historians of geometry, others less so. Among the latter, his [*Treatise on Algebraic Plane Curves*]{} [@Coolidge1931] is easily overlooked. Certainly its style and contents appear very old-fashioned today, especially when set alongside a text like [@B-K], despite obvious similarities in the subject matter. Coolidge cultivated an unusually informal writing style, even when describing rather technical matters. He was also disarmingly honest, informing the reader whenever he happened to discuss a work without actually having held it in his hands.[^1]

One of the authors Coolidge admired most deeply was Max Noether,[^2] whose publications from the 1870s exerted a lasting influence on Italian algebraic geometers [@CES]. Noether followed in the footsteps of his principal mentor, Alfred Clebsch, who opened the doors to exploring the rich possibilities of Riemann’s theory of complex functions for algebraic geometry, in particular the birational geometry of curves [@Klein1926 295–309].

The present paper discusses a central theorem in birational geometry first proved by Eugenio Bertini in [@Bertini1891]. Coolidge described the main ideas behind Bertini’s proof in [@Coolidge1931 208–212], but he attributed the theorem to Clebsch. He did so owing to a short note that Felix Klein appended to the republication of Bertini’s article in [*Mathematische Annalen*]{} [@Bertini1894 160]. 