Observations by the Large Area Telescope (LAT) on the Fermi mission of diffuse gamma-rays in a mid-latitude region in the third quadrant (Galactic longitude l from 200 degrees to 260 degrees and latitude vertical bar b vertical bar from 22 degrees to 60 degrees) are reported. The region contains no known large molecular cloud and most of the atomic hydrogen is within 1 kpc of the solar system. The contributions of gamma-ray point sources and inverse Compton scattering are estimated and subtracted. The residual gamma-ray intensity exhibits a linear correlation with the atomic gas column density in energy from 100 MeV to 10 GeV. The measured integrated gamma-ray emissivity is (1.63 +/- 0.05) x 10(-26) photons s(-1)sr(-1) H-atom(-1) and (0.66 +/- 0.02) x 10(-26) photons s(-1)sr(-1) H-atom(-1) above 100 MeV and above 300 MeV, respectively, with an additional systematic error of similar to 10%. The differential emissivity from 100 MeV to 10 GeV agrees with calculations based on cosmic ray spectra consistent with those directly measured, at the 10% level. The results obtained indicate that cosmic ray nuclei spectra within 1 kpc from the solar system in regions studied are close to the local interstellar spectra inferred from direct measurements at the Earth within similar to 10%.