We present new addition formulae for the Weierstrass functions associated
with a general elliptic curve. We prove the structure of the formulae in
n-variables and give the explicit addition formulae for the 2- and 3-variable
cases. These new results were inspired by new addition formulae found in the
case of an equianharmonic curve, which we can now observe as a specialisation
of the results here. The new formulae, and the techniques used to find them,
also follow the recent work for the generalisation of Weierstrass' functions to
curves of higher genus.Comment: 20 page
