Although in the second third of the seventeenth century Oughtred's Key and Harriot's Praxis converted key English thinkers to the analytic way, neither work seemed to satisfy the needs of less talented students wanting to pursue algebra. The Key was too brief, and both it and the Praxis were too dependent on symbols for the general student. The Praxis, designed as a supplement to Viète's Analytic Art, was not a general algebra textbook. The Key – with its focus on quadratic equations and positive real roots – had been, to a certain extent, obsolete as an introductory algebra textbook even at the time of its original publication. Furthermore, subsequent editions of The Key, which continued to be reissued through 1702, took no explicit account of Renè; Descartes's Gèomètrie of 1637 or other later algebraic developments.

Of all the analytic mathematicians in England during the second half of the seventeenth century, John Collins (1625–1683) most persistently pushed for the preparation of an English algebra textbook that both elaborated the principles of the subject in a fashion appropriate for university men and sophisticated practitioners, and covered the main algebraic developments of the century. Collins coaxed Isaac Newton and, at times, John Wallis to produce the desired book. He encouraged John Pell to complete his English edition of a German algebra as well as John Kersey to finish his textbook on the subject.