(Latin > French: device for calculating a distance traveled (in a vehicle for hire) and the corresponding fare is charged)

taxi (s) (noun), taxis (pl)
An abbreviation of taximeter-cabriolet, taximeter, and taxicab.
taxicab (s) (noun), taxicabs (pl)
An abbreviation of taximeter cab.
taximeter (s) (noun), taximeters (pl)
An automatic instrument installed in taxicabs showing the fare to be charged for a trip.
taximeter-cabriolet (s) (noun), taximeter-cabriolets (pl)
English adopted the French word taxi which came from taximeter-cabriolet.

The meter part refers to a measuring device. Taxi, from taxe, is "a charge"; so, a taximeter naturally, refers "to measure the charge".

Cabriolet is pure French for a "two-wheeled carriage". The "cab" which anyone hails or arranges for a pick up is simply the first syllable of cabriolet.

The original cabriolet , or cabriole, as it was also called, was built in France in the latter part of the eighteenth century. It was a light two-wheeled transport pulled by one horse, and it had a large hood, usually made of leather, and a leather apron to protect the legs of the one, or two passengers, from the mud that was splattered from the roads.

The term cabriolet is from French cabri, a "kid" or young goat because the vehicle seemed to be jumping around based on the spring system (capering or making frolicsome leaps) similar to the way a very young goat jumps around.

In England, where the carriage was introduced in the early nineteenth century, its name was shortened to cab. It was simply too much trouble for the British to call it a cabriolet.

Etymology: from French, diminutive of cabriole, "caper, leap of a goat"; from cabrioler, caprioler, "to leap like a goat, to caper", from Italian capriolare, from capriuolo, "roebuck", from Latin capriolus, formed from caper, "he goat", and capra, "she-goat".