COTES, ROGZ, a celebrated mathematician and philosopher, was born in 1682, at Burbach, in the county of Leicester, of which his father was rector or curate. Before his twelfth year he showed a decided predilection for the mathematics, which one of his uncles afforded him the means of cultivating; and he made such rapid progress in science, and in the learned languages, that, in 1706, when he had only attained the age of twenty-four, he was appointed to the professorship of astronomy and experimental philosophy, then newly founded by Thomas Plume, archdeacon of Rochester. He took orders in 1713, and, the same year, he published, at the request of his friend Dr Bentley, the second edition of the Principia Mathematica of Newton, which he enriched with an excellent 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 the author himself
published, having been prematurely cut off, on the 5th of Coteswold June 1716, at the early age of thirty-three. He had commenced 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; expressions which had already exercised the ingenuity of Leibnitz, and of John Bernoulli, by whose labours, in conjunction with those of Euler, this branch of the integral calculus soon assumed a more convenient and simple form. Cotes having kept this theorem among his papers, along with other writings which indicated great sagacity, these fragments were collected and arranged by Robert Smith, his relative and successor in the chair of astronomy, who published them under the title of Harmonia Mensurarum, sive Analysis et Synthesis per Rationum et Angularum mensuras promotæ; accedunt alia Opuscula Mathematica. Cambridge, 1722, 4to. The "Analyse des Mésures, des Rapports, et des Angles, ou Réduction des Integrations aux Logarithmes et aux Arcs de Cercle," Paris, 1747, published by the English Benedictin Walmsley, is rather a paraphrase than a translation of the Harmonia Mensurarum. Cotes also left a valuable work on natural philosophy, which was published by Robert Smith, and translated into French, under the title of "Leçons de Physique Expérimentale sur l'Équilibre des Liquéurs," Paris, 1740, 4to, with figures. At Lemgo and at Paris was reprinted the Memoir entitled Estimation Errorum in mixta Mathesi, seu Variationes partium Trianguli plani et sphaerici, which had originally appeared along with, and subjoined to, the Harmonia Mensurarum. Cotes was much regretted by his most distinguished contemporaries; and Dr Bentley honoured his memory with an elegant Latin epitaph.