1. See Ref. 1–1, pp. 27 and 30–36. (Note: The work of Jacob Bernoulli, Euler, and many others with respect to elastic curves is also described in Ref. 1–2. 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, who wrote the first book on calculus and included this theorem, which today we know as L’Hôpital’s rule; see Ref. 7–2. Daniel’s nephew, Jacob Bernoulli, 1759–1789, who is also known as James or Jacques, was a pioneer in the theory of plate bending and plate vibrations. Much interesting information about the many prominent members of the Bernoulli family, as well as other pioneers in mechanics and mathematics, can be found in books on the history of mathematics; for instance, see Refs. 7–3, 7–4, and 7–5.)
2. Struik, D. J., “The origin of L’Hôpital’s rule,” The Mathematics Teacher, vol. 56, no. 4, April 1963, pp. 257–260.
3. Newman, J. R., The World of Mathematics, Vols. 1–4, Simon and Schuster, New York, 1956, 2469 pages. 7–4
4. Struik, D. J., A Concise History of Mathematics, 4th Ed., Dover Publications, Inc., New York, 1987.
5. Cajori, F., A History of Mathematics, 4th Ed., Chelsea Publishing Co., New York, 1985.