  The positive curved three body problem is a natural extension of the planar
Newtonian three body problem to the sphere $\mathbb{S}^2$. In this paper we
study the extensions of the Euler and Lagrange Relative equilibria ($RE$ in
short) on the plane to the sphere.
  The $RE$ on $\mathbb{S}^2$ are not isolated in general. They usually have
one-dimensional continuation in the three-dimensional shape space. We show that
there are two types of bifurcations. One is the bifurcations between Lagrange
$RE$ and Euler $RE$. Another one is between the different types of the shapes
of Lagrange $RE$. We prove that bifurcations between equilateral and isosceles
Lagrange $RE$ exist for equal masses case, and that bifurcations between
isosceles and scalene Lagrange $RE$ exist for partial equal masses case.
