  We present a general result of simultaneous approximation to several
transcendental real, complex or p-adic numbers xi_1,...,xi_t by conjugate
algebraic numbers of bounded degree over Q, provided that the given
transcendental numbers xi_1,...,xi_t generate over Q a field of transcendence
degree one. We provide sharper estimates for example when xi_1,...,xi_t form an
arithmetic progression with non-zero algebraic difference, or a geometric
progression with non-zero algebraic ratio different from a root of unity. In
this case, we also obtain by duality a version of Gel'fond's transcendence
criterion expressed in terms of polynomials of bounded degree taking small
values at xi_1,...,xi_t.
