667greg. in Basel; † 1. Januar 1748 in Basel) war Schweizer Mathematiker und Arzt, der jüngere Bruder von …   Deutsch Wikipedia

  • Johann Bernoulli — Retrato de Johann Bernoulli. Nacimiento 27 de julio de 1667 …   Wikipedia Español

  • Johann II. Bernoulli — (* 18. Mai 1710 in Basel; † 17. Juli 1790 ebenda) war ein Schweizer Mathematiker, Physiker und Jurist aus der berühmten Familie Basler Mathematiker Bernoulli. Leben und Wirken Johann II. Bernoulli war der dritte von fünf Söhnen von Johann… …   Deutsch Wikipedia

  • Johann III. Bernoulli — Johann Bernoulli (* 4. November 1744 in Basel; † 13. Juli 1807 in Berlin) war ein Schweizer Astronom aus der Familie Bernoulli. Johann III. war der älteste Sohn von Johann II. Bernoulli u …   Deutsch Wikipedia

  • Johann Jakob Bernoulli — auf einem Ölgememälde von Ernst Stückelberg aus dem Jahr 1964, im Besitz der Familie Bernoulli Johann Jakob Bernoulli (* 18. Januar 1831 in Basel; † 22. Juli 1913 ebenda) war ein Schweizer Archäologe aus der Gelehrtenfamilie Bernoull …   Deutsch Wikipedia

  • Johann II Bernoulli — Nacimiento 28 de mayo de 1710 Basilea, Confederación Suiza Fallecimiento 17 de julio de 1790 …   Wikipedia Español

  • Johann Bernoulli — Infobox Scientist name = Johann Bernoulli |200px image width = 200px caption = Johann Bernoulli birth date = birth date|df=yes|1667|7|27 birth place = Basel, Switzerland death date = death date and age|df=yes|1748|1|1|1667|7|27 death place =… …   Wikipedia

  • Johann Bernoulli — Jean Bernoulli Pour les articles homonymes, voir Bernoulli. Jean Bernoulli Naissance …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.