Cayley A. An elementary treatise on elliptic functions

2nd edition. — London: George Bell and sons, 1895. — 386 p.General Outline
The Addition-Equation. Landen's Theorem
Miscellaneous Investigations
On the Elliptic Functions sn, cn, dn
The three kinds of Elliptic Integrals
The functions П(u,a), Zu, Theta u, Hu
Transformation. General Outline
The quadric transformation n=2; and the odd-prime transformations n=3,5,7. Properties of the modular equation and the multiplier
Jacobi's partial differential equations for the functions H, Theta, and for the numerators and denominators in the multiplication and transformation of the elliptic functions sn, cn, dn
Transformation for an odd and in particular an odd-prime order: development of the theory by means of the n-division of the complete functions
The q-functions: further theory of the functions H, Theta
Reduction of a differential expression Rdx/\sqrt{X}
Quadric transformation of the elliptic integrals of the first and second kinds: the arithmetico-geometrical mean
The general differential equation dx/\sqrt{X}=dy/\sqrt{Y}
On the determination of certain curves the arc of which is represented by an elliptic integral of the first kind
On two integrals reducible to elliptic integrals
ADDITION. Further theory of the linear and quadric transformations