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Mathematical Treasures - Richard Sault's New Treatise of Algebra

Frank J. Swetz and Victor J. Katz

Richard Sault's title page


This is the title page of A New Treatise of Algebra by Richard Sault (d. 1702). Not much is known about Sault, except that he ran a mathematical school in London in the 1690s near the Royal Exchange and was an editor of and contributor to the Athenian Mercury, a literary journal that was published between 1690 and 1697. The Treatise of Algebra was published as an appendix to William Leybourne's Pleasure with Profit, and included a chapter by Joseph Raphson on converging series.


Sault p. 1


On page 1, Sault describes algebra as the "art of reasoning with unknown quantities, in order to discover their habitude or relation to such as are known."


Sault p. 19


On page 19, Sault describes in some detail, with an example, how to convert a word problem into algebraic notation. Note that he generalizes his problem by using arbitrary constants, instead of just the given numbers.


Sault p. 20


On page 20, Sault continues his description of solving equations, giving more examples and then various questions for practice.


Sault p. 33


On page 33, Sault introduces quadratic equations, showing how the solution procedure for these equations enables one to solve a problem that Clavius was unable to solve in his own treatise on algebra.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Richard Sault's New Treatise of Algebra," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University