Thomas Harriot on continuous compounding. (English) Zbl 1305.01014

Biggs, Norman

BSHM Bull. 28, No. 2, 66-74 (2013).

The article deals with a calculation of continuous compounding of interest found in Harriot’s manuscript, probably written before 1620. The author also describes the historical and mathematical significance of Harriot’s calculation, relating it with the development of the logarithm and its use in the compilation of tables of logarithms and of antilogarithms. Hence the author continues with a brief historical description of the relation between the logarithm and the area under the hyperbola \(xy= 1\). He goes through works by Gregoire de Saint Vincent (1647), Sarasa, Mercator (1668) and finally Newton in a manuscript of 1671. Moreover, the author also describes the results related with this calculation of continuous compounding, drawing on the development of infinite series by several authors. To the mathematicians already quoted above, he adds Wallis (1685), Bernoulli (1713), de Moivre (1718) and Arbuthnot (1727), where the result of development of a power series for solving a problem of compound interest is applied. The author ends the article with Euler’s result (1736) which shows the exponential function is the inverse of the logarithmic function, that is, Harriot’s result for all \(x\) approaches \(ex\) as \(n\) (the number of years) becomes larger.

Reviewer: Maria Rosa Massa Esteve (Barcelona)

MSC:

01A45	History of mathematics in the 17th century
40C15	Function-theoretic methods (including power series methods and semicontinuous methods) for summability

Keywords:

infinite series; compounding of interest; Thomas Harriot; seventeenth century

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