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LANDEN, JOHN (1719–1790), mathematician, was born at Peakirk, near Peterborough in Northamptonshire, on 28 Jan. 1719. He was brought up to the business of a surveyor, and acted as land agent to William Wentworth, earl Fitzwilliam [q. v.], from 1762 to 1788. Cultivating mathematics during his leisure hours, he became a contributor to the ‘Ladies' Diary’ in 1744, published ‘Mathematical Lucubrations’ in 1755, and from 1754 onwards communicated to the Royal Society valuable investigations on points connected with the fluxionary calculus. His attempt to substitute for it a purely algebraical method, expounded in book i. of 'Residual Analysis’ (London, 1784) was further prosecuted by Lagrange Book’ ii. never appeared. The remarkable theorem known by Landen's name, for expessing a hyperbolic arc in terms of two elliptic arcs, was inserted in the ‘Philosophical Transactions’ for 1775, and specimens of its use were given in the first volume of his ‘Mathematical Memoirs’ (1780). In a paper on rotary motion laid before the Royal Society on 17 March 1785 he obtained results differing from those of Euler and D'Alembert, and defending them in the second volume of ‘Mathematical Memoirs' prepared for the press during the intervals of a painful disease, and placed in his hands, printed, the day before his death at Milton, near Peterborough, the seat of the Earl Fitzwilliam on 15 Jan. 1790. In the same work he solved the problem of the spinning of a top, and explained Newton's error in calculating the effects of precession.

Landen was elected a fellow of the Royal Society on 16 Jan. 1766, and was a member of the Spalding Society. Though foreigners gave him a high rank among English analysts, he failed to develope and combine his discoveries. He led a retired life, chiefly at Walton in Northamptonshire. Though humane and honourable, he was too dogmatic in society. Besides the works above mentioned, he wrote: ‘A Discourse concerning the Residual Analysis’ (1758) and ‘Animadversions on Dr. Stewart's computation of the Sun’s Distance from the Earth’ (1771). Papers by him included in ‘Philosophical Transactions,' vols. xlviii. li. lvii. lx. 1xi. lxvii. lxxv.

[Gent. Mag. vol. lx. pt. i. pp. 90, 191; Phil. Trans. Abidged, x. 469 (Hutton); Hutton's Mathematical Dict. 1815; Montucla's Hist. des Mathématiques; iii. 240; Montferrier's Dict. des Mathématiques; Poggendorff's Biographisch-Literarisches Handwörterbuch: Masres Scriptores Logarithmici, ii, 172; Richelot's Die Landensche Transformation in ihrer Anwendung auf die Entwickelung der eliptischen Functionen, 1868; Watt's Bibl. Brit.]

A. M. C.