A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions.
For an abstract algebraic curve, if 
and 
are nonconstant rational functions of a parameter, the curve
so defined has curve genus 0. Furthermore, 
and 
may be expressed rationally in terms of a parameter which
is rational in them (Coolidge 1959, p. 246).
For simple transcendental extensions, all proper extensions of a field 
which are contained in a simple transcendental extension of
are also simple transcendental. In particular,
if 
is an intermediate field between 
and the field 
of rational functions over 
, then 
for some nonconstant rational
function 
(van der Waerden 1966, p. 198).
