Brook Taylor
Encyclopedia
Brook Taylor FRS (18 August 1685 – 30 November 1731) was an English
mathematician who is best known for Taylor's theorem
and the Taylor series
.
(at that time in Middlesex
) to John Taylor of Bifrons House, Kent
, and Olivia Tempest, daughter of Sir Nicholas Tempest, Bart., of Durham
. Brook entered St John's College, Cambridge
as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. in 1709 and 1714, respectively. Having studied mathematics
under John Machin
and John Keill
, in 1708 he obtained a remarkable solution of the problem of the "centre of oscillation," which, however, remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli
. Taylor's Methodus Incrementorum Directa et Inversa (1715) added a new branch to the higher mathematics, now designated the "calculus
of finite difference
s." This work is available in translation on the web http://www.17centurymaths.com. Among other ingenious applications, he used it to determine the form of movement of a vibrating string, by him first successfully reduced to mechanical principles. The same work contained the celebrated formula known as Taylor's theorem
, the importance of which remained unrecognised until 1772, when J. L. Lagrange
realized its powers and termed it "le principal fondement du calcul différentiel" ("the main foundation of differential calculus").
In his 1715 essay Linear Perspective, Taylor set forth the true principles of the art in an original and more general form than any of his predecessors; but the work suffered from the brevity and obscurity which affected most of his writings, and needed the elucidation bestowed on it in the treatises of John Joshua Kirby
(1754) and Daniel Fournier (1761).
Taylor was elected a fellow of the Royal Society
early in 1712, and in the same year sat on the committee for adjudicating the claims of Sir Isaac Newton
and Gottfried Leibniz
, and acted as secretary to the society from 13 January 1714 to 21 October 1718. From 1715 his studies took a philosophical and religious bent. He corresponded, in that year, with the Comte de Montmort on the subject of Nicolas Malebranche
's tenets; and unfinished treatises, On the Jewish Sacrifices and On the Lawfulness of Eating Blood, written on his return from Aix-la-Chapelle in 1719, were afterwards found among his papers.
His marriage in 1721 with Miss Brydges of Wallington
, Surrey
, led to an estrangement from his father, which ended in 1723 after her death in giving birth to a son, who also died. The next two years were spent by him with his family at Bifrons, and in 1725 he married this time with his father's approval, Sabetta Sawbridge of Olantigh, Kent, who also died in childbirth in 1730 ; in this case, however, his daughter, Elizabeth, survived. Taylor's fragile health gave way; he fell into a decline, died at Somerset House
, and was buried at St Ann's, Soho
. By the date of his father's death in 1729 he had inherited the Bifrons estate. As a mathematician, he was the only Englishman after Sir Isaac Newton and Roger Cotes
capable of holding his own with the Bernoullis, but a great part of the effect of his demonstrations was lost through his failure to express his ideas fully and clearly.
Taylor died, aged 46, on 30 November 1731 in Somerset House, London. He was buried in London on 2 December 1731, near his first wife, in the churchyard of St Anne's, Soho.
A posthumous work entitled Contemplatio Philosophica was printed for private circulation in 1793 by Taylor's grandson, Sir William Young, 2nd Bart., (d 10 January 1815) prefaced by a life of the author, and with an appendix containing letters addressed to him by Bolingbroke, Bossuet, and others. Several short papers by Taylor were published in Phil. Trans., vols. xxvii. to xxxii., including accounts of some interesting experiments in magnetism
and capillary
attraction. In 1719 he issued an improved version of his work on perspective, with the title New Principles of Linear Perspective, revised by John Colson
in 1749, and reprinted again, with portrait and life of the author, in 1811. A French translation appeared in 1753 at Lyon
. Taylor gave (Methodus Incrementorum, p. 108) the first satisfactory investigation of astronomical refraction.
.
.
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 who is best known for Taylor's theorem
Taylor's theorem
In calculus, Taylor's theorem gives an approximation of a k times differentiable function around a given point by a k-th order Taylor-polynomial. For analytic functions the Taylor polynomials at a given point are finite order truncations of its Taylor's series, which completely determines the...
and the Taylor series
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
.
Life and work
Brook Taylor was born in EdmontonEdmonton, London
Edmonton is an area in the east of the London Borough of Enfield, England, north-north-east of Charing Cross. It has a long history as a settlement distinct from Enfield.-Location:...
(at that time in Middlesex
Middlesex
Middlesex is one of the historic counties of England and the second smallest by area. The low-lying county contained the wealthy and politically independent City of London on its southern boundary and was dominated by it from a very early time...
) to John Taylor of Bifrons House, Kent
Kent
Kent is a county in southeast England, and is one of the home counties. It borders East Sussex, Surrey and Greater London and has a defined boundary with Essex in the middle of the Thames Estuary. The ceremonial county boundaries of Kent include the shire county of Kent and the unitary borough of...
, and Olivia Tempest, daughter of Sir Nicholas Tempest, Bart., of Durham
Durham
Durham is a city in north east England. It is within the County Durham local government district, and is the county town of the larger ceremonial county...
. Brook entered St John's College, Cambridge
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. in 1709 and 1714, respectively. Having studied mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
under John Machin
John Machin
John Machin, , a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.Machin's formula is:...
and John Keill
John Keill
John Keill was born in Edinburgh, Scotland, and was primarilya mathematician and important disciple of Isaac Newton. He studied at Edinburgh University, under David Gregory, and obtained his bachelors degree in 1692 with a distinction in physics and mathematics...
, in 1708 he obtained a remarkable solution of the problem of the "centre of oscillation," which, however, remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli
Johann Bernoulli
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...
. Taylor's Methodus Incrementorum Directa et Inversa (1715) added a new branch to the higher mathematics, now designated the "calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
of finite difference
Finite difference
A finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...
s." This work is available in translation on the web http://www.17centurymaths.com. Among other ingenious applications, he used it to determine the form of movement of a vibrating string, by him first successfully reduced to mechanical principles. The same work contained the celebrated formula known as Taylor's theorem
Taylor's theorem
In calculus, Taylor's theorem gives an approximation of a k times differentiable function around a given point by a k-th order Taylor-polynomial. For analytic functions the Taylor polynomials at a given point are finite order truncations of its Taylor's series, which completely determines the...
, the importance of which remained unrecognised until 1772, when J. L. 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...
realized its powers and termed it "le principal fondement du calcul différentiel" ("the main foundation of differential calculus").
In his 1715 essay Linear Perspective, Taylor set forth the true principles of the art in an original and more general form than any of his predecessors; but the work suffered from the brevity and obscurity which affected most of his writings, and needed the elucidation bestowed on it in the treatises of John Joshua Kirby
John Joshua Kirby
John Joshua Kirby , was an 18th century landscape painter, engraver, and writer from the United Kingdom, famed for his pamphlet on linear perspective based on Brook Taylor's math.-Biography:...
(1754) and Daniel Fournier (1761).
Taylor 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"...
early in 1712, and in the same year sat on the committee for adjudicating the claims of Sir Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
and Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
, and acted as secretary to the society from 13 January 1714 to 21 October 1718. From 1715 his studies took a philosophical and religious bent. He corresponded, in that year, with the Comte de Montmort on the subject of Nicolas Malebranche
Nicolas Malebranche
Nicolas Malebranche ; was a French Oratorian and rationalist philosopher. In his works, he sought to synthesize the thought of St. Augustine and Descartes, in order to demonstrate the active role of God in every aspect of the world...
's tenets; and unfinished treatises, On the Jewish Sacrifices and On the Lawfulness of Eating Blood, written on his return from Aix-la-Chapelle in 1719, were afterwards found among his papers.
His marriage in 1721 with Miss Brydges of Wallington
Wallington, London
Wallington is a town in the London Borough of Sutton situated south south-west of Charing Cross. Prior to the merger of the Municipal Borough of Beddington and Wallington into the London Borough of Sutton, it was part of the county of Surrey.- History :...
, Surrey
Surrey
Surrey is a county in the South East of England and is one of the Home Counties. The county borders Greater London, Kent, East Sussex, West Sussex, Hampshire and Berkshire. The historic county town is Guildford. Surrey County Council sits at Kingston upon Thames, although this has been part of...
, led to an estrangement from his father, which ended in 1723 after her death in giving birth to a son, who also died. The next two years were spent by him with his family at Bifrons, and in 1725 he married this time with his father's approval, Sabetta Sawbridge of Olantigh, Kent, who also died in childbirth in 1730 ; in this case, however, his daughter, Elizabeth, survived. Taylor's fragile health gave way; he fell into a decline, died at Somerset House
Somerset House
Somerset House is a large building situated on the south side of the Strand in central London, England, overlooking the River Thames, just east of Waterloo Bridge. The central block of the Neoclassical building, the outstanding project of the architect Sir William Chambers, dates from 1776–96. It...
, and was buried at St Ann's, Soho
Soho
Soho is an area of the City of Westminster and part of the West End of London. Long established as an entertainment district, for much of the 20th century Soho had a reputation for sex shops as well as night life and film industry. Since the early 1980s, the area has undergone considerable...
. By the date of his father's death in 1729 he had inherited the Bifrons estate. As a mathematician, he was the only Englishman after Sir Isaac Newton and Roger Cotes
Roger Cotes
Roger Cotes FRS was an English mathematician, known for working closely with Isaac Newton by proofreading the second edition of his famous book, the Principia, before publication. He also invented the quadrature formulas known as Newton–Cotes formulas and first introduced what is known today as...
capable of holding his own with the Bernoullis, but a great part of the effect of his demonstrations was lost through his failure to express his ideas fully and clearly.
Taylor died, aged 46, on 30 November 1731 in Somerset House, London. He was buried in London on 2 December 1731, near his first wife, in the churchyard of St Anne's, Soho.
Selected writings
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...
and capillary
Capillary
Capillaries are the smallest of a body's blood vessels and are parts of the microcirculation. They are only 1 cell thick. These microvessels, measuring 5-10 μm in diameter, connect arterioles and venules, and enable the exchange of water, oxygen, carbon dioxide, and many other nutrient and waste...
attraction. In 1719 he issued an improved version of his work on perspective, with the title New Principles of Linear Perspective, revised by John Colson
John Colson
Johnathan "John" Colson was an English clergyman and mathematician, Lucasian Professor of Mathematics at Cambridge University.John Colson was educated at Lichfield School before becoming an undergraduate at Christ Church, Oxford, though he did not take a degree there...
in 1749, and reprinted again, with portrait and life of the author, in 1811. A French translation appeared in 1753 at Lyon
Lyon
Lyon , is a city in east-central France in the Rhône-Alpes region, situated between Paris and Marseille. Lyon is located at from Paris, from Marseille, from Geneva, from Turin, and from Barcelona. The residents of the city are called Lyonnais....
. Taylor gave (Methodus Incrementorum, p. 108) the first satisfactory investigation of astronomical refraction.
.
.
External links
- Beningbrough HallBeningbrough HallBeningbrough Hall is a large Georgian mansion near the village of Beningbrough, North Yorkshire, England overlooking the River Ouse. It boasts one of Britain's finest baroque interiors and an attractive walled garden, as well as being home to over 100 portraits on loan from the National Portrait...
has a painting by John ClostermanJohn ClostermanJohn Closterman , portrait-painter, born in Osnabrück, the son of an artist, who taught him the rudiments of design.-Career:...
of Taylor aged about 12 with his brothers and sisters. See also NPG 5320: The Children of John Taylor of Bifrons Park - Brook Taylor's pedigree