KEILL, JOHN, a distinguished British mathematician and natural philosopher, was born at Edinburgh in 1671, and having received the rudiments of education in that city, he completed his course of study in its university, of which the celebrated Dr. Gregory was then the mathematical professor. In 1691 be was entered in Balie! College, Oxford, where ha distinguished himself by the lectures which he delivered in private on various subjects relating to natural philosophy, principally from the works of Newton ; and in 1698 he published in London ' An Examination of Dr. Burnet's Theory of the Earth, with some Remarks on Whietou's New Theory.' In this work Keill pointed out, not without some harshness, the errors into which those theorists had fallen ; and the severity of his strictures drew from each of them a reply : it is evident however that the advantage in the argument is on the aide of Keill. In 1700 ho was elected a Fellow of tho Royal Society of London, and in tho same year he succeeded Dr. Millington ae Sedleian professor of natural philosophy. Two years afterwards he published a work in Latin tinder the title of ' Intro duetio ad veram Physicam,' which was well received in this country, and was also much esteemed in France—it being there considered as an excellent key to the Principle' of Newton. An edition of it in English was published in London in 1733, under the title of An Introduction to Natural Philosophy,' &c.
In 1709 Keill went to Now England with the appointment of trea surer to the Palatines, who were sent to America as emigrants at the expense of the British government; these persons had been induced to leave Germany, and were living in London in great poverty : be returned however in the following year, and was immediately chosen Savilian Professor of Astronomy at Oxford. In the year 1711 lie was charged by Queeu Anne with the duty of deciphering papers; and it is mentioned as a proof of his sagacity that he once deciphered a letter written in Swedish, though ho knew not a word of the language. Ile held this poet about five years.
In 1713 the University of Oxford conferred on him the degree of Doctor in Physic ; istid in that year he published an edition of Corn mandine's ' Elements' of Euclid, with a tract on Trigonometry, and one ou the Nature of Logarithms. Iu 1718 ho published a work entitled ' Introductio ad veram Astronomiam,' which he afterwards translated into English, and published in 1721 under the title of An Introduction to the true Astronomy, or Astronomical Lectures delivered at Oxford.'
In the 'Philosophical Transactions' for 1708 there are two papers by Keill, of which the first is entitled On the Laws of Attraction and other Physical Principles,' and the other, 'Of the Laws of Centri fugal Force.' In the volume for 1713 there is a paper by him on The Newtonian Solution of Kepler'e Problem,' itc. He nlso gave a paper entitled Theoremata qureclam Infinitam 3laterito Divisibilitatcm spectantia;' and one which ie designated 'Observations on Mr. John Bernoulli's Remarks on the Inverse Problems of Central Forces, with a Now Solution of the Problems; both of those were published in the ' Transactions' for 1714.
Dr. Keill died September 1, 1721, in the fiftieth year of his age.
A writer iu the Acta Eruditorum' having, in a notice of Newton's Treatise on the Quadrature of Curves, stated that the English philo sopher had taken the method of Fluxions from Leibnitz, the indignation of Newton's friends was excited; and in the paper on the Laws of Attraction, dm, which, as above mentioned, was published in tho 'Philosophical Transactions,' Keill formally asserted the claims of Newton to priority in the discovery. This paper gave offence to Leibnitz, who, in a letter to the secretary of tho Royal Society, required that Keill should be compelled to retract his assertion : this was not done; and Keill, in a letter to the eecretary, detailed the evidences of what he had stated.
Dr. Keill was not fortunate on another occasion. Entering into the war of problems which was at that time carried ou between the English mathematicians and those of the Continent, he somewhat presumptu ously challenged John Bernoulli to determine the path of a body when projected in a medium which exercised on it a resistance varying with the square of the velocity : the challenge was accepted, and before Keill could complete his own solution, Bernoulli announced that lie had succeeded in obtaining one. Keill was, in consequence, compelled to endure in silence the reproof which the foreign mathematician did not fail, unsparingly, to administer.
An edition, in Latin, of Dr. Keill's principal works was published at Milan, in 1742, in 4to, under the title Introductio ad veram Physicam et Astronomiam (Huygenii Theoremata do Vi Centrifuga), quibns accedunt Trigonometria; de Viribus Centralibus; do Legibus Attractionis.'