The Applications of Elliptic Functions

1+cos Addition Theorem algebraical angular velocity axes axis c₁ catenary Catenoid centre circle cn a dn confocal constant corresponding cosh cubic curve d₁ denoting differential relation do² du² e₁ e₂ Elastica electrodes elliptic functions elliptic integral expressed factors formulas given herpolhode hyperbola hyperbolic functions II(u imaginary infinite invariable plane Jacobi's notation Landen's Transformation Legendre Legendre's linear Messenger of Mathematics modular angle Modular Equation modulus momental ellipsoid motion negative obtain oscillations pendulum period polhode positive Prove quadric quartic radius rectangle sinh sn²u spherical Spherical Pendulum suppose tangent tanh transformation triangle u₁ U₂ v₁ values vector function vertical w₂ Weierstrass's writing X₁ συ