We present results from EUVE measurements obtained during the all-sky survey of interplanetary and geocoronal He I 584-¿ emission. The data consist of count rates from the long wavelength spectrometer and the long wavelength photometric band (520--750 ¿) of scanner C obtained over a 1-year period from July 1992 to July 1993. During this period, EUVE was in survey mode so that the scanners made 5¿¿360¿ sweeps of the sky in a plane perpendicular to the Sun-Earth line, while the spectrometers were aligned with the antisolar direction. The interplanetary He I signal is morphologically consistent with previous observations with similar observing geometry, such as Prognoz 6 [Dalaudier et al., 1984>. However, unlike the Prognoz 6 data, the EUVE measurements were made from low Earth orbit (520 km) and so contain geocoronal emission as well. As a result, along sight lines where the relative speed between the interplanetary wind and the Earth is at a minimum, extinction of the interplanetary signal through resonance scattering by the He geocorona occurs. We believe this to be the first detection of line extinction of the local interstellar He wind emissions by the geocorona. We find that the geocoronal extinction signatures provide a new means of determining the interstellar He wind vector and emission line profile and add further constraints on the values of other interplanetary and solar He parameters and the morphology of the He geocorona. On the basis of model fits of the observed interplanetary emission and geocoronal extinction, we determine values for the interplanetary wind ecliptic longitude &lgr;=76.0¿0.4¿, latitude ϕ=-5.4¿0.6¿ (downwind direction), speed v0=26.4¿1.5 km s-1, and temperature T0=6900¿600 K. In addition, assuming an interplanetary He density of 0.01 cm-3, we determine an average solar He I 584-¿ line center flux of 1.4¿0.3¿1010 photons cm-2 s-1 ¿-1 for the data analyzed here. ¿ 1998 American Geophysical Union