Lagrange and the secular equation
Résumé
In Lagrange, the mechanical stability of the oscillations of a system of bodies was characterised by the nature of the roots of a specific algebraic equation. The latter was commonly known in the nineteenth century as the “equation to the secular inequalities in plantetary theory” because of its role in the study of the stability of the solar system. It is, in modern terms, the characteristic equation of a symmetrical linear system; its study sheds light on an important part of the history of linear algebra. In the nineteenth century, the secular equation played a pivotal role in both celestial mechanics and in geometry, in complex analysis as well as in arithmetic. This transversality shows that the work of Lagrange was fundamental for the constitution of a culture of algebra that was shared throughout Europe.