Question: What handgun cartridge designed by John Browning in 1905, for use in his prototype Colt semi-automatic pistol, is chambered in a third-generation semi-automatic pistol from Smith & Wesson's 4500 series of handguns?
Context: .32 ACP (Automatic Colt Pistol), also known as the .32 Automatic is a centerfire pistol cartridge.  It is a semi-rimmed, straight-walled cartridge developed by firearms designer John Browning, initially for use in the FN M1900 semi-automatic pistol.  It was introduced in 1899 by Fabrique Nationale, and is also known as the 7.65×17mmSR Browning or 7.65 mm Browning Short. The Smith & Wesson Model 457 is a compact semi-automatic pistol from Smith & Wesson's metal frame series of handguns.  The 457 is chambered for the .45 ACP cartridge.  The 457 is a traditional double-action pistol, meaning that the first shot is fired in double-action mode and the following shots are fired in single-action mode.  The 457 has a 3.75-inch barrel and 7-round magazine capacity.  It is available in all black as the Model 457, in stainless steel as the Model 457S, or in two tone with aluminum frame with a matte blue carbon steel slide as the Model 457 TDA. The .380 ACP (9x17mm) (Automatic Colt Pistol) is a rimless, straight-walled pistol cartridge developed by firearms designer John Moses Browning.  The cartridge headspaces on the mouth of the case.  It was introduced in 1908 by Colt, for use in its new Colt Model 1908 pocket hammerless semi-automatic, and has been a popular self-defense cartridge ever since, seeing wide use in numerous handguns (typically smaller weapons).  Other names for .380 ACP include .380 Auto, 9mm Browning, 9mm Corto, 9mm Kurz, 9mm Short, 9×17mm and 9 mm Browning Court (which is the C.I.P. designation).  It is not to be confused with .38 ACP, 9mm Ultra, 9×18mm Makarov, 9×19mm Parabellum nor the rimmed .380 Long Revolver CF & .380 Rook Rifle cartridges, introduced around 1870. Vis (Polish designation "pistolet wz.  35 Vis", German designation "9 mm Pistole 35(p)", or simply the Radom in English sources) is a 9×19mm caliber, single-action, semi-automatic pistol.  Inspired by American firearms inventor John Browning's 9mm "Browning GP" pistol design which was completed after Browning's death by designers at Fabrique Nationale in Herstal Belgium, this Polish gun began production at the Fabryka Broni (Arms Factory) in Radom in 1935, and was adopted as the standard handgun of the Polish Army the following year.  The pistol was valued by the Germans, and towards the end of the war issued to the German paratroopers.  As a pistol largely based on the Colt 1911 and using 9 mm rounds, it is highly prized among collectors of firearms. The .45 ACP (Automatic Colt Pistol), or .45 Auto (11.43×23mm) is a handgun cartridge designed by John Browning in 1905, for use in his prototype Colt semi-automatic pistol.  After successful military trials it was adopted, along with the Browning .45 Colt handgun, as the .45 M1911 cartridge.  The handgun was designated M1911 pistol. The Smith & Wesson Model 4506 is a third-generation semi-automatic pistol from Smith & Wesson's 4500 series of handguns.  The 4506 is chambered for the .45 ACP cartridge and, with the purchase of special springs, the stronger .45 Super.  It is constructed almost entirely from stainless steel and is thus extremely resistant to harsh weather conditions.  The 4506 is a traditional double-action/single-action pistol.  The first shot is fired in double-action mode.  Each subsequent shot is fired single-action mode.  It features one-piece Xenoy wrap-around grips with either a curved or straight back strap.  The 4506 was produced from 1988 to 1999. The FN Model 1903 (M1903, FN Mle 1903), or Browning No.2 was a self-loading semi-automatic pistol engineered by John Browning and made by Belgian arms manufacturer Fabrique Nationale (FN).  It was introduced in 1903 and fired the 9×20mmSR Browning Long cartridge.  It should not be confused with the US-made Colt Model 1903 Pocket Hammerless (in .32 ACP), nor with the Colt Model 1903 Pocket Hammer (in .38 ACP).  The FN Model 1903 is based on the same mechanical design as the Colt Model 1903 Pocket Hammerless, which Browning sold to both companies (and others as well), but enlarged to handle the more powerful 9mm Browning Long cartridge.  Due to its reliability, accuracy, light weight, and quick reloading, the M1903 was an issued sidearm for many police forces and militaries.  The pistol was initially introduced by FN as the Browning Modèle de Guerre (Browning War Model) or Browning Grand Modèle (Browning Large Model). The Smith & Wesson 645 and Smith & Wesson 745 are second-generation semi-automatic pistols which predates Smith & Wesson's 4500 series of handguns.  The S&W 645/745 is chambered for the .45 ACP cartridge.  The S&W 645 is constructed almost entirely from stainless steel and is thus extremely resistant to harsh weather conditions, whereas the S&W 745 has a stainless steel frame and a blued carbon steel slide.  The S&W 645 was introduced in 1985 and discontinued in 1988.  The S&W 745 was produced from 1986 to 1990, primarily as a single-action competition gun for IPSC shooting. The Star Model S was a Spanish semi-automatic pistol manufactured by Star Bonifacio Echeverria, S.A. and designed to use the .380 ACP cartridge.  Like many semi-automatic handguns, the basic design of the Star Model S is based on the .45 calibre Colt 1911.  But it is much smaller, lighter, and lacks some of the safety features of the Colt pistol.  It is this lightness and lack of safety features that make this a fast gun. The Colt Model 1903 Pocket Hammer was a short-recoil, semi-automatic pistol, designed by famous American arms designer John Browning.  It was a compact version of the Colt Model 1902 Sporting Model pistol derived from the original Colt M1900.  The Colt M1902 Sporting Model and 1903 Pocket Hammer model have significant differences to the military inspired Colt 1902 Military Model although they fire the same cartridge.  Its design is in no way related to the Colt Model 1903 Pocket Hammerless or the FN Model 1903 pistol.
Answer: .45 ACP