projection of $C'$ back into the plane will only introduce double points as singularities. As Coolidge shows in some detail [@Coolidge1931 210–212], the point $Q$ has to be chosen so as not to fall on a line that happens to belong to any of four different 1-parameter systems, which of course can always be done. The image of $C'$ is then a new planar curve $C''$ on which the singular point $P\in C_n$ now corresponds to $m$ nonsingular points; moreover, the only new singularities that arise will be simple nodes. Repeating this argument for each higher singularity then yields a new curve birationally equivalent to $C_n$ and whose only singularities are double points.

![Clebsch’s Mapping of a Plane to a Cubic Surface from [@Clebsch1866] (Pictures Courtesy of Oliver Labs)](ClebschDiag){width="12cm" height="7cm"}

Klein’s request that Noether inform Bertini of these oral communications from 1869 left Noether at a loss as to what he should do. He regarded Klein’s intervention as a very belated and also highly unexpected attempt to set the record straight. Under normal circumstances, Noether would have surely wanted to clarify such matters as well. This particular case, however, put him in a very awkward situation. He was certainly less 