John Landen
Encyclopedia
John Landen was an English
mathematician
,
He was born at Peakirk near Peterborough
in Northamptonshire
, and died 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 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 algebraic 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 Landen's transformation
(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 function
s 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
.
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
,
He was born at Peakirk near Peterborough
Peterborough
Peterborough is a cathedral city and unitary authority area in the East of England, with an estimated population of in June 2007. For ceremonial purposes it is in the county of Cambridgeshire. Situated north of London, the city stands on the River Nene which flows into the North Sea...
in Northamptonshire
Northamptonshire
Northamptonshire is a landlocked county in the English East Midlands, with a population of 629,676 as at the 2001 census. It has boundaries with the ceremonial counties of Warwickshire to the west, Leicestershire and Rutland to the north, Cambridgeshire to the east, Bedfordshire to the south-east,...
, and died 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
Earl FitzWilliam
Earl Fitzwilliam was a title in both the Peerage of Ireland and the Peerage of Great Britain held by the head of the Fitzwilliam family. This family claim descent from William the Conqueror. The Fitzwilliams acquired extensive holdings in South Yorkshire, largely through strategic alliances through...
, and held that office to within two years of his death. He was first known as a mathematician by his essays in the The Ladies' Diary
The Ladies' Diary
The Ladies' Diary: or, Woman's Almanack appeared annually in London from 1704 to 1841. It featured material relating to calendars etc. including sunrise and sunset times and phases of the moon, as well as important dates , and a chronology of remarkable events.The subtitle indicated its serious...
for 1744. In 1766 he was elected a fellow of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
.
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
Method of Fluxions
Method of Fluxions is a book by Isaac Newton. The book was completed in 1671, and published in 1736. Fluxions is Newton's term for differential calculus...
by a purely algebraic method. The idea may be compared with that of Joseph Louis Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...
'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
Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert was a French mathematician, mechanician, physicist, philosopher, and music theorist. He was also co-editor with Denis Diderot of the Encyclopédie...
and Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
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 Landen's transformation
Landen's transformation
Landen's transformation, independently rediscovered by Gauss, is a mapping of the parameters of an elliptic integral, which leaves the value of the integral unchanged.In Gauss's formulation,...
(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
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...
in terms of two elliptic arcs. His researches on elliptic function
Elliptic function
In complex analysis, an elliptic function is a function defined on the complex plane that is periodic in two directions and at the same time is meromorphic...
s 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
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
.
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)