In this work we recall well known results related to the Helgason-Ludwig Data Consistency Conditions (DCCs) of the 2D Radon transform. These DCCs are based on moments of each projection. The center of mass of each projection is the projection of the center of mass of the measured object. This property is very useful for aligning the data in case of misalignments. However reversed projection angles, a global constant shift of the projection angles or a global sinusoïdal shift of the line index at each projection angle lead to consistent projection data. Thus these acquisition parameter modifications can not be estimated from DCCs. In this work we propose a generalization of these results to parallel and fan-beam linograms.