In their book Rolex Wristwatches, An Unauthorized History, authors Jeffrey Hess and James Dowling note that in the 1920s Rolex produced a limited run of watches using the Borgel screw-in case. “It is a very important development in Rolex watch design. It was the first model produced by Rolex in which the case was specifically designed to give protection against some of the elements,” Hess and Dowling write.
In other words, the first true Rolex sports watches, were courtesy of Borgel. The Rolex Oyster case, released soon after, in 1926, is quite reminiscent of this Borgel screw case; in fact, Hans Wilsdorf and Rolex later purchased one of Borgel’s case patents. While evidence of the relationship between Rolex and Borgel at the time is mostly circumstantial, it seems quite apparent that the Oyster case design was at least heavily influenced by Borgel’s work.
By this time, Borgel’s patents protecting its original screw-in mechanism would have long expired (not to mention also having been surpassed by advancements from other manufacturers). Taubert & Fils recognised this, and iterated through various prototypes before arriving at its next case innovation, the one that it's most recognisable for, to vintage wrist watch collectors: the decagonal case.