In this paper we describe a method to perform Euclidean reconstruction with a perspective camera model. It incrementally performs reconstruction with a paraperspective camera in order to converge towards a perspective model. With respect to other methods that compute shape and motion from a sequence of images with a calibrated perspective camera, this method converges in a few iterations, is computationally efficient, and does not suffer from the non linear nature of the problem. Moreover, the behaviour of the algorithm may be simply explained and analysed, which is an advantage over classical non linear optimization approaches. With respect to 3-D reconstruction using an approximated camera model, our method solves for the sign (reversal) ambiguity in a very simple way and provides much more accurate reconstruction results.