Sophus Lie considered the same problem, though from a different standpoint. He argued that a rigid body would be such that when one of its points was fixed, any other of its points would describe a surface. When one of its lines was fixed, any other of it's points would describe a curve, and finally, when three points were fixed, the rigid body would be unable to move. As a result of these investigations it was proved that there existed bodies which, as contrasted with Euclidean solids, would squirm when displaced. Yet, in spite of this fact, these non-Euclidean bodies would present all the mathematical requirements of congruent bodies. These alternative types of bodies may be called Riemannian bodies and Lobatchewskian bodies, respectively. If we select Euclidean congruence for the purpose of measuring space, non-Euclidean bodies will appear to squirm as they move; if we select non-Euclidean congruence, it will be the Euclidean bodies which appear to vary in form when displaced. It is usual, however, to reserve the term rigid for the Euclidean bodies; but this is only in order to conform to the ordinary understanding of rigidity as derived from experience. If we omit to take into consideration the physical behaviour of material bodies which has forced a certain conception of rigidity upon us, there appears to be no mathematical reason for assigning greater importance to Euclidean measurements than to non-Euclidean ones. It follows that the non-Euclidean bodies are just as much entitled to the appellation “rigid” as are the better-known Euclidean ones. When it comes to deciding which of the types of rigidity represents conservation of absolute shape and size, the problem appears to be entirely meaningless. Accordingly we shall refer to the various types of bodies as Euclideanly or as non-Euclideanly rigid.