We introduce a unified framework for developing matching constraints of multiple affine views and rederive 2-view (affine epipolar geometry) and 3-view (affine image transfer) constraints within this framwork. We then describe a new linear method for Euclidean motion and structure from 3 calibrated affine images, based on insight into the particular structure of these multiple-view constraints. Compared with the existing linear method of Huang and Lee [7], the new method uses different and more appropriate constraints. It has no failure mode of the Euclidean factorisation method of Tomasi and Kanade [18]. We demonstrate the method on real image sequences.