1911 Encyclopædia Britannica/Landen, John

LANDEN, JOHN (1719–1790), English mathematician, was born at Peakirk near Peterborough in Northamptonshire on the 23rd of January 1719, and died on the 15th of January 1790 at Milton in the same county. He lived a very retired life, and saw little or nothing of society; when he did mingle in it, his dogmatism and pugnacity caused him to be generally shunned. In 1762 he was appointed agent to the Earl Fitzwilliam, and held that office to within two years of his death. He was first known as a mathematician by his essays in the Ladies’ Diary for 1744. In 1766 he was elected a fellow of the Royal Society. He was well acquainted with the works of the mathematicians of his own time, and has been called the “English d’Alembert.” In his Discourse on the “Residual Analysis,” he proposes to avoid the metaphysical difficulties of the method of fluxions by a purely algebraical method. The idea may be compared with that of Joseph Louis Lagrange’s Calcul des Fonctions. His memoir (1775) on the rotatory motion of a body contains (as the author was aware) conclusions at variance with those arrived at by Jean le Rond, d’Alembert and Leonhard Euler in their researches on the same subject. He reproduces and further develops and defends his own views in his Mathematical Memoirs, and in his paper in the Philosophical Transactions for 1785. But Landen’s capital discovery is that of the theorem known by his name (obtained in its complete form in the memoir of 1775, and reproduced in the first volume of the Mathematical Memoirs) for the expression of the arc of an hyperbola in terms of two elliptic arcs. His researches on elliptic functions are of considerable elegance, but their great merit lies in the stimulating effect which they had on later mathematicians. He also showed that the roots of a cubic equation can be derived by means of the infinitesimal calculus.

The list of his writings is as follows:—Ladies’ Diary, various communications (1744–1760); papers in the Phil. Trans. (1754, 1760, 1768, 1771, 1775, 1777, 1785); Mathematical Lucubrations (1755); A Discourse concerning the Residual Analysis (1758); The Residual Analysis, book i. (1764); Animadversions on Dr Stewart’s Method of computing the Sun’s Distance from the Earth (1771); Mathematical Memoirs (1780, 1789).