LANDEN, JOHN

born Jan. 23, 1719, Peakirk, Northamptonshire, Eng. died Jan. 15, 1790, Milton, Northamptonshire British mathematician who made important contributions on elliptic integrals. Landen became known as a mathematician by his essays in The Ladies' Diary for 1744, and he was elected a fellow of the Royal Society of London in 1766. His researches on elliptic integrals are remembered for Landen's point and Landen's transformations. The theorem known by his name appeared in his memoir of 1775 and later was included in the first volume of his Mathematical Memoirs, 2 vol. (178089). Landen's theorem expresses the arc of a hyperbola in terms of the arcs of two ellipses. Landen also wrote on a variety of subjects, including astronomy and physics. He made early contributions to the study of rotary motion and explained a minor error Newton had made in calculating the effects of precession (the slow rotation of a rotating body's axis). In A Discourse Concerning the Residual Analysis (1758), Landen tried to rid calculus of the difficult concept of infinitesimals by basing it on the accepted principles of algebra and geometry.