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 day of his death.[45] He dictated to his servant his Anleitung zur Algebra, 1770, which, though purely elementary, is meritorious as one of the earliest attempts to put the fundamental processes on a sound basis.

Euler wrote an immense number of works, chief of which are the following: Introductio in analysin infinitorum, 1748, a work that caused a revolution in analytical mathematics, a subject which had hitherto never been presented in so general and systematic manner; Institutiones calculi differentialis, 1755, and Institutiones calculi integralis, 1768–1770, which were the most complete and accurate works on the calculus of that time, and contained not only a full summary of everything then known on this subject, but also the Beta and Gamma Functions and other original investigations; Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, 1744, which, displaying an amount of mathematical genius seldom rivalled, contained his researches on the calculus of variations (a subject afterwards improved by Lagrange), to the invention of which Euler was led by the study of isoperimetrical curves, the brachistochrone in a resisting medium, and the theory of geodesics (subjects which had previously engaged the attention of the elder Bernoullis and others); the Theoria motuum planetarum et cometarum, 1744, Theoria motus lunæ, 1753, Theoria motuum lunae, 1772, are his chief works on astronomy; Ses lettres à une princesse d'Allemagne sur quelques sujets de Physique et de Philosophie, 1770, was a work which enjoyed great popularity.

We proceed to mention the principal innovations and inventions of Euler. He treated trigonometry as a branch of analysis, introduced (simultaneously with Thomas Simpson in England) the now current abbreviations for trigonometric functions, and simplified formulæ by the simple expedient of designating the angles of a triangle by $\scriptstyle{A}$, $\scriptstyle{B}$, $\scriptstyle{C}$, and the