Jacob Bernoulli
(1654-1705)

Jacob Bernoulli, also known by the names James, Jacques, and Jakob, was a member of the famous family of mathematicians and scientists of Basel, Switzerland. He did important work in connection with elastic curves of beams and was a pioneer in the theory of plate bending and plate vibrations. He was the first to determine that beam curvature is proportional to the bending moment. Bernoulli also developed polar coordinates and became famous for his work in theory of probability, analytic geometry, and other fields.

Another member of the Bernoulli family, Daniel Bernoulli (1700-1782), proposed to Euler that he obtain the differential equation of the deflection curve by minimizing the strain energy, which Euler did. Daniel Bernoulli, a nephew of Jacob Bernoulli, is renowned for his work in hydrodynamics, kinetic theory of gases, beam vibrations, and other subjects. His father, John Bernoulli (1667-1748), a younger brother of Jacob, was an equally famous mathematician and scientist who first formulated the principle of virtual displacements, solved the problem of the brachystochrone, and established the rule for obtaining the limiting value of a fraction when both the numerator and denominator tend to zero. He communicated this last rule to G. F. A. de l’Hôpital (1661-1704), a French nobleman who wrote the first book on calculus (1696) and included this theorem, which consequently became known as L’Hôpital’s rule.

From Mechanics of Materials, 4th Ed., by J.M. Gere and S.P. Timoshenko, PWS Publishing, 1997, pp. 835-42.