Cotes, Roger

, a celebrated mathematician, philosopher, and astronomer, was born July 10, 1682, at Burbach in Leicestershire, where his father Robert was rector. He was first placed at Leicester school; where, at only twelve years of age, he discovered a strong inclination to the mathematics. This being observed by his uncle, the rev. Mr. John Smith, he gave him all imaginable encouragement; and prevailed with his father to send him for some time to his house in Lincolnshire, that he might assist him in those studies. Here he laid the foundation of that deep and extensive knowledge, for which he was afterwards so deservedly famous. He removed from thence to London, and was sent to St. Paul’s school; where also he made a great progress in classical learning; yet found so much leisure as to keep a constant correspondence with his uncle, not only in mathematics, but also in metaphysics, philosophy, and divinity. This fact is said to have been often mentioned by professor Saunderson. His next remove was to Cambridge; where, April 6, 1699, he was admitted of Trinity college; and at Michaelmas 1705, after taking his first degree in arts, chosen fellow of it. He was at the same time tutor to Anthony earl of Harold, and the lord Henry de Grey, sons of the then marquis (afterwards duke of) Kent, to which noble family Mr. Cotes was related.

January 1706, he was appointed professor of astronomy and experimental philosophy, upon the foundation of Dr. Thomas Plume, archdeacon of Rochester; being the first that enjoyed that office, to which he was unanimously chosen, on account of his high reputation and merits. He took the degree of M. A. in 1706 and went into orders in 1713. The same year, at the desire of Dr. Bentley, he published at Cambridge the second edition of sir Isaac Newton’s “Mathematica Principia, &c.” and inserted all the improvements which the author had made to that time. To this edition he prefixed a most admirable preface, in which he expressed the true method of philosophising, shewed the foundation on which the Newtonian philosophy | was built, and refuted the objections of the Cartesians and all other philosophers against it. It may not be amiss to transcribe a paragraph from this preface, in which the editor has given an answer to those who supposed that gravity or attraction, in sir Isaac Newton’s system, was in no wise a clearer principle, and more adapted to explain the phaenomena of nature, than the occult qualities of the peripatetics; because there are still philosophers who persist in the same supposition. Gravity, say the objectors, is an occult cause; and occult causes have nothing to do with true philosophy. To this Mr. Cotes replies, that “occult causes are, not those whose existence is most clearly demonstrated by observation and experiment, but those only whose existence is occult, fictitious, and supported by no proofs. Gravity therefore can never be called an occult cause of the planetary motions; since it has been demonstrated from the phenomena, that this quality really exists. Those rather have recourse to occult causes, who make vortices to govern the heavenly motions; vortices, composed of a matter entirely fictitious, and unknown to the senses. But shall gravity, therefore, be called an occult cause, and on that account be banished from philosophy, because the cause of gravity is occult, and as yet undiscovered? Let those, who affirm this, beware of laying down a principle, which will serve to undermine the foundation of every system of philosophy that can be established. For causes always proceed, by an uninterrupted connexion, from those that are compound, to those that are more simple; and when you shall have arrived at the most simple, it will be impossible to proceed farther. Of the most simple cause therefore no mechanical solution can be given;. for if there could, it would not be the most simple. Will you then call these most simple causes occult, and banish them from philosophy? You rnay so; but you must banish at the same time the causes that are next to them, and those again that depend upon the causes next to them, till philosophy at length will be so thoroughly purged of causes, that there will not be one left whereon to build it.” The publication of this edition of Newton’s Principia added greatly to his reputation nor; was the high opinion the public now conceived of him in the least diminished, but rather much increased, by several productions of his own, which afterwards appeared. He gave a description of the great fiery meteor, that was seen March 6, 1716, | which was published in the Phil. Trans, a little after his death. He left hehind hirn also some admirable and judicious tracts, part of which, after his decease, were published by Dr. Robert Smith, his cousin and successor in his professorship, afterwards master of Trinity college. His “Harmonia Mensurarum,” &c. was published at Cambridge, 1722, 4to, and dedicated to Dr. Mead by the learned editor; who, in an elegant and affectionate preface, gives us a copious account of the performance itself, the pieces annexed to it, and of such other of the author’s works as were unpublished. He tells us how much this work was admired by professor Saunderson, and how dear the author of it was to Dr. Bentley. The first treatise of the miscellaneous works annexed to the “Harmonia Mensurarum” is “Concerning the estimation of errors in mixed mathematics/' The second,” Concerning ^he differential method;“which he handles in a manner somewhat different from sir Isaac Newton’s treatise upon that subject, having written it before he had seen that treatise. The name of the third piece is” Canonotechnia, or concerning the construction of tables by differences.“The book concludes with three small tracts,” Concerning the descent of bodies, the motion of pendulums in the cycloid, and the motion of projectiles;“which tracts, the editor informs us, were all composed by him when very young. He wrote alsoA compendium of arithmetic, of the resolutions of equations, of dioptrics, and of the nature of curves.“Besides these pieces, he drew up a course of” Hydrostatical and Pneumatical Lectures" in English, which were published by Dr. Smith in 1737, and again in 1747, 8vo.

This uncommon genius in mathematics died, to the regret of the university, and all lovers of that science, June 5, 1716, in the very prime of his life; for he was advanced no farther than to his 33d year. He was buried in the chapel of Trinity college; and an inscription fixed over him, from which we learn that he had a very beautiful person. The inscription was written by Dr. Bentley, and is very elegant; but the most lasting and decisive tribute to his memory was paid by sir Isaac Newton, who said, <e Had Cotes lived, we should have known something."

When Dr. Plume’s professorship for astronomy and experimental philosophy was contended for, Mr. Whiston was one of the electors. Besides Mr. Cotes, there was another candidate, who had been a scholar of Dr. Harris’s. | As Mr. Whiston was the only professor of mathematics who was directly concerned in the choice, the rest of the electors naturally paid a great regard to his judgment. At the time of election, Mr. Whiston said, that he pretended himself to be not much inferior to the other candidate’s master, Dr. Harris; but he confessed “that he was but a child to Mr. Cotes.” The votes were unanimous for Mr. Cotes, who was then onJy in the twenty-fourth year of his age.

In 1707, Mr. Whiston and Mr. Cotes united together in giving a course of philosophical experiments at Cambridge. Among other parts of the undertaking, certain hydrostatic and pneumatic lectures were composed. They were in number twenty-four, of which twelve were written by Mr. Cotes, and twelve by Mr. Whiston. But Mr. Whiston esteemed his own lectures to be so far inferior to those of Mr. Cotes, that he could never prevail upon himself to revise and improve them for publication.

The early death of Mr. Cotes is always spoken of with regret by every mathematician and every philosopher; since, if his life had been continued, he would undoubtedly have proved one of the greatest men which this country has produced. 1

1 Biog. Brit. Nichols’s Bowyer, and Hist, of Leicestershire. Whiston’s Life. Knight’s Life of Colet.