Lagrange's Method of Solving Polynomial Roots
Today, by chance, I decided to check out Joseph-Louis Lagrange's works, Oeuvres Lagrange , in particular tome 3. It's a remarkable coincidence, because I have only downloaded one book (tome) of Oeuvres Lagrange, book 3, and for no reason in particular I decided to browse it, finding that the first article relates to the solution of general algebraic and transcendental equations! This is a coincidence because the papers from Euler and Lambert that I've been working on (see Welcome article for now) relate to this very topic, and Lagrange is essentially picking up where Lambert left off, using series to represent the roots of polynomials. Lagrange's paper, Nouvelle méthode pour résoudre les équations littérales par le moyen des séries (Mémoires de l'Académie royale des Sciences et Belles-Lettres de Berlin, t. XXIV, 1770) does a far superior job to Lambert's series solution of the same problem, because Lambert's series could only determine any power of ...