On the rectification and quadrature of the spherical ellipse

Abstract

The author, at the commencement of this paper, adverts to a rather complex discussion of a portion of the subject of his inquiry by M. Catalan, published in the Journal de Mathématiques , edited by M. Lionville. He then proceeds to establish two fundamental theorems, applicable to, —1st, the quadrature, and 2nd, the rectification of the spherical ellipse.