The ionizing fluxes from quasars and other active galactic nuclei ( AGN ) are critical for interpreting their emission-line spectra and for photoionizing and heating the intergalactic medium ( IGM ) . Using far-ultraviolet spectra from the Cosmic Origins Spectrograph ( COS ) on the Hubble Space Telescope ( HST ) , we directly measure the rest-frame ionizing continua and emission lines for 159 AGN at redshifts 0.001 < z _ { AGN } < 1.476 and construct a composite spectrum from 475–1875 Å . We identify the underlying AGN continuum and strong EUV emission lines from ions of oxygen , neon , and nitrogen after masking out absorption lines from the H i Ly \alpha forest , 7 Lyman-limit systems ( N _ { HI } \geq 10 ^ { 17.2 } cm ^ { -2 } ) and 214 partial Lyman-limit systems ( 15.0 < \log N _ { HI } < 17.2 ) . The 159 AGN exhibit a wide range of FUV/EUV spectral shapes , F _ { \nu } \propto \nu ^ { \alpha _ { \nu } } typically with -2 \leq \alpha _ { \nu } \leq 0 and no discernible continuum edges at 912 Å ( H i ) or 504 Å ( He i ) . The composite rest-frame continuum shows a gradual break at \lambda _ { br } \approx 1000 Å , with mean spectral index \alpha _ { \nu } = -0.83 \pm 0.09 in the FUV ( 1200–2000 Å ) steepening to \alpha _ { \nu } = -1.41 \pm 0.15 in the EUV ( 500–1000 Å ) . We discuss the implications of the UV flux turnovers and lack of continuum edges for the structure of accretion disks , AGN mass inflow rates , and luminosities relative to Eddington values .