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We introduce a linear algorithm to recover the Euclidean motion between an orthographic and two perspective cameras from straight line correspondences filling the gap in the analysis of motion estimation from line correspondences for various projection models. The general relationship between lines in three views is described by the trifocal tensor. Euclidean structure from motion for three perspective views is a special case in which the relationship is defined by a collection of three matrices. Here, we describe the case of two calibrated perspective views and an orthographic view. Similar to the other cases, our linear algorithm requires 13 or more line correspondences to recover 27 coefficients of the trifocal tensor.