External static library within Cygwin

[Jeff Josephs]

I have a third party external static library in native Windows, and I am
trying to use it within my Cygwin project. After looking at the static
library, I noticed that it uses name mangling, and when compiling the
Cygwin project, I get undefined references.

Aside from modifying the third party library to not do the name mangling,
is there anything within Cygwin that I can do to solve the undefined
references with the name mangled functions?