Introductory Remarks About the Mémoire (1761/1768)

The historical importance of Lambert’sLambert Lambert, J. H. (1728–1777) Mémoire turns out evident as soon as one realizes the issues tackled by the Swiss. There is little doubt that fame goes to the first part of the article, in which LambertLambert Lambert, J. H. (1728–1777), showing a high level of skill with such then-recent analytic tools like continued fractions, demonstrates with unusual rigour for the 18th century standards the irrationality of \(\pi \) . The issue of the nature of this constant had taken a new impulse since the herculean efforts by Ludolph van CeulenCeulen, L. van (1540–1610) at the end of the 16th century with the use of new analytic tools and their application to some geometric problems. Authors like GregoryGregory, J. (1638–1675), HuygensHuygens, C. (1629–1695), MengoliMengoli, P. (1626–1686), LeibnizLeibniz, G. W. von (1646–1716) or WallisWallis, J. (1616–1703) faced these issues, and in particular, the circle-squaring problem, in which \(\pi \) played a central role. LambertLambert Lambert, J. H. (1728–1777) takes up the baton of this analytic tradition —enriched by EulerEuler, L. (1707–1783) with his first systematic study of continued fractions— and settles the question of its irrationality.