Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician and barrister best known for several results in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

. Taylor's most famous developments are Taylor's theorem and the Taylor series, essential in the infinitesimal approach of functions in specific points.

Life and work

Brook Taylor was born in

Edmonton Edmonton is the capital city of the Provinces and territories of Canada, Canadian province of Alberta. It is situated on the North Saskatchewan River and is the centre of the Edmonton Metropolitan Region, which is surrounded by Central Alberta ...

(former

Middlesex Middlesex (; abbreviation: Middx) is a Historic counties of England, former county in South East England, now mainly within Greater London. Its boundaries largely followed three rivers: the River Thames, Thames in the south, the River Lea, Le ...

). Taylor was the son of John Taylor, MP of Patrixbourne, Kent and Olivia Tempest, the daughter of Sir Nicholas Tempest, Baronet of Durham. He entered

St John's College, Cambridge St John's College, formally the College of St John the Evangelist in the University of Cambridge, is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, founded by the House of Tudor, Tudor matriarch L ...

, as a fellow-commoner in 1701, and took degrees in LL.B. in 1709 and LL.D. in 1714. Taylor studied

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

under John Machin and John Keill, leading to Taylor obtaining a solution to the problem of " center of oscillation". Taylor's solution remained unpublished until May 1714, when his claim to priority was disputed by

Johann Bernoulli Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...

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

calculus Calculus 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 generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

finite difference A finite difference is a mathematical expression of the form . Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference operator, commonly d ...

s". Taylor used this development to determine the form of movement in vibrating strings. Taylor also wrote the first satisfactory investigation of astronomical refraction. The same work contains the well-known Taylor's theorem, 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 (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 () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

and

Gottfried Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...

. 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 synthesise the thought of St. Augustine and Descartes, in order to demonstrate the ...

's tenets. Unfinished treatises written on his return from Aix-la-Chapelle 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, 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,

Kent Kent is a Ceremonial counties of England, ceremonial county in South East England. It is bordered by Essex across the Thames Estuary to the north, the Strait of Dover to the south-east, East Sussex to the south-west, Surrey to the west, and Gr ...

. 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 architecture, neoclassical building complex situated on the south side of the Strand, London, Strand in central London, overlooking the River Thames, just east of Waterloo Bridge. The Georgian era quadran ...

, London.

Selected writings

Taylor's grandson, Sir William Young, printed a posthumous work 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, 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 occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, ...

and

capillary A capillary is a small blood vessel, from 5 to 10 micrometres in diameter, and is part of the microcirculation system. Capillaries are microvessels and the smallest blood vessels in the body. They are composed of only the tunica intima (the inn ...

attraction. In 1719, Brook issued an improved version of his work on perspective, ''New Principles of Linear Perspective'', which was revised by John Colson 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 Taylor, Taylors or Taylor's may refer to: People * Taylor (surname) ** List of people with surname Taylor * Taylor (given name), including Tayla and Taylah * Taylor sept, a branch of Scottish clan Cameron * Justice Taylor (disambiguation) ...

is an

impact crater An impact crater is a depression (geology), depression in the surface of a solid astronomical body formed by the hypervelocity impact event, impact of a smaller object. In contrast to volcanic craters, which result from explosion or internal c ...

located on the

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

, named in honor of Brook Taylor in 1935.

References

External links

* * * Beningbrough Hall has a painting by

John Closterman John Closterman (also spelt Cloosterman, Klosterman; 1660 – 24 May 1711 (buried)) was a Westphalian portrait painter of the late 17th and early 18th centuries. His subjects were mostly European noblemen and their families. Career Born in Osna ...

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 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