[FOM] Number theory proof mentioned by Frege

[Chris Gray]

In "The Foundations of Arithmetic", Frege mentions a proof from pp.106-7 
of Hermann Henkel's Theorie der complexen Zahlensysteme.

"Hankel proves that any closed field of complex numbers of higher order 
than the ordinary, if made subject to all the laws of addition and 
multiplication, contains a contradiction."  Frege p. 106

I have no copy of the Henkel book available to me.  Is this a well-known 
result?  Is this proof discussed or given elsewhere?

Thanks,
Chris Gray
University of Waterloo Library