John Landen (23 January 1719 – 15 January 1790) was an English
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
Peterborough
Peterborough ( ) is a City status in the United Kingdom, cathedral city in the City of Peterborough district in the Ceremonial counties of England, ceremonial county of Cambridgeshire, England. The city is north of London, on the River Nene. A ...
in
Northamptonshire
Northamptonshire ( ; abbreviated Northants.) is a Ceremonial counties of England, ceremonial county in the East Midlands of England. It is bordered by Leicestershire, Rutland and Lincolnshire to the north, Cambridgeshire to the east, Bedfordshi ...
, on 28 January 1719. He was brought up to the business of a surveyor, and acted as land agent to Earl Fitzwilliam, 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
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
valuable investigations on points connected with the fluxionary calculus.
His attempt to substitute for it a purely algebraic method, expounded in book i. of ''Residual Analysis'' was further prosecuted by
Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaLanden's transformation, for expressing 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
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
and
D'Alembert
Jean-Baptiste le Rond d'Alembert ( ; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanics, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''E ...
, 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 January 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
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...
.
Landen was elected a
fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
on 16 January 1766, and was a member of the Spalding Society.
Though foreigners gave him a high rank among English analysts, he failed to develop and combine his discoveries.
He led a retired life, chiefly at Walton in Northamptonshire.
Works
* ''The 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 Stewarts Method of computing the Sun's Distance from the Earth'' (1771)
* ''Mathematical Memoirs'' 1780 1789)