John Keill FRS (1 December 1671 – 31 August 1721) was a Scottish mathematician, natural philosopher, and cryptographer who was an important defender of Isaac Newton.
He instructed his students on the laws of motion, the principles of hydrostatics and optics, and Newtonian propositions on light and colours.
His volume contained scientific attacks on Burnet, René Descartes, Baruch Spinoza, Thomas Hobbes and Nicolas Malebranche.
However, after failing to get an academic appointment at Oxford in 1709, Keill left the university to seek a government position.
At Hart Hall the innovatory nature of Keill's demonstrations, and his teaching, were continued after 1710 by his student John Theophilus Desaguliers.
In 1709, Keill was appointed treasurer of a charitable fund to resettle war refugees from the German states.
In 1717, Keill married Mary Clements, a woman 25 years his junior and the daughter of an Oxford bookbinder.
He spent £500 to his household furniture and plate to his wife and his books, instruments and other money in trust for his son.Keill's publisher at Oxford, Henry Clements, sometimes bound Keill's Trigonometriae and Logarithmorum with Federico Commandino's translation of Euclid's Elements.