NEWTON Isaac Arithmetica Universalis; sive de compositione et resolutione arithmetica liber.

Gray, 279; Wallis, 279 ("includes much new material"); Babson, 204.

This third edition (first Cambridge 1707) , much enlarged, edited by s'Gravesande and with additional material by Halley, Moivre, MacLaurin, Campbell, etc., is based on Newton's notes on lectures given between 1673-1683.

The work is an important complement to his Principia.

"The Arithmetica Universalis was first printed in London in 1707, edited by William Whiston, who 'extracted from Newton a somewhat reluctant permission to print it. Among several new theorems on various points in algebra and the theory of equations, Newton here enunciates the following important results. He explains that the equation whose roots are a solution of a given problem will have as many roots as there are different probable cases… He extends Descartes' rules of signs to give limits to the number of imaginary roots… The most interesting theorem contained in the work is his attempt to find a rule (analogous to that of Descartes for real roots) by which the number of imaginary roots of a equation can be determined" (Ball, A Short History of Mathematics, pp. 330-331).