by A. M. Clerke, rev. Marco Panza

© Oxford University Press 2004 All rights reserved

**Landen, John** (1719-1790), mathematician, was born on 23 January 1719, at Peakirk, near Peterborough, Northamptonshire, the son of Matthew Landen and Elizabeth Cole *(d.* 1750). He was brought up to the business of a surveyor, and he practised at Peterborough from 1740 to 1762. From 1762 to 1788 he acted as land agent to William Fitzwilliam, Earl Fitzwilliam (1748-1833). Cultivating mathematics during his leisure hours, he was a contributor to the *Ladies' Diary* from 1744 to 1772. He published eight papers in the *Philosophical Transactions of the Royal Society* between 1754 and 1785, which particularly concerned series, areas of curvilinear figures, rectification, and rotatory motion. In 1755 he published *Mathematical Lucubrations,* and in 1764 *The Residual Analysis,* book 1 (book 2 never appeared), which followed *A Short Discourse Concerning the Residual Analysis* (1758). In these last two works he attempted to replace the fluxional calculus with an analytic method 'founded entirely on the *anciently received* principles of algebra' *(Short Discourse,* 5). According to Lacroix this was the first attempt to reduce the infinitesimal calculus to 'purely algebraic notions' (S. F. Lacroix, *Traité Du calcul différentiel,* 2nd edn, 1810-19, 1.237). Lagrange evoked Landen's theory at the very beginning of his *Théorie des fonctions analytiques* (1797) but judged it jejune and embarrassing.

The remarkable theorem, known by Landen's name, for expressing a hyperbolic arc in terms of two elliptic arcs was inserted in the *Philosophical Transactions* for 1775, and formed a worthy conclusion to researches opened in the *Transactions* of 1771. This theorem forms one of the foundation stones of the theory of elliptic functions and was generally cited in eighteenth-century literature on the subject. Specimens of its use were given in the first volume of Landen's *Mathematical Memoirs* (1780). In a paper on rotatory motion laid before the Royal Society on 17 March 1785 Landen obtained results differing from those of Euler and D'Alembert, and he defended 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. 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 member of the Spalding Society in 1761 and a fellow of the Royal Society on 16 January 1766. Although continental mathematicians gave him a high rank among English analysts, he failed to develop and combine his discoveries. Humane and honourable as an individual, he was dogmatic in society. He led a retired life, chiefly at Walton in Northamptonshire. With his wife, Elizabeth *(d.* 1789), he had two daughters. He died at Milton (the seat of the Fitzwilliam family), near Peterborough, on 15 January 1790, and was buried at Castor church, Northamptonshire.

A. M. CLERKE, *rev.* MARCO PANZA

**Sources **

*GM,* 1st ser., 60 (1790), 90, 191-5

C. Hutton, *Philosophical and mathematical dictionary* (1815)

H. G. Green and H. J. J. Winter, 'John Landen, FRS (1719-1790)--mathematician', *Isis,* 35 (1944), 6-10

G. N. Watson, 'The marquis and the land-agent', *Mathematical Gazette,* 17 (1933), 5-17

H. J. J. Winter, 'John Landen FRS (1719-1790)', *Annual Report of the Peterborough Natural History, Scientific, and Archaeological Society* (1943), 3-14

N. Guicciardini, *The development of Newtonian calculus in Britain* (1989)

F. Cajori, *A history of the conceptions of limits and fluxions in Great Britain from Newton to Woodhouse* (1919)

L. J. Montucla, *Histoire des mathématiques,* 2nd edn, 3 (1793-1802), 240

J. C. Poggendorf, *Biografisch-literarisches Handwörterbuch zur Geschichte der exakten Wissenschaften,* 1 (1863), col. 1364-1365

GEC, *Peerage*

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