This paper offers a precise and almost final solution to one of the most debated problems connected with the astrogeodetic ‘fix’ by azimuth differences. The rectangular and linear solution on the gnomonic plane, tangent to the celestial globe and the dead reckoning position, enables the use of azimuth differences and is connected to Pothenot's solution. Thus this problem may be solved with simple linear algorithms that require neither differential modes, nor the introduction of the unknown origin error.