Brook Taylor

See also: Taylor

Brook Taylor is an eclectic scientist English, born in Edmonton (England) on August 18th 1685, and died in London on December 29th 1731. It was interested in mathematics, with the music, painting and philosophy.

In 1712 Taylor was allowed with the Royal Society of London (the equivalent of the Academy of Science of Paris). It was on April 3rd, and it is clear that its election was based on an expertise of Machin, Keill and the other famous ones, that on the publications of its results. Thus Taylor wrote in Machin in 1712 to provide him the solution of a problem concerning the second law of Kepler on the movements of planets. In 1712 also, it belonged to a committee to decide between Isaac Newton and Leibniz.

In 1714 Taylor was elected secretary of Royal Society, and there remained there from January 14th, 1714 to October 21st 1718, when he had to resign himself for health reasons on the one hand, on the other hand for lack of motivation. The period when he was secretary of Royal Society of London was that of its life where he was most productive in mathematics. It published two works in 1715, Methodus incrementorum directa and reversed and Linear Perspective which is extremely important for the history of the Mathématiques. Two second editions were published, respectively in 1717 and 1719.

Taylor made many stays in France. It was on the one hand following health issues and on the other hand to return visit to friends. It met Pierre Rémond De Montmort and corresponded with him on various subjects of mathematics after its return. They discussed in particular the infinite series and probabilities. Taylor also corresponded with Abraham de Moivre on the probabilities. At that time, these mathematicians communicated much to three.

He added to mathematics a new branch called “calculation of finished Différences”, invented integration by part, and discovered the series called “Développement of Taylor”. Its ideas were published in its book of 1715, Methodus incrementorum directa and reversed . In fact, the first mention by Taylor of what is called today Théorème of Taylor appears in a letter that this last wrote with Machin on July 26th, 1712. In this letter, Taylor explains clearly from where this idea came to him, i.e. of a comment which Machin in Child' S Coffeehouse made, using the “series of Sir Isaac Newton” to solve a problem of Kepler, and also using “the methods of Dr. Halley for extraires the roots” of polynomial equations. There are in fact two versions of the theorem of Taylor given on the paper of 1715. In the first version, the theorem appears in the Proposal 11 which is a generalization of the methods of Halley of approximation of roots of the equation of Kepler, which was going soon to become a consequence of the series of Bernoulli. It is this version which was inspired by the conversations of Coffeehouse described previously. In the second version is Corollary 2 of the Proposal 7 and which is a method to find more solutions of the equations fluxionales in the infinite series. Taylor was first has to discover this result!

James Gregory, Isaac Newton, Leibniz, Johann Bernoulli and of Moivre has all overdraft an alternative of the theorem of Taylor. All these mathematicians made their discoveries separately, and the work of Taylor was also independent of that of the others. The importance of the theorem of Taylor was not perceived before 1772 when Lagrange proclaimed that it was the basic principle of differential calculus! The term “Série of Taylor” seems to be used for the first time by Lhuilier in 1786. Taylor presented also the basic principles of the prospect in Linear Prospect (1715). The second edition was called New principles off linear perspective .

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