Logarithms

Abstract

The first tables of logarithms appeared in the early part of the seventeenth century, the best known being due to John Napier and Henry Briggs. We will see something of the ingenuity that went into the creation of these tables in this precalculus era. A little later in the seventeenth century Gregory of St. Vincent cleverly deduced that the logarithm may be expressed as the area under a hyperbola. Following the development of the calculus, his result is seen to be obvious! As so often in the history of mathematics, a hard-won mathematical truth is subsequently viewed as “only” a special case of some grander truth. Yet such pioneering discoveries, including that of Gregory of St. Vincent, remain wonderful achievements.

Population, when unchecked, increases in a geometrical ratio. Subsistence only increases in an arithmetical ratio.