  We develop the basic formulae of hyperspherical trigonometry in
multidimensional Euclidean space, using multidimensional vector products, and
their conversion to identities for elliptic functions. We show that the basic
addition formulae for functions on the 3-sphere embedded in 4-dimensional space
lead to addition formulae for elliptic functions, associated with algebraic
curves, which have two distinct moduli. We give an application of these
formulae to the cases of a multidimensional Euler top, using them to provide a
link to the Double Elliptic model.
