Cotes
# Roger Cotes

### Born: 10 July 1682
in Burbage, Leicestershire, England

Died: 5 June 1716
in Cambridge, Cambridgeshire, England

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**Cotes** was a Fellow of Trinity College Cambridge in 1707. At the age of 26 he became the first Plumian Professor of Astronomy and Experimental Philosophy. At Cambridge he became friends with William Whiston.
From 1709 until 1713 much of Cotes's time was taken up editing the second edition of Newton's Principia . He did not simply proof-read the work, rather he conscientiously studied the work gently but persistently arguing points with Newton. 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.

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 William Jones in 1712. In particular his work on logarithms led him to study the curve r = a/q which he named the reciprocal spiral.

Jones urged Cotes to publish his work in the Philosophical Transactions of the Royal Society, but Jones 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.

Some of the work which Cotes hoped to publish with Cambridge University Press was published eventually by Thomas Simpson in The Doctrine and Application of Fluxions (2 Vols, London, 1750).

**References (7 books/articles)**

**References elsewhere in this archive:**

Tell me about Cotes's work on orbits and gravitation

Cotes worked on the Hyperbolic Spiral and on the Lituus

Roger Cotes was elected to the Royal Society of London in 1711. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.

JOC/EFR December 1996