The history goes back further, and is also interesting. When John Browning first thought about making an autoloading pistol, he experimented with revolver cartridges, specifically the .32 S&W and the .38 S&W. The black powder loads of those days didn't work well, but the new smokeless powder gave a lot of improvement. The rims interfered with feeding through a magazine, but Browning needed a rim to support the cartridge and as a way to extract an unfired cartridge or a fired case in a recoil operated pistol. (In a blowback, the case blew itself out of the chamber.)
So Browning kept reducing the rim and deepening the extractor groove until he had something that worked, but the cartridges still had to be supported (headspace) on the rim, since Browning couldn't think of any other way.
Meanwhile, across the pond, one Hugo Borchardt made a pistol which supported its cartridges like the Mauser rifle, on a case shoulder. And Mauser soon followed suit, as did Georg Luger. But Luger had his own problem when the German army wanted to increase the bullet diameter. That eliminated the shoulder! So Luger hit on the idea of supporting the case on its mouth. And it worked. Probably sometime around 1904, Browning heard about the Luger idea and the light went on. Browning dropped the idea of cartridges with a little rim and the two cartridges he developed after that were rimless and supported on the case mouth (the .380 ACP and the .45 ACP).
Jim