taxamètre + cabriolet

The first half comes from taxamètre, coined in 1890 by German inventor Wilhelm Bruhn, who combined the Medieval Latin taxa (tax, charge) with the Greek metron (measure). His device was a mechanical meter that calculated fares based on distance traveled. It was mounted on horse-drawn cabs in German cities, and the vehicles carrying them became known as Taxameter-Droschken — taximeter cabs.

The second half is cabriolet, from the French word for a light, two-wheeled carriage that bounced on the road. Cabriolet itself comes from cabriole, meaning a goat's leap — from Italian capriola, from Latin caper, goat. The carriage bounced like a goat. English shortened cabriolet to cab by the 1820s, and cab became the standard word for a hired vehicle in London long before the taximeter existed.

The merger happened around 1907, when motorized cabs fitted with Bruhn's taximeters appeared on the streets of London, New York, and Paris simultaneously. The vehicles were called taximeter cabs, then taxi-cabs, then taxicabs, and finally just taxis. Harry N. Allen imported the first fleet of gasoline-powered taxicabs to New York City in October 1907, painting them yellow for visibility. The 600 vehicles he imported were Darracqs, built in France.

The word split in two directions. Americans favored 'cab' and 'taxi' almost equally. The British stuck with 'cab,' preserving the goat-leap half of the word. Neither side remembers the German meter or the French carriage. The full compound taxicab survives mainly in official contexts — taxi licenses, insurance documents, and the occasional period film.