  In 1776, L. Euler proposed three methods, called prima methodus, secunda
methodus and tertia methodus, to calculate formulae for double zeta values.
However strictly speaking, his last two methods are mathematically incomplete
and require more precise reformulation and more sophisticated arguments for
their justification. In this paper, we reformulate his formulae, give their
rigorous proofs and also clarify that the formulae can be derived from the
extended double shuffle relations.
