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The Far Ultraviolet Spectroscopic Explorer (FUSE) has surveyed a large sample (> 100) of active galactic nuclei in the low-redshift universe (z < 1). Its response at short wavelengths makes it possible to measure directly the far ultraviolet spectral properties of quasistellar objects (QSOs) and Seyfert 1 galaxies at z < 0.3. Using archival FUSE spectra, we form a composite extreme ultraviolet (EUV) spectrum of QSOs at z < 0.67. After consideration of many possible sources of systematic error in our analysis, we find that the spectral slope of the FUSE composite spectrum, α= -0.56^+0.38_-0.28 for F_ν\propto ν^α, is significantly harder than the EUV (λ\lesssim 1200 A) portion of the composite spectrum of QSOs with z > 0.33 formed from archival Hubble Space Telescope spectra, α=-1.76 \pm 0.12. We identify several prominent emission lines in the \fuse composite and find that the high-ionization O VI and Ne VIII emission lines are enhanced relative to the HST composite. Power law continuum fits to the individual FUSE AGN spectra reveal a correlation between EUV spectral slope and AGN luminosity in the FUSE and FUSE + HST samples in the sense that lower luminosity AGNs show harder spectral slopes. We find an anticorrelation between the hardness of the EUV spectral slope and AGN black hole mass, using estimates of this quantity found in the literature. We interpret these results in the context of the well-known anticorrelation between AGN luminosity and emission line strength, the Baldwin effect, given that the median luminosity of the FUSE AGN sample is an order of magnitude lower than that of the HST sample.