The ionizing fluxes from quasars and other active galactic nuclei ( AGN ) are critical for interpreting the emission-line spectra of AGN and for photoionization and heating of the intergalactic medium . Using ultraviolet spectra from the Cosmic Origins Spectrograph ( COS ) on the Hubble Space Telescope ( HST ) , we have directly measured the rest-frame ionizing continua and emission lines for 22 AGN . Over the redshift range 0.026 < z < 1.44 , COS samples the Lyman continuum and many far-UV emission lines ( Ly \alpha \lambda 1216 , C iv \lambda 1549 , Si iv/O iv ] \lambda 1400 , N v \lambda 1240 , O vi \lambda 1035 ) . Strong EUV emission lines with 14–22 eV excitation energies ( Ne viii \lambda \lambda 770 , 780 , Ne v \lambda 569 , O ii \lambda 834 , O iii \lambda 833 , \lambda 702 , O iv \lambda 788 , 608 , 554 , O v \lambda 630 , N iii \lambda 685 ) suggest the presence of hot gas in the broad emission-line region . The rest-frame continuum , F _ { \nu } \propto \nu ^ { \alpha _ { \nu } } , shows a break at wavelengths \lambda < 1000 Å , with spectral index \alpha _ { \nu } = -0.68 \pm 0.14 in the FUV ( 1200–2000 Å ) steepening to \alpha _ { \nu } = -1.41 \pm 0.21 in the EUV ( 500–1000 Å ) . The COS EUV index is similar to that of radio-quiet AGN in the 2002 HST /FOS survey ( \alpha _ { \nu } = -1.57 \pm 0.17 ) . We see no Lyman edge ( \tau _ { HI } < 0.03 ) or He i \lambda 584 emission in the AGN composite . Our 22 AGN exhibit a substantial range of FUV/EUV spectral indices and a correlation with AGN luminosity and redshift , likely due to observing below the 1000 Å break .