An early history of logarithms.

Abstract

A large number of reference works on the history of mathematics seem to suggest either that an in-depth discussion of the ideas which led up to the simultaneous discovery of logarithms by Napier and Burgi would be too arcane to be of interest, or that not much did lead up to the achievement of these two discoverers and that the idea of logarithms simply spontaneously created itself in Napier and Burgi, as if of nothing. Much the same attitude seems prevalent in the area of what the discovery of logarithms meant in subsequent developments in mathematical thinking. Ease of calculations is of course mentioned, but subsequent contributions to the development of calculus and the considerable scientific importance of the discovery of the number e, which occurred as a direct result of the discovery of logarithms, most often receives scant attention. In fact, however, the history of logarithms stretches from Babylon to Newton, and a considerable number of interesting problems and ingenious solutions can be encountered along the way. The purpose of this thesis has been to explore in considerable detail the development of the idea of logarithms and of logarithms themselves from the first logarithmic-like tables of the Babylonians through the work of Isaac Newton. No known study of the history of logarithms in such detail either exists or is currently available. This work attempts to fill that void. Additionally, the history of logarithms runs parallel to, is influenced by, or is in turn influential in a number of other significant developments in the history of mathematics and science, not the least of which is the development of trigonometry. These parallels and influences are an interesting source of study in their own right.