## Bernoulli Sentence Examples

**Bernoulli**, Die erhaltenen Darstellungen Alexanders d.- 1 3p6xcv-ros, shortest, and Xpovos, time), a term invented by John
**Bernoulli**in 1694 to denote the curve along which a body passes from one fixed point to another in the shortest time. **Bernoulli**, this theory was advanced by the successive labours of John Herapath, J.- Xnyviaicos, ribbon), a quartic curve invented by Jacques
**Bernoulli**(Acta Eruditorum, 1694) and afterwards investigated by Giulio Carlo Fagnano, who gave its principal properties and applied it to effect the division of a quadrant into 2 2 m, 3.2 m and 5.2 m equal parts. - The lemniscate of
**Bernoulli**may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points. - 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. - In 1740 Maclaurin divided with Leonhard Euler and Daniel
**Bernoulli**the prize offered by the French Academy of Sciences for an essay on tides. - In Bode's Jahrbuch (1776-1780) he discusses nutation, aberration of light, Saturn's rings and comets; in the Nova acta Helvetica (1787) he has a long paper "Sur le son des corps elastiques," in
**Bernoulli**and Hindenburg's Magazin (1787-1788) he treats of the roots of equation and of parallel lines; and in Hindenburg's Archiv (1798-1799) he writes on optics and perspective. - Diophantine problems were revived by Gaspar Bachet, Pierre Fermat and Euler; the modern theory of numbers was founded by Fermat and developed by Euler, Lagrange and others; and the theory of probability was attacked by Blaise Pascal and Fermat, their work being subsequently expanded by James
**Bernoulli**, Abraham de Moivre, Pierre Simon Laplace and others. - It was investigated by Galileo, who erroneously determined it to be a parabola; Jungius detected Galileo's error, but the true form was not discovered until 1691, when James
**Bernoulli**published it as a problem in the Aeta Eruditorum. **Bernoulli**also considered the cases when (I) the chain was of variable density, (2) extensible, (3) acted upon at each point by a force directed to a fixed centre.- These curves attracted much attention and were discussed by John
**Bernoulli**, Leibnitz, Huygens, David Gregory and others. - In 1738 Daniel
**Bernoulli**(1700-1782) published his Hydrodynamica seu de viribus et motibus fluidorum commentarii. - Colin Maclaurin (1698-1746) and John
**Bernoulli**(1667-1748), who were of this opinion, resolved the problem by more direct methods, the one in his Fluxions, published in 1742, and the other in his Hydraulica nunc primum detecta, et demonstrata directe ex fundamentis pure mechanicis, which forms the fourth volume of his works. - The method employed by Maclaurin has been thought not sufficiently rigorous; and that of John
**Bernoulli**is, in the opinion of Lagrange, defective in clearness and precision. - The theory of Daniel
**Bernoulli**was opposed also by Jean le Rond d'Alembert. - 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. - He made use of the same suppositions as Daniel
**Bernoulli**, though his calculus was established in a very different manner. - Newton gave no proof, and it was in the Ars Conjectandi (1713) that James
**Bernoulli's**proof for positive integral values of the exponent was first published, although**Bernoulli**must have discovered it many years previously. **BERNOULLI**, or Bernouilli, the name of an illustrious family in the annals of science, who came originally from Antwerp. Driven from their country during the oppressive government of Spain for their attachment to the Reformed religion, thesought first an asylum at Frankfort (1583), and afterwards at Basel, where they ultimately obtained the highest distinctions.**Bernoullis**- Jacques
**Bernoulli**(1654-I 705), mathematician, was born at Basel on the 27th of December 1654. - Jacques
**Bernoulli**cannot be strictly called an independent discoverer; but, from his extensive and successful application of the calculus and other mathematical methods, he is deserving of a place by the side of Newton and Leibnitz. - 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. - These are: - Jacobi
**Bernoulli**Basiliensis Opera (Genevae, 1 744), 2 tom. - [[Jean
**Bernoulli**]] (1667-1748), brother of the preceding, was born at Basel on the 27th of July 1667. - His dissertation on the "barometric light," first observed by Jean Picard, and discussed by Jean
**Bernoulli**under the name of mercurial phosphorus, or mercury shining in vacuo (Diss. - His writings were collected under his own eye by Gabriel Cramer, professor of mathematics at Geneva, and published under the title of Johannis
**Bernoulli**Operi Omnia (Lausan. - Leibnitii et Johannis
**Bernoulli**Commercium Philosophicum et Mathematicum (Lausan. - Nicolas
**Bernoulli**(1695-1726), the eldest of the three sons of Jean**Bernoulli**, was born on the 27th of January 1695. - Daniel
**Bernoulli**(1700-1782), the second son of Jean**Bernoulli**, was born on the 29th of January 1700, at Groningen. - With a success equalled only by Leonhard Euler, Daniel
**Bernoulli**gained or shared no less than ten prizes of the Academy of Sciences of Paris. - The problem of vibrating cords, which had been some time before resolved by Brook Taylor (1685-1731) and d'Alembert, became the subject of a long discussion conducted in a generous spirit between
**Bernoulli**and his friend Euler. - Jean
**Bernoulli**(1710-1790), the youngest of the three sons of Jean**Bernoulli**, was born at Basel on the 18th of May 1710. - 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. - Jean
**Bernoulli**' (1744-1807), grandson of the first Jean**Bernoulli**, and son of the second of that name, was born at Basel on the 4th of November 1744. - Jacques
**Bernoulli**(1759-1789), younger brother of the preceding, and the second of this name, was born at Basel on the 17th of October 1759. - 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. - Although Bessel was the first to systematically treat of these functions, it is to be noted that in 1732 Daniel
**Bernoulli**obtained the function of zero order as a solution to the problem of the oscillations of a chain suspended at one end. - On Pliny's supposed portrait, see
**Bernoulli**, Rom. - Stauffacher (Basel, 1899) August
**Bernoulli**, and in his elaborate Geschichte d. - This is (in part) the celebrated principle of virtual velocities, now often described as the principle of virtual work, enunciated by John
**Bernoulli**(1667-1748). - 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. - The investigation of caustics, being based on the assumption of the rectilinear propagation of light, and the validity of the experimental laws of reflection and refraction, is essentially of a geometrical nature, and as such it attracted the attention of the mathematicians of the 17th and succeeding centuries, more notably John
**Bernoulli**, G. **Bernoulli**, Aphrodite (1873); W.- His mathematical genius gained for him a high place in the 'esteem of Jean
**Bernoulli**, who was at that time one of the first mathematicians in Europe, as well as of his sons Daniel and Nicolas**Bernoulli**. - In 1730 he became professor of physics, and in 1733 he succeeded Daniel
**Bernoulli**in the chair of mathematics. - The Academy of Sciences at Paris in 1738 adjudged the prize to his memoir on the nature and properties of fire, and in 1740 his treatise on the tides shared the prize with those of Colin Maclaurin and Daniel
**Bernoulli**- a higher honour than if he had carried it away from inferior rivals. **Bernoulli**, Winkelrieds That bei Sempach (Basel, 1886); W.- Newton's solution of the celebrated problems proposed by John
**Bernoulli**and Leibnitz deserves mention among his mathematical works. - In June 1696
**Bernoulli**addressed a letter to the mathematicians of Europe challenging them to solve two problems - (1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P 1, P 2, then AP 1 m +AP 2 m will be constant.