The Mg/Ne abundance ratio in the quiet Sun is measured in both network and supergranule cell centre regions through EUV spectra from the Coronal Diagnostic Spectrometer on SOHO. Twenty four sets of data over the period 1996 March to 1998 June (corresponding to solar minimum and the onset of the next cycle) are studied. Emission lines of the sequences Ne IV-VII and Mg V-VIII are simultaneously analysed by comparing with theoretical emissivities from the CHIANTI database to yield the Mg/Ne abundance and emission measure over the temperature region 5.0≤log T≤ 6.1. The average enhancements over the photospheric Mg/Ne abundance are found to be 1.25± 0.10 (network) and 1.66± 0.23 (cell centres), implying that the structures making up the transition region have close-to photospheric abundances. In particular, this implies that only a small fraction of the quiet Sun can connect to the solar wind where the Mg/Ne abundance ratio is found to be factors 4-5 greater than the photospheric value. The quiet Sun spectra are also utilised to determine the coronal density and temperature, leading to average values of 2.6+0.5-0.4× 108 cm-3 and log (T/K)=5.95± 0.02. No significant trend with the rise in solar activity during 1996-98 is found for any of the derived quantities, implying that quiet Sun regions show little dependence on the solar cycle.