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We present a comprehensive set of spectral data from two quiescent solar prominences observed in parallel from space and ground: with the VTT, simultaneous two-dimensional imaging of Hβ 4862 Å and Ca ii 8542 Å yields a constant ratio, indicating small spatial pressure variations over the prominence. With the Gregory, simultaneous spectra of Ca ii 8542 Å and He i 10830 Å were taken, their widths yielding 8000 K <Tkin<9000 K and 3<vnth<8 km s−1. The integrated line intensities show a distinct relation E(He i) versus E(Ca ii) for each prominence (‘branching’). The intensity ratio of the helium triplet components is used for a simple estimate of the optical thickness, which is τ<1.0 for the fainter prominence but reaches up to τ=2.0 for the brighter one. The τ0 values allow us to deduce the source function from the central line intensities and thus a mean excitation temperature Texmean=3750 K, which determines the relative populations of the helium 3S and 3P levels. With SUMER, we sequentially observed six spectral windows containing higher Lyman lines, ‘cool’ emission lines from neutrals and singly charged atoms, as well as ‘hot’ emission lines from ions like O iv, S v, N v, O v, and S vi. The spatial variation of the EUV lines along the SUMER slit shows a pronounced maximum at the main prominence body and ‘side-regions’ where the ‘hot’ lines are significantly enhanced with respect to the ‘cool’ lines from neutral and singly-ionized atoms. These selected locations were averaged over 7′′ and the resulting mean EUV lines were fitted by Gaussians yielding realistic widths and integrated line intensities. The intensities of ‘hot’ lines blue-wards of the Lyman series limit appear reduced in the main prominence body but enhanced in the ‘side-regions’. This absorption is also visible in TRACE images of Fe ix/x 171 Å as fine dark structure which covers only parts of the main (‘cool’) prominence body. The Lyman lines show a smooth decrease of both line widths and integrated emission, with increasing upper level k = 5 to k = 19; the widths are smaller for the prominence that yields lower Tkin from the ground-based spectra. The level populations along the line of sight follow for 5 lek le a smooth Boltzmann distribution with Tex>6×104 K, the levels k > 8 appearing more and more overpopulated. The larger widths of the Lyman lines require high non-thermal broadening close to that of ‘hot’ EUV lines. In contrast, the He ii emission is more related to the ‘cool’ lines.