In quasars with strong radio cores, the inverse-Compton process is bel
ieved to be the dominant source X-ray emission. For objects with parse
c-scale radio jets, simple models have predicted that components in th
e jet emerging from the quasar nucleus generate the observed X-ray emi
ssion. We have tested this hypothesis in detail for the quasar 3C 345
using a ROSAT X-ray observation in 1990 July, together with quasi-simu
ltaneous VLBI imaging of the parsec-scale jet at five frequencies. The
ROSAT spectrum is well fitted by a power law with index alpha = -0.96
+/- 0.13, consistent with models in which the X-ray emission results
from inverse-Compton scattering of radio radiation from high-energy el
ectrons in compact components. We show that the radio properties of br
ightest '' knot '' in the jet ('' C5 '') can be fitted with a homogene
ous sphere model whose parameters require bulk relativistic motion of
the emitting material; otherwise the predicted inverse-Compton X-ray e
mission exceeds the observed flux. If C5 is the origin of the X-ray em
ission, then it has a Doppler factor delta = 7.5(-2)+3. If the nucleus
or other components contribute to the X-ray emission, then this becom
es a firm lower limit to delta. The inhomogeneous jet model of Konigl
is a good fit both to the barely resolved (< 1 pc) flat-spectrum nucle
us in the radio, and also to the ROSAT X-ray spectrum. The synchrotron
and inverse-Compton emitting fluid moves down a narrow cone (opening
angle 2phi almost-equal-to 5-degrees) nucleus relativistically, with d
elta almost-equal-to 4.6. Doppler factors for the nucleus and C5, deri
ved from our ROSAT observation, provide evidence for bulk relativistic
motion in the jet. By combining these constraints with the well-known
superluminal motion of jet components, we can deduce the jet geometry
. For epoch 1990.5 we infer the Lorentz factor gamma = 7.5(-1.5)=1.0 a
nd angle to the line of sight theta = 8(-3-degrees)+2-degrees for H-0
= 100 km s-1 Mpc-1. These values are the most reliable yet derived usi
ng this method, because of the near-simultaneity of our X-ray and VLBI
observations and the quality of the multifrequency VLBI images and co
mponent radio spectra.