cab (n.) Look up cab at Dictionary.com
1826, "light, two- or four-wheeled horse-drawn carriage," shortening of cabriolet, a type of covered horse-drawn carriage (1763), from French cabriolet (18c.), diminutive of cabriole "a leap, a caper," earlier capriole (16c.), from Italian capriola "a caper, frisk, leap," literally "a leap like that of a kid goat," from capriola "a kid, a fawn," from Latin capreolus "wild goat, roebuck," from PIE *kap-ro- "he-goat, buck" (source also of Old Irish gabor, Welsh gafr, Old English hæfr, Old Norse hafr "he-goat"). The carriages were noted for their springy suspensions.

Extended to hansoms and other types of carriages, then extended to similar-looking parts of locomotives (1851). Applied especially to public horse carriages, then to automobiles-for-hire (1899) when these began to replace them.