KEILL (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 New-
ton'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 mathe-
matical and philosophical knowledge, was his Exami-
nation of Dr Burnet's theory of the earth, with Re-
marks 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 phy-
sicam, 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, be-
ing made fellow of the Royal Society, he published,
in the Philosophical Transactions, a paper, of the law 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 tenuity of its compo-
sition. But while he was engaged in this dispute,
queen Anne was pleased to appoint him her decy-
pherer; and he continued in that place under king
George I. till the year 1716. He had also the de-
gree of doctor of physic conferred on him by the uni-
versity of Oxford in 1713. He died in 1721. He
published, besides the works already mentioned, In-
troductio ad veram astronomiam, which was translated in-
to English by Dr Keill himself; and an edition of
Commandinus's Euclid, with additions of his own.