The invention of logarithms

At the start of the seventeenth century astronomers were buried in computation: multiplying many-digit numbers, as required for planetary positions, was slow and error-prone. The idea of logarithms was born precisely here, from the observation that the properties of powers let one turn a multiplication into an addition. Indeed, if $x = a^m$ and $y = a^n$, then $xy = a^{m+n}$: passing to the exponents, that is to the logarithms, the product $\log_a(xy) = \log_a x + \log_a y$ becomes a simple sum.

The Scotsman John Napier — Italianised as Nepero — published in 1614 the Mirifici Logarithmorum Canonis Descriptio, the first table of logarithms, the fruit of about twenty years of calculation. In almost the same years, and entirely independently, the Swiss Joost Bürgi, a clockmaker and instrument builder at the court of Prague, had compiled analogous tables (the Arithmetische und Geometrische Progress-Tabulen, printed in 1620): his work, however, appeared later and circulated less, so the historical credit for the invention is traditionally given to Napier (Boyer; Katz).

It was then the Englishman Henry Briggs, a professor at Oxford, who made logarithms truly practical. Discussing the matter with Napier, he proposed adopting base $10$ and setting $\log_{10} 1 = 0$ and $\log_{10} 10 = 1$: thus were born the common (decimal) logarithms, the most convenient for our number system. Briggs published extensive many-digit tables (the Arithmetica Logarithmica, 1624), which for over three centuries were the calculating tool of astronomers, engineers and navigators, before being embodied in the slide rule and finally superseded by the electronic calculator (Dunham).

Links

Topics: Logarithmic function Concepts: Logarithm People: John Napier (Nepero) · Joost Bürgi · Henry Briggs