Yes, the word "cab" is a shortening of cabriolet, a type of light, two-wheeled, horse-drawn carriage that was popular in 19th-century France and London. The word cabriolet itself comes from the French cabrioler, meaning "to leap" or "to caper," referring to the carriage's springy motion as it moved over cobblestone streets. When these carriages were fitted with an automatic meter to record distance and fare (a taximeter), the vehicles became known as taxicabriolets, which was eventually shortened to taxicab and finally just taxi or cab. Interestingly, the "taximeter" part comes from the German Taxameter, rooted in the Latin taxa (tax or charge). So, when you call a "cab" today, you are using a term that literally describes a "leaping carriage with a fare meter," a linguistic relic of the transition from horse-drawn transport to the modern automobile.