Algebra is the analytical method . It has been contrived to facilitate the operations of the understanding, to make reasoning more concise, and to contract into a few lines what would have needed many pages of discussion. In short, to lead by a more convenient, rapid, and unerring method, to the solution of the most complicated questions. But a moment's reflection readily shows us that algebra is a real language. Like all languages it has its representative signs, its methods, its grammar, if I may use this expression. Thus and analytical method is a language, and a language is an analytical method. And these two expressions are, in some sense, synonymous.