John Pell  

John Pell (16111685).


Born  1
March 1611 Southwick, Sussex, England 
Died  12
December 1685 (aged 74) Westminster, London, England 
Residence  England 
Nationality  English 
Fields  Mathematician and linguist 
Institutions  University of Amsterdam 
Alma mater  Trinity College, Cambridge 
Doctoral students  William Brereton 
Known for  Pell's
equation Pell number 
Influences  Henry Briggs 
Notes
He was the brother of Thomas Pell 
John Pell (1 March 1611 – 12 December 1685), was an English mathematician.
Contents 
He was born at Southwick in Sussex. He was educated at Steyning Grammar School, and entered Trinity College, Cambridge, at the age of thirteen.^{[1]} During his university career he became an accomplished linguist, and even before he took his B.A. degree (in 1629) corresponded with Henry Briggs and other mathematicians. In 1630 he was teaching in the shortlived Chichester Academy, set up by Samuel Hartlib.^{[2]}^{[3]} Shortly afterwards he married Ithamara Reginald, sister of Bathsua Makin.^{[4]}
Pell spent much of the 1630s working under Hartlib's influence, on a variety of topics in the area of pedagogy, encyclopedism and pansophy, combinatorics and the legacy of Trithemius. By 1638 he had formulated a proposal for a universal language.^{[5]} In mathematics, he concentrated on expanding the scope of algebra in the theory of equations, and on mathematical tables.^{[6]} As part of a joint lobbying effort with Hartlib to find himself support to continue as a researcher, he had his short Idea of Mathematics printed in October 1638.^{[7]} The campaign brought interested responses from Johann Moriaen and Marin Mersenne.^{[8]}
His reputation and the influence of Sir William Boswell, the English resident, with the StatesGeneral procured his election in 1644 to the chair of mathematics in Amsterdam, after an earlier attempt immediately after Martin van den Hove left for Leiden had failed.^{[9]} From 1644 he worked on a polemical work, against Longomontanus. For this he put in a large effort soliciting help and testimonials: from Bonaventura Cavalieri, his patron Sir Charles Cavendish, René Descartes, Thomas Hobbes, Mersenne, Claude Mydorge, and Gilles de Roberval. It finally appeared as Controversy with Longomontanus concerning the Quadrature of the Circle (1647).^{[10]}^{[11]}
Pell moved in 1646, on the invitation of Frederick Henry, Prince of Orange, to Breda, and remained there until 1652.
From 1654 to 1658 Pell acted as Oliver Cromwell's political agent to the Protestant cantons of Switzerland; he cooperated with Samuel Morland at Geneva.^{[12]} A mathematical pupil and disciple there, from 1657, was Johann Heinrich Rahn, known as Rhonius.^{[13]} Rahn is credited with the invention of the division sign ÷ (obelus); it has also been attributed to Pell, who taught Rahn a threecolumn spreadsheetstyle technique of tabulation of calculations, and acted as editor for Rahn's 1659 book Teutsche Algebra in which it appeared. This book by Rahn also contained what would become known as the "Pell equation".^{[14]}^{[15]} Diophantine equations was a favorite subject with Pell; he lectured on them at Amsterdam. He is now best remembered, if perhaps erroneously, for the indeterminate equation
which is known as Pell's equation. This problem was in fact proposed by Pierre de Fermat first to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians. Pell's connection with the problem is through Rahn. It consisted of the publication of the solutions of John Wallis and Lord Brouncker, in his edition of Thomas Branker's Translation of Rhonius's Algebra (1668); added to his earlier editorial contributions, whatever they were, to the 1659 algebra book written by Rahn (i.e. Rhonius). ^{[16]} This new edition of what was essentially Rahn's work, by Pell, included a great deal of additional material on number theory, amounting to a reply to the 1657 book Exercitationes mathematicae by Frans van Schooten. It is also notable for its inclusion of a Table of Incomposits, an early large factor table.^{[17]}
After his return to England he took orders, in 1661, when he became rector of Fobbing in Essex. In 1663 he was given an honorary D.D. (Lambeth degree), and was also elected a Fellow of the Royal Society. At the same time he was presented by Bishop Gilbert Sheldon to the rectory of Laindon, Essex; Sheldon expected him to treat the positions as sinecures.^{[18]}^{[19]}^{[11]} He spent time as mathematics teacher to William Brereton, 3rd Baron Brereton, at Brereton Hall.^{[3]}
In 1673 he met Leibniz in London, and was able to inform him that some of his mathematical work had been anticipated by François Regnaud and Gabriel Mouton.^{[20]}^{[21]} His devotion to mathematics seems to have interfered with his advancement in the Church and with his private life. For a time he was confined as a debtor in the King's Bench Prison. He lived, on the invitation of Dr Whistler, for a short time in 1682 at the College of Physicians, but died at the house of Mr Cothorne, reader of the church of St Gilesinthe Fields.
Many of Pell's manuscripts fell into the hands of Richard Busby, master of Westminster School, and afterwards came into the possession of the Royal Society; they are still preserved in nearly forty folio volumes in the British Library, which contain, not only Pell's own memoirs, but much of his correspondence with the mathematicians of his time.
His chief works are:
The Idea was a short manifesto. It made three suggestions: a mathematical encyclopedia and bibliography; a complete mathematics research library and collection of instruments, with state sponsorship; and a threevolume comprehensive set of mathematical textbooks, able to convey the state of the art to any scholar.^{[22]}
Upon the death of John Pell's brother, Thomas Pell, in 1670, the mathematician's son, Sir John Pell inherited lands in New York, where he lived as the first Lord of the Manor of Pelham. His descendants have continued to be prominent in the American polity, including Ambassador and U.S. Representative Herbert Pell and U.S. Senator Claiborne Pell.
John Pell  

Born 
1 March 1611 Southwick, Sussex, England 
Died 
12 December 1685 (aged 74) Westminster, London, England 
Residence  England 
Nationality  English 
Fields  Mathematician and linguist 
Institutions  University of Amsterdam 
Alma mater  Trinity College, Cambridge 
Doctoral students  William Brereton 
Known for 
Pell's equation Pell number 
Influences  Henry Briggs 
Notes He was the brother of Thomas Pell 
John Pell (1 March 1611 – 12 December 1685) was an English mathematician.
Contents 
He was born at Southwick in Sussex. He was educated at Steyning Grammar School, and entered Trinity College, Cambridge, at the age of thirteen.^{[1]} During his university career he became an accomplished linguist, and even before he took his B.A. degree (in 1629) corresponded with Henry Briggs and other mathematicians. In 1630 he was teaching in the shortlived Chichester Academy, set up by Samuel Hartlib.^{[2]}^{[3]} Shortly afterwards he married Ithamara Reginald, sister of Bathsua Makin.^{[4]}
Pell spent much of the 1630s working under Hartlib's influence, on a variety of topics in the area of pedagogy, encyclopedism and pansophy, combinatorics and the legacy of Trithemius. By 1638 he had formulated a proposal for a universal language.^{[5]} In mathematics, he concentrated on expanding the scope of algebra in the theory of equations, and on mathematical tables.^{[6]} As part of a joint lobbying effort with Hartlib to find himself support to continue as a researcher, he had his short Idea of Mathematics printed in October 1638.^{[6]} The campaign brought interested responses from Johann Moriaen and Marin Mersenne.^{[7]}
His reputation and the influence of Sir William Boswell, the English resident, with the StatesGeneral procured his election in 1644 to the chair of mathematics in Amsterdam, after an earlier attempt immediately after Martin van den Hove left for Leiden had failed.^{[8]} From 1644 he worked on a polemical work, against Longomontanus. For this he put in a large effort soliciting help and testimonials: from Bonaventura Cavalieri, his patron Sir Charles Cavendish, René Descartes, Thomas Hobbes, Mersenne, Claude Mydorge, and Gilles de Roberval. It finally appeared as Controversy with Longomontanus concerning the Quadrature of the Circle (1647).^{[9]}^{[10]}
Pell moved in 1646, on the invitation of Frederick Henry, Prince of Orange, to Breda, and remained there until 1652.
From 1654 to 1658 Pell acted as Oliver Cromwell's political agent to the Protestant cantons of Switzerland; he cooperated with Samuel Morland at Geneva.^{[11]} A mathematical pupil and disciple there, from 1657, was Johann Heinrich Rahn, known as Rhonius.^{[12]} Rahn is credited with the invention of the division sign ÷ (obelus); it has also been attributed to Pell, who taught Rahn a threecolumn spreadsheetstyle technique of tabulation of calculations, and acted as editor for Rahn's 1659 book Teutsche Algebra in which it appeared. This book by Rahn also contained what would become known as the "Pell equation".^{[13]}^{[14]} Diophantine equations was a favorite subject with Pell; he lectured on them at Amsterdam. He is now best remembered, if perhaps erroneously, for the indeterminate equation
which is known as Pell's equation. This problem was in fact proposed by Pierre de Fermat first to Bernard Frénicle de Bessy, and in 1657 to all mathematicians. Pell's connection with the problem is through Rahn. It consisted of the publication of the solutions of John Wallis and Lord Brouncker, in his edition of Thomas Branker's Translation of Rhonius's Algebra (1668); added to his earlier editorial contributions, whatever they were, to the 1659 algebra book written by Rahn (i.e. Rhonius).^{[15]} This new edition of what was essentially Rahn's work, by Pell, included a great deal of additional material on number theory, amounting to a reply to the 1657 book Exercitationes mathematicae by Frans van Schooten. It is also notable for its inclusion of a Table of Incomposits, an early large factor table.^{[16]}
After his return to England he took orders, in 1661, when he became rector of Fobbing in Essex. In 1663 he was given an honorary D.D. (Lambeth degree), and was also elected a Fellow of the Royal Society. At the same time he was presented by Bishop Gilbert Sheldon to the rectory of Laindon, Essex; Sheldon expected him to treat the positions as sinecures.^{[10]}^{[17]}^{[18]} He spent time as mathematics teacher to William Brereton, 3rd Baron Brereton, at Brereton Hall.^{[3]}
In 1673 he met Leibniz in London, and was able to inform him that some of his mathematical work had been anticipated by François Regnaud and Gabriel Mouton.^{[19]}^{[20]} His devotion to mathematics seems to have interfered with his advancement in the Church and with his private life. For a time he was confined as a debtor in the King's Bench Prison. He lived, on the invitation of Dr Daniel Whistler, for a short time in 1682 at the College of Physicians, but died at the house of Mr Cothorne, reader of the church of St Gilesinthe Fields.
Many of Pell's manuscripts fell into the hands of Richard Busby, master of Westminster School, and afterwards came into the possession of the Royal Society; they are still preserved in nearly forty folio volumes in the British Library, which contain, not only Pell's own memoirs, but much of his correspondence with the mathematicians of his time.
His chief works are:
The Idea was a short manifesto. It made three suggestions: a mathematical encyclopedia and bibliography; a complete mathematics research library and collection of instruments, with state sponsorship; and a threevolume comprehensive set of mathematical textbooks, able to convey the state of the art to any scholar.^{[21]}
Upon the death of John Pell's brother, Thomas Pell, in 1670, the mathematician's son, Sir John Pell inherited lands in New York, where he lived as the first Lord of the Manor of Pelham. His descendants have continued to be prominent in the American polity, including Ambassador and U.S. Representative Herbert Pell and U.S. Senator Claiborne Pell.
JOHN PELL (16so1685), English mathematician, was born on the 1st of March 1610 at Southwick in Sussex, where his father was minister. He was educated at Steyning, and entered Trinity College, Cambridge, at the age of thirteen. During his university career he became an accomplished linguist, and even before he took his M.A. degree (in 1630) corresponded with Henry Briggs and other mathematicians. His great reputation and the influence of Sir William Boswell, the English resident, with the statesgeneral procured his election in 1643 to the chair of mathematics in Amsterdam, whence he removed in 1646, on the invitation of the prince of Orange, to Breda, where he remained till 1652.
From 1654 to 1658 Pell acted as Cromwell's political agent to the Protestant cantons of Switzerland. On his return to England he took orders and was appointed by Charles II. to the rectory of Fobbing in Essex, and in 1673 he was presented by Bishop Sheldon to the rectory of Laindon in the same county. His devotion to mathematical science seems to have interfered alike with his advancement in the Church and with the proper management of his private affairs. For a time he was confined as a debtor in the king's bench prison. He lived, on the invitation of Dr Whistler, for a short time in 1682 at the College of Physicians, but died on the 12th of December 1685 at the house of Mr Cothorne, reader of the church of St Gilesinthe Fields. Many of Pell's manuscripts fell into the hands of Dr Busby, master of Westminster School, and afterwards came into the possession of the Royal Society; they are still preserved in something like forty folio volumes, which contain, not only Pell's own memoirs, but much of his correspondence with the mathematicians of his time.
The Diophantine analysis was a favourite subject with Pell; he lectured on it at Amsterdam; and he is now best remembered for the indeterminate equation ax 2 +1 = y 2 , which is known by his name. This problem was proposed by Pierre de Fermat first to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians. Pell's connexion with the problem simply consists of the publication of the solutions of John Wallis and Lord Brounker in his edition of Branker's Translation of Rhonius's Algebra 0.668). His chief works are: Astronomical History of Observations of Heavenly Motions and Appearances (1634); Ecliptica prognostica (1634); Controversy with Longomontanus concerning the Quadrature of the Circle (1646?); An Idea of the Mathematics, 12m0 (1650); A Table of Ten Thousand Square Numbers (fol.; 1672).
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