## Algebra## Exponents and Logarithms |

## What was the progression of logarithm development? |

The invention of logarithms was a long process, starting with Scottish mathematician John Napier (1550-1617; also known as Laird of Merchiston), who first came up with the idea of logarithms in 1594. But the actual invention and announcement of logarithms would take another 20 years: In 1614, Napier would publish *Mirifici logarithmorum canonis descripto (Description of the Wonderful Canon of Logarithms),* offering tables and rules for their use.

Not long afterward, in 1617, English mathematician Henry Briggs (1561–1630) published *Logarithmorum chilias prima (Logarithms of Numbers from 1 to 1,000),* introducing the concept of common logarithms—or logarithms based on the powers of ten. And finally, independently from Briggs and Napier came Swiss mathematician Joost Bürgi (1552–1632), who in 1620, presented *Arithmetische und geometrische progress-tabulen,* a German work presenting the discovery of logarithms.

The discoveries differed in several ways: Napier’s approach was algebraic; Bürgi’s was geometric. There were differences from the common and natural logarithms used today. And neither Napier nor Bürgi mentioned the concept of a logarithmic base— something that Briggs presented.

By 1624, Briggs would write *Arithmetica logarithmica (The Arithmetic of Logarithms),* extending his common log tables from 1 to 20,000 and from 90,000 to 100,000. But the work on logarithms did not end with Napier, Briggs, or Bürgi. Natural logarithms eventually evolved out of Napier’s original work. And defining logarithms as exponents was finally recognized by English mathematician John Wallis (1616–1703), who presented them in his 1685 publication *De algebra tractatus (Treatise of Algebra).*