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Roger Cotes

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This is a stub for Roger Cotes

Stephensonia

Just another young mathmatician that worked with Jeova sanctus unus.

Community entry: Roger Cotes

Bits from the Wikipedia and MacTutor History of Mathemathics

Roger Cotes born July 10, 1682 in Burbage, Leicestershire, England died June 5, 1716 in Cambridge, Cambridgeshire. He was the first of the newly-created Plumian Professors of Astronomy and Experimental Philosophy, at Trinity College, Cambridge. One of the most distinguished, and certainly one of the most ardent, of the early Newtonians.

Chiefly known for working closely with Isaac Newton by proofreading the 2nd edtion of his famous book Principia Mathematica before publication. He did not simply proof-read the work, rather he conscientiously studied the work gently but persistently arguing points with Newton doing the rigorous math that Newton no longer could. At the beginning of the correspondence between the two the tone is very friendly, however, toward the end of the task, there are signs that they are cooling towards one another (which seems to be typical of Newton's relationships). He also invented the quadrature formulas known as Newton-Cotes formulas.

Cotes only published one paper in his lifetime, namely Logometria. Cotes was particularly pleased with his rectification of the logarithmic curve as he makes clear in a letter to his friend mathematician William Jones in 1712.

In particular his work on logarithms led him to study the curve: r = a/^\infty which he named the reciprocal spiral.

Jones urged Cotes to publish his work in the Philosophical Transactions of the Royal Society, but Cotes resisted this wishing to support Cambridge and publish with Cambridge University Press. His early death was to prevent this publication. Cotes discovered an important theorem on the nth roots of unity, anticipated the method of least squares and discovered a method of integrating rational fractions with binomial denominators. His substantial advances in the theory of logarithms, the integral calculus, in numerical methods particularly interpolation and table construction led Newton to say “if he had lived we might have known something,” indicates the opinion of his abilities held by most of his contemporaries.

Cotes's writings were collected and published in 1722 under the titles Harmonia Mensurarum and Opera Miscellanea. His lectures on hydrostatics were published in 1738. A large part of the Harmonia Mensurarum is given up to the decomposition and integration of rational algebraical expressions. That part which deals with the theory of partial fractions was left unfinished, but was completed by Demoivre. Cotes wrote a preface defending the theory of gravitation given in the Principia. Cotes was himself to provide the next mathematical steps by finding the derivatives of the trigonometric functions, results published after his death. Leonhard Euler developed methods of integrating linear differential equations in 1739 and made known Cotes' work on trigonometric functions. He drew up lunar tables in 1744, clearly already studying gravitational attraction in the Earth, Moon, Sun system. Thomas Simpson published some of the work which Cotes hoped to publish with Cambridge University Press The Doctrine and Application of Fluxions (1750).