In this paper the author proposes to investigate the true geometrical basis of that entire class of algebraical expressions, known to mathematicians as elliptic functions or integrals. He sets out by showing what had already been done in this department of the subject by preceding geometers. That the elliptic integral of the second order represented an arc of a plane ellipse, was evident from the beginning.
On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of Jacobi
