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Mathematical Treasure: Raphson's Root Approximation

Frank J. Swetz (Pennsylvania State University)

Joseph Raphson (ca. 1648-1715) was an English mathematician. In 1690, he published Analysis equationum universalis in which he introduced a method for approximating roots of a given equation. Today, this technique is known as the “Newton-Raphson Method.” The 1702 edition of this work is examined here.


On page 11, extraction of the fourth root of the number 2,741,583,974 is demonstrated, and is found to be 228.82337560198. The modern reader may verify this result.


The images above are provided courtesy of Columbia University Libraries.

Index to Mathematical Treasures 

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Raphson's Root Approximation," Convergence (April 2018)