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Taylor added to mathematics a new branch now called the 'calculus of finite differences', invented integration by parts, and discovered the celebrated formula known as Taylor's expansion.
In 1708 Taylor produced a solution to the problem of the centre of oscillation which, since it went unpublished until 1714, resulted in a priority dispute with Johann Bernoulli.
Taylor's Methodus incrementorum directa et inversa (1715) added to mathematics a new branch now called the 'calculus of finite differences' and he invented integration by parts. It also contained the celebrated formula known as Taylor's expansion, the importance of which remained unrecognised until 1772 when Lagrange proclaimed it the basic principle of the differential calculus.
Taylor also devised the basic principles of perspective in Linear Perspective (1715). Together with New principles of linear perspective the first general treatment of the vanishing points are given.
Taylor gives an account of an experiment to discover the law of magnetic attraction (1715) and an improved method for approximating the roots of an equation by giving a new method for computing logarithms (1717).
Taylor was elected a Fellow of the Royal Society in 1712 and was appointed in that year to the committee for adjudicating the claims of Newton and of Leibniz to have invented the calculus.
References elsewhere in this archive:
Tell me about Taylor series and show me the series for cosine and the series for sine
Tell me about Taylor's part in the rise of calculus and about his part in mathematics in St Andrews
References:
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