Methods of integration by arcs of conic sections in echelons of modules. Legendre as reader of Landen
In 1786, \textit{A.-M. Legendre} published two papers on integration by arcs of ellipse [``Memoire sur les int'egrations par arcs d'ellipse'', Histoire de l'Académie Royale des Sciences, 616--643 (1786); Second memoire sur les intégrations par arcs d'ellipse, et sur la comparaison de ces arcs. Histoire de l'Acad'emie Royale des Sciences, 644--683 (1786)]. In the intervening period he became acquainted with \textit{J. Landen}'s article [``An investigation of a general theorem for finding the length of any conic hyperbola, by means of two elliptic arcs'' (1775)]. The present author analyzes in detail how Landen's results influenced on Legendre's constructions.
scientific article; zbMATH DE number 5916732