Thomas Simpson and Dido’s problem

Abstract

An elegant geometrical argument concerning Dido’s problem, traditionally credited to Jakob Steiner in about 1840, appears to have been invented by Thomas Simpson, almost 100 years earlier. The argument itself uses only the idea of triangle area and the converse of Thales’ theorem about the angle in a semicircle. It appears in Simpson’s book Elements of Geometry, published in 1760, as part of a highly original section on ‘The Maxima and Minima of Geometrical Quantities’, but traces of the argument can even be found in an earlier edition dated 1747.