John, a celebrated astronomer and mathematician, was born at Edinburgh in 1671, and studied in the university of that city. In 1694 he went to Oxford, where, being admitted of Balliol College, he began to read lectures according to the Newtonian system, in his private chamber in that college. He is said to have been the first who taught Sir Isaac Newton's principles by the experiments on which they are founded; and this, it seems, he did by an apparatus of instruments of his own providing, by which means he acquired a great reputation in the university. The first specimen he gave to the public of his skill in mathematical and philosophical knowledge, was his Examination of Burnet's Theory of the Earth, with remarks on Mr Whiston's Theory; and these theories being defended by their respective inventors, Mr Keill published an Examination of the Reflections on the Theory of the Earth, together with a Defence of the Remarks on Mr Whiston's New Theory. In 1701, he published his celebrated treatise, entitled Introductio ad verum Physicam, which only contains fourteen lectures; but in the following editions he added two more. This work has been translated into English, under the title of an Introduction to Natural Philosophy. Afterwards, being made fellow of the Royal Society, he published, in the Philosophical Transactions, a paper on the laws of attraction; and, being offended at a passage in the Acta Eruditorum of Leipsic, warmly vindicated against Leibnitz, Sir Isaac Newton's right to the honour of priority in the invention of the method of Fluxions. In 1709 he went to New England as treasurer of the Palatines. About the year 1711, several objections being urged against Sir Isaac Newton's philosophy, in support of Descartes's notions of a plenum, Mr Keill published a paper in the Philosophical Transactions, on the rarity of matter, and the tenacity of its composition. But whilst he was engaged in this dispute, Queen Anne appointed him her decipherer; and he continued in that situation under King George I. until the year 1716. He had also the degree of doctor of physic conferred upon him by the university of Oxford in 1713. Besides the works already mentioned, Dr Keill published Introductio ad verum Astronomiam, which was translated into English by the author himself; and an edition of Commandinus's Euclid, with additions of his own.