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Mathematical Treasure: Arithmetica Logarithmica of Henry Briggs

Frank J. Swetz (The Pennsylvania State University)

Henry Briggs (1561-1630) was a geometer and an active applied mathematician. He was the first Professor of Geometry at Gresham College, London, and later became the first Savilian Professor of Geometry at Oxford University, appointed by Henry Savile (1549-1622) himself.

Arithmetica Logarithmica title page

Briggs was impressed by John Napier’s (1550-1617) invention of logarithms and their facility in easing calculations. However, he considered their basis to be somewhat awkward and conceived his own system of logarithms with a base of 10. Briggs published his first extensive table of these logarithms in 1624 in Arithmetica Logarithmica. His table contained the logarithms of 30,000 natural numbers, each carried out to fourteen decimal places. Today, we refer to Briggs’ logarithms as “common logarithms.”

Arithmetica Logarithmica ellipses

In Chapter 26 of his Arithmetica, Briggs demonstrated the use of his logarithms in computing the properties of the ellipse.

Arithmetica Logarithmica polygons

In Chapter 28, Briggs used logarithms to solve more complex geometric problems involving inscribed polygons.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Swetz, Frank J., "Mathematical Treasure: Arithmetica Logarithmica of Henry Briggs," Loci (March 2013), DOI: 10.4169/loci003959

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: [i]Arithmetica Logarithmica[/i] of Henry Briggs," Convergence (April 2013), DOI:10.4169/loci003959