Elements of Algebra

EULER. XV and Analysis. Whatever physical inquiry he began with, this always came in view, and very frequently received more of his attention than that which was professedly the main subject. His ideas ran so naturally in this train, that even in the perusal of Virgil's poetry, he met with images that would recall the associations of his more familiar studies, and lead him back, from the fairy scenes of fiction, to mathematical abstraction, as to the element, most congenial to his nature. That the sources of analysis might be ascertained in their full extent, as well as the various modifications of form and restrictions of rule that become necessary in applying it to different views of nature; he appears to have nearly gone through a complete course of philosophy. The theory of rational mechanics, the whole range of physical astronomy, the vibrations of elastic fluids, as well as the movements of those which are incompressible, naval architecture and tactics, the doctrine of chances, probabilities, and political arithmetic, were successively subjected to the analytical method; and all these sciences received from him fresh confirmation and further improvement*. It cannot be denied that, in general, his attention is more occupied with the analysis itself, * A complete edition of his works, comprising the numerous papers which he sent to the academies of St. Petersburg, Berlin, Paris, and other public societies, his separate Treatises on Curves, the Analysis of Infinites, the differential and integral Calculus, &c. would occupy, at least, forty quarto volumes.