  We report on the detection of a hot subdwarf component in the Be binary
system, 59 Cygni. The spectral signature is found in cross-correlation
functions of photospheric model spectra with far-ultraviolet spectra obtained
by the International Ultraviolet Explorer Satellite, and we used radial
velocities from the cross-correlation functions to determine a double-lined
spectroscopic orbit. The individual spectra of the binary components were
extracted using a Doppler tomography algorithm. The flux of the system is
dominated by the rapidly rotating Be star. However, the subdwarf contributes
approximately 4% of the UV flux, and its spectrum bears a strong resemblance to
that of the hot sdO star BD +75 325. Based upon the appearance of the UV
spectrum and the orbital elements, we present estimates for the stellar masses,
radii, and temperatures. The presence of the hot companion causes excess
emission from the outer part of the Be disk facing the companion. We present a
set of red spectra that show the orbital phase variations of the He I 6678
emission formed in the heated region of the disk, which probably occurs near
the disk outer boundary. 59 Cygni, FY Canis Majoris, and phi Persei comprise
the known set of Be binaries with detected hot evolved companions, which are
the stripped down remains of mass transfer. Their properties demonstrate that
some fraction of Be stars were spun up through angular momentum transfer by
Roche lobe overflow.
