(Dr 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 the public of his skill in mathematical and philosophical knowledge, was his Examination of Dr Burnet's theory of the earth, with Remarks on Mr Whiston's theory: and these theories being defended by their respective inventors, drew from Mr Keill 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, intitled, Introductio ad veram physicam, which only contains 14 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, of the laws of attraction; and being offended at a passage in the Acta eruditorum of Leipzig, warmly vindicated against Mr Leibnitz Sir Isaac Newton's right to the honour of the first invention of his 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 Des Cartes'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 while he was engaged in this dispute, queen Anne was pleased to appoint him her decipherer; and he continued in that place under king George I. till the year 1716. He had also the degree of doctor of physic conferred on him by the university of Oxford in 1713. He died in 1721. He published, besides the works already mentioned, Introductio ad veram astronomiam, which was translated into English by Dr Keill himself; and an edition of Commandinus's Euclid, with additions of his own.

(James), M.D., an eminent physician, and brother of the former, was born in Scotland about the year 1673; and having travelled abroad, read lectures of anatomy with great applause in the universities of Oxford and Cambridge, by the latter of which he had the degree of doctor of physic conferred upon him. Kaisersberg In 1700 he settled at Northampton, where he had considerable practice as a physician; and died there of a cancer in the month in 1719. He published, 1. An English translation of Lemery's chemistry. 2. An account of animal secretion, the quantity of blood in the human body, and muscular motion. 3. A treatise on anatomy. 4. Several pieces in the Philosophical Transactions.