cab (n.) Look up cab at Dictionary.com
1826, "light, horse-drawn carriage," shortening of cabriolet (1763), from French cabriolet (18c.), diminutive of cabrioler "leap, caper" (16c./17c.), from Italian capriolare "jump in the air," from capriola, properly "the leap of a kid," from Latin capreolus "wild goat, roebuck," from PIE *kap-ro- "he-goat, buck" (cognates: Old Irish gabor, Welsh gafr, Old English hæfr, Old Norse hafr "he-goat"). The carriages had 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.