Life. Cauchy’s father, Louis-François Cauchy, was born in Rouen in 1760. A brilliant student of classics at Paris University, after graduating he established himself as a barrister at the parlement of Normandy. At the age of twenty-three he became secretary general to Thiroux de Crosnes, the intendant of Haute Normandie. Two years later he followed Thiroux to Paris, where the latter had been appointed to the high office of lieutenant de police.
Louis-François gradually advanced to high administrative positions, such as that of first secretary to the Senate. He died in 1848. In 1787 he married Marie-Madeleine Desestre, who bore him four sons and two daughters. She died in 1839. Of their daughters, Thérèse died young and Adèle married her cousin G. de Neuburg. She died in 1863. The youngest son, Amédée, died in 1831, at the age of twenty-five; Alexandre (1792–1857) held high judicial posts; and Eugène (1802–1877) held administrative posts and became known as a scholar in the history of law. Augustin was the eldest child.
Cauchy enjoyed an excellent education; his father was his first teacher. During the Terror the family escaped to the village of Arcueil, where they were neighbors of Laplace and Berthollet, the founders of the celebrated Société d’Arcueil. Thus, as a young boy Augustin became acquainted with famous scientists. Lagrange is said to have forecast his scientific genius while warning his father against showing him a mathematical text before the age of seventeen.
Figures & Tables
In this chapter, we give a brief synopsis of each of the classic papers referred to in this collection. Where relevant, we reproduce the basic equations, recast in modern notation. Supporting works also are referred to. They are listed in the “General References” section.
Table 1 is a quick outline of the key contributions of each paper reprinted in this book.
Robert Hooke, “Potentia Restitutiva, or Spring” (Oxford, 1678)
The article by Robert Hooke, “Potentia Restitutiva, or Spring,” contains the statement of the proportional relation between stress and strain universally referred to as Hooke’s law. Although the English language has evolved somewhat since 1678, the article does not require translation. Hooke describes a variety of experiments, accompanied by illustrations, confirming the stress/strain relation over a wide range of applied loads. He emphasizes the great generality of his results.
Based on his experimental work from 1660 onward, Hooke first published his law in 1676 in the form of an anagram in Latin,
which he later revealed to be “ut tensio sic vis.” Roughly translated, this means “as the force, so is the displacement” (Love, 1911; Boyce and DiPrima, 1976).
In his treatise, Hooke examined the behavior of springs, so his first casting of the equations dealt with the restoring force on a spring, for a given displacement: