Context. After several generations of interferometers in radioastronomy, wide-field imaging at high angular resolution is today a major goal for trying to match optical wide-field performances. Aims: All the radio-interferometric, wide-field imaging methods currently belong to the mosaicking family. Based on a 30 years old, original idea from Ekers & Rots, we aim at proposing an alternate formalism. Methods: Starting from their ideal case, we successively evaluate the impact of the standard ingredients of interferometric imaging, i.e. the sampling function, the visibility gridding, the data weighting, and the processing of the short spacings either from single-dish antennas or from heterogeneous arrays. After a comparison with standard nonlinear mosaicking, we assess the compatibility of the proposed processing with 1) a method of dealing with the effect of celestial projection and 2) the elongation of the primary beam along the scanning direction when using the on-the-fly observing mode. Results: The dirty image resulting from the proposed scheme can be expressed as a convolution of the sky brightness distribution with a set of wide-field dirty beams varying with the sky coordinates. The wide-field dirty beams are locally shift-invariant as they do not depend strongly on position on the sky: their shapes vary on angular scales typically larger or equal to the primary beamwidth. A comparison with standard nonlinear mosaicking shows that both processing schemes are not mathematically equivalent, though they both recover the sky brightness. In particular, the weighting scheme is very different in both methods. Moreover, the proposed scheme naturally processes the short spacings from both single-dish antennas and heterogeneous arrays. Finally, the sky gridding of the measured visibilities, required by the proposed scheme, may potentially save large amounts of hard-disk space and cpu processing power over mosaicking when handling data sets acquired with the on-the-fly observing mode. Conclusions: We propose to call this promising family of imaging methods wide-field synthesis because it explicitly synthesizes visibilities at a much finer spatial frequency resolution than the one set by the diameter of the interferometer antennas.