An Annotated Translation of Lambert’s Mémoire (1761/1768)

Proving that the diameter of the circle is not to its circumference as an integer number to an integer number is something that will hardly surprise geometers. We know Ludolph’s numbers, the ratios found by ArchimedesArchimedes (287–212 BC), by MetiusMetius, A. (1571–1635) etc. as well as a large number of infinite series, all of which refer to the quadrature of the circle. And if the sum of these series is a rational quantity, we must naturally conclude that it will be either an integer number or a very simple fraction.