 Once again, I.4 is problematic. Consider, for the purpose of a reduction ad absurdum, that one has two triangles, \(ABC\) and \(A'BC\) on the same side of their common base \(BC\), and such that \(BA = BA'\) and \(CA = CA'\). It is intended to show that therefore the vertices \(A\) and \(A'\) coincide, and for this one must, as Gauss observed (in unpublished remarks, see Gauss Werke 8, 193), use the fact that the triangles lie in the same plane. A good definition of a plane is required, one that allows this result to be proved.