COTES, ROGER, a celebrated English mathematician and philosopher, born at Burbach, Leicestershire, of which place his father was rector. Before his twelfth year he showed a decided predilection for mathematical study; and afterwards made such rapid progress in that science, that when only twenty-four years of age he was appointed Plumian professor of astronomy and experimental philosophy. He took orders in 1713; and that same year, at the request of Dr Bentley, he published the second edition of Newton's Principia Mathematica, enriched with an original preface. This, with an analytical memoir entitled Logometria, and a description of the great meteor which appeared in England on the 6th March 1716, inserted in the Philosophical Transactions, is all that Cotes lived to publish. He died June 5, 1716, at the age of thirty-three, and was buried in Trinity chapel, where a monument was raised to his memory, bearing a Latin inscription from the pen of Dr Bentley. He left 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 the 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. These expressions had already exercised the ingenuity of Leibnitz, and of John Bernoulli, and by their labours, in con-
junction with those of Euler, this branch of the integral calculus soon assumed a more convenient and simple form. His papers were collected by his successor, Dr Robert Smith, and published under the title of Harmonia Mensurarum, sive Analysis et Synthesis per Rationum et Angularum mensuras promotæ; accedunt alia Opuscula Mathematica. Cambridge, 1722, 4to. Of this work, the "Analyse des Mésures, des Rapports, et des Angles, ou Réduction des Intégrations aux Logarithmes et aux Arcs de Cercle," published (Paris, 1747) by the English Benedictin Walmsley, is rather a paraphrase than a translation. Cotes left a valuable treatise on hydrostatics and pneumatics, which was also published by Smith, and afterwards appeared in a French translation, under the title of "Leçons de Physique Expérimentale sur l'Équilibre des Liquéurs," Paris, 1740, 4to.