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We present an algebraic approach to multibody motion segmentation from line correspondences. Given three perspective views containing multiple linearly moving objects, we demonstrate that after applying a polynomial embedding to the line correspondences, they became related by the so-called multibody line constraint of translational motions. We show how to linearly estimate the multibody trifocal epipole from line-line-line correspondences. The individual trifocal epipoles are then obtained from the derivatives of the multibody line constraint (up to an unknown factor). Given normalized trifocal epipoles, we can use any special clustering technique to obtain the clustering of the motions and the correspondences. The limitations of the proposed algorithm are also discussed. Experimental results on synthetic and real dynamic scenes are presented.