Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician best known for creating

Taylor's theorem In calculus, Taylor's theorem gives an approximation of a ''k''-times differentiable function around a given point by a polynomial of degree ''k'', called the ''k''th-order Taylor polynomial. For a smooth function, the Taylor polynomial is th ...

and the

Taylor series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...

, which are important for their use in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied ...

Life and work

Brook Taylor was born in

Edmonton Edmonton ( ) is the capital city of the Canadian province of Alberta. Edmonton is situated on the North Saskatchewan River and is the centre of the Edmonton Metropolitan Region, which is surrounded by Alberta's central region. The city an ...

(former

Middlesex Middlesex (; abbreviation: Middx) is a historic county in southeast England. Its area is almost entirely within the wider urbanised area of London and mostly within the ceremonial county of Greater London, with small sections in neighbour ...

). Taylor was the son of John Taylor, MP of

Patrixbourne Patrixbourne is a rural English village south-east of Canterbury in Kent. It is mostly taken up by agricultural hills and along with almost contiguous Bekesbourne to the north it makes up the civil parish of Bekesbourne-with-Patrixbourne in th ...

, Kent and Olivia Tempest, the daughter of Sir Nicholas Tempest, Baronet of Durham. He entered

St John's College, Cambridge St John's College is a constituent college of the University of Cambridge founded by the Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corporation established by a charter dated 9 April 1511. The ...

, as a

fellow-commoner A commoner is a student at certain universities in the British Isles who historically pays for his own tuition and commons, typically contrasted with scholars and exhibitioners, who were given financial emoluments towards their fees. Cambridge ...

in 1701, and took degrees in

LL.B. Bachelor of Laws ( la, Legum Baccalaureus; LL.B.) is an undergraduate law degree in the United Kingdom and most common law jurisdictions. Bachelor of Laws is also the name of the law degree awarded by universities in the People's Republic of Chi ...

in 1709 and

LL.D. Legum Doctor (Latin: “teacher of the laws”) (LL.D.) or, in English, Doctor of Laws, is a doctorate-level academic degree in law or an honorary degree, depending on the jurisdiction. The double “L” in the abbreviation refers to the early ...

in 1714. Taylor studied

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

under

John Machin John Machin (bapt. c. 1686 – June 9, 1751) was a professor of astronomy at Gresham College, London. He is best known for developing a quickly converging series for pi in 1706 and using it to compute pi to 100 decimal places. History ...

and

John Keill John Keill FRS (1 December 1671 – 31 August 1721) was a Scottish mathematician, natural philosopher, and cryptographer who was an important defender of Isaac Newton. Biography Keill was born in Edinburgh, Scotland on 1 December 1671. His f ...

, leading to Taylor obtaining a solution to the problem of "

center of oscillation The center of percussion is the point on an extended massive object attached to a pivot where a perpendicular impact will produce no reactive shock at the pivot. Translational and rotational motions cancel at the pivot when an impulsive blow is st ...

." Taylor's solution remained unpublished until May 1714, when his claim to priority was disputed by

Johann Bernoulli Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educating Le ...

. Taylor's ''Methodus Incrementorum Directa et Inversa'' (1715) ("Direct and Indirect Methods of Incrementation") added a new branch to higher mathematics, called "

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

finite difference A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for t ...

s". Taylor used this development to determine the form of movement in vibrating strings. Taylor also wrote the first satisfactory investigation of

astronomical refraction Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of height. This refraction is due to the velocity of light t ...

. The same work contains the well-known

, the importance of which remained unrecognized until 1772, when

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia In Taylor's 1715 essay ''Linear Perspective'', Taylor set forth the principles of perspective in a more understandable form, but the work suffered from brevity and obscurity problems which plagued most of his writings, meaning the essay required further explanation in the treatises of

Joshua Kirby Joshua Kirby (1716, Parham, Suffolk – 1774, Kew), often mistakenly called John Joshua Kirby, was an English 18th-century landscape painter, engraver, writer, draughtsman and architect famed for his publications and teaching on linear perspect ...

(1754) and Daniel Fournier (1761). Taylor was elected as a fellow in 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 ...

in 1712. In the same year, Taylor sat on the committee for adjudicating the claims of Sir

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...

and

Gottfried Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...

. He acted as secretary to the society from 13 January 1714 to 21 October 1718. From 1715 onward, Taylor's studies took a philosophical and religious bent. He corresponded with the Comte de Montmort on the subject of

Nicolas Malebranche Nicolas Malebranche ( , ; 6 August 1638 – 13 October 1715) was a French Oratorian Catholic priest and rationalist philosopher. In his works, he sought to synthesize the thought of St. Augustine and Descartes, in order to demonstrate the a ...

's tenets. Unfinished treatises written on his return from

Aix-la-Chapelle Aachen ( ; ; Aachen dialect: ''Oche'' ; French and traditional English: Aix-la-Chapelle; or ''Aquisgranum''; nl, Aken ; Polish: Akwizgran) is, with around 249,000 inhabitants, the 13th-largest city in North Rhine-Westphalia, and the 28th- ...

in 1719, ''On the Jewish Sacrifices'' and ''On the Lawfulness of Eating Blood'', were afterwards found among his papers. Taylor was one of few English mathematicians, along with Isaac Newton and

Roger Cotes Roger Cotes (10 July 1682 – 5 June 1716) 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 quadratur ...

, who was capable of holding his own with the Bernoullis, but a lack of clarity affected a great part of his demonstrations and Taylor lost brevity through his failure to express his ideas fully and clearly. His health began to fail in 1717 after years of intense work. Taylor married Miss Brydges of Wallington, Surrey in 1721 without his father's approval. The marriage led to an estrangement with his father, which improved in 1723 after Taylor's wife died in childbirth while giving birth to a son. Taylor's son did not survive. He spent the next two years with his family at Bifrons, and in 1725 he married with his father's approval, Sabetta Sawbridge of

Olantigh Olantigh is an English house north of Wye in the civil parish of Wye with Hinxhill. The garden terraces and towered stable block were Grade II listed in 1989 and extend to , beside the Great Stour river. Garden features include a wide variet ...

Kent Kent is a county in South East England and one of the home counties. It borders Greater London to the north-west, Surrey to the west and East Sussex to the south-west, and Essex to the north across the estuary of the River Thames; it faces ...

. She died in childbirth in 1730, though his only daughter, Elizabeth, survived. Taylor's father died in 1729, leaving Taylor to inherit the Bifrons estate. Taylor died at the age of 46, on 29 December 1731, at

Somerset House Somerset House is a large Neoclassical complex situated on the south side of the Strand in central London, overlooking the River Thames, just east of Waterloo Bridge. The Georgian era quadrangle was built on the site of a Tudor palace ("O ...

, London.

Selected writings

Taylor's grandson, Sir William Young, printed a

posthumous work The following is a list of works that were published posthumously. An asterisk indicates the author is listed in multiple subsections. (Philip Sidney appears in four.) Literature Novels and short stories * Douglas Adams* — '' The Salmo ...

entitled ''Contemplatio Philosophica'' for private circulation in 1793, (2nd Bart., 10 January 1815). The work was prefaced by a biography, and had an appendix containing letters addressed to him by Bolingbroke,

Bossuet Bossuet is a French surname. Notable people with the surname include: * Jacques-Bénigne Bossuet Jacques-Bénigne Lignel Bossuet (; 27 September 1627 – 12 April 1704) was a French bishop and theologian, renowned for his sermons and other addr ...

, and others. Several short papers by Taylor were published in ''Phil. Trans.,'' vols. xxvii to xxxii,which including accounts of experiments in

magnetism Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...

and

capillary A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the bod ...

attraction. In 1719, Brook issued an improved version of his work on perspective, ''New Principles of Linear Perspective'', which was revised by

John Colson John Colson (1680 – 20 January 1760) was an English clergyman, mathematician, and the Lucasian Professor of Mathematics at Cambridge University. Life John Colson was educated at Lichfield School before becoming an undergraduate at Christ Chu ...

in 1749. A French translation was published in 1757., 1757. "Patrice Murdoch" is Patrick Murdoch. The name of the publisher and city of publication on the title page are misleading—then a common practice. J. M. Quérard writes that the book was actually published in Lyon
"Murdoch (Patrice)". ''La France littéraire, ou Dictionnaire…'', vol. 6, p. 365
; he errs on the name of the translator, who was Antoine Rivoire (1709-1789) ( SUDOCbr>record
. It was reprinted, with a portrait and short biography, in 1811. * . *

* .

Tribute

Taylor is an

impact crater An impact crater is a circular depression in the surface of a solid astronomical object formed by the hypervelocity impact of a smaller object. In contrast to volcanic craters, which result from explosion or internal collapse, impact crater ...

located on the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

, named in honor of Brook Taylor in 1935.

References

External links

* * *

Beningbrough Hall Beningbrough Hall is a large Georgian mansion near the village of Beningbrough, North Yorkshire, England, and overlooks the River Ouse. It has baroque interiors, cantilevered stairs, wood carving and central corridors which run the length of ...

has a painting by John Closterman of Taylor aged about 12 with his brothers and sisters. See als
NPG 5320: ''The Children of John Taylor of Bifrons Park''

Brook Taylor's pedigree

Taylor, a crater on the Moon named after Brook Taylor
{{DEFAULTSORT:Taylor, Brook 1685 births 1731 deaths English mathematicians 18th-century English mathematicians Mathematical analysts Alumni of St John's College, Cambridge Fellows of the Royal Society People from Edmonton, London Freemasons of the Premier Grand Lodge of England

Life and work

Selected writings

Tribute

References

Further reading

External links