COTES, ROGER (1682-1716), an English mathematician and philosopher, born at Burbage, Leicestershire, of which place his father was rector. When only twenty-four years of age he was appointed Plumian professor of astronomy and experimental philosophy in the university of Cambridge. He took orders in 1713 ; and the same year, at the request of Dr Bentley, be published the second edition of Newton's Principia with an original preface. He died June 5, 1716, at the age of thirty-three, leaving unfinished a series of elaborate researches on optics, in reference to which Newton observed, "If Mr Cotes had lived, we should have known something." With regard to pure mathematics, the principal discovery of Cotes consists in a theorem which still bears his name, and which furnishes the means of integrating by logarithms and arcs of• the circle the rational fractions whose denominator is -a binomial. His papers were collected and published by his successor Dr Robert Smith.