ALIMONY

Molvre, Stirling, Simpson, and others. The nature and composition of algebraic equations has been fully investigated, and the methods of approximating to their roots reduced to order and system. The investigation of the relations of angular sections, begun by Vieta, conducted Kuler to the arithmetic of sines and a complete theory of plane and spherical trigonometry. Applied to problems concerning the motion of bodies or points, algebra has given rise to the doctrine of fluxions, and the refined methods of the differential and integral calculus. It has completely superseded the use of the elegant, but comparatively feeble, ancient analysis, and may be now regarded as forming the basis of the whole edifice of mathematical science. {See Binomial Theorem, Equation, Notation.) [s. 44]