  We describe a generalization of a result of Boshernitzan and Carroll: an
extension of Lagrange's Theorem on continued fraction expansion of quadratic
irrationals to interval exchange transformations. In order to do this, we use a
two-sided version of the Rauzy induction. In particular, we show that starting
from an interval exchange transforma- tion whose lengths are defined over a
quadratic field and applying the two-sided Rauzy induction, one can obtain only
a finite number of new transformations up to homothety.
