Context. Most observations of the solar corona beyond 2 R consist of broadband visible light imagery carried out with coronagraphs. The associated diagnostics mainly consist of kinematics and derivations of the electron number density. While the measurement of the properties of emission lines can provide crucial additional diagnostics of the coronal plasma (temperatures, velocities, abundances, etc.), these types of observations are comparatively rare. In visible wavelengths, observations at these heights are limited to total eclipses. In the ultraviolet (UV) to extreme UV (EUV) range, very few additional observations have been achieved since the pioneering results of the Ultraviolet Coronagraph Spectrometer (UVCS). Aims. One of the objectives of the Full Sun Imager (FSI) channel of the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter mission has been to provide very wide field-of-view EUV diagnostics of the morphology and dynamics of the solar atmosphere in temperature regimes that are typical of the lower transition region and of the corona. Methods. FSI carries out observations in two narrowbands of the EUV spectrum centered on 17.4 nm and 30.4 nm that are dominated, respectively, by lines of FeIX/X (formed in the corona around 1 MK) and by the resonance line of HeII (formed around 80 kK in the lower transition region). Unlike previous EUV imagers, FSI includes a moveable occulting disk that can be inserted in the optical path to reduce the amount of instrumental stray light to a minimum. Results. FSI detects signals at 17.4 nm up to the edge of its field of view (7 R), which is about twice further than was previously possible. Operation at 30.4 nm are for the moment compromised by an as-yet unidentified source of stray light. Comparisons with observations by the LASCO and Metis coronagraphs confirm the presence of morphological similarities and differences between the broadband visible light and EUV emissions, as documented on the basis of prior eclipse and space-based observations. Conclusions. The very-wide-field observations of FSI out to about 3 and 7 R, without and with the occulting disk, respectively, are paving the way for future dedicated instruments
