Origin of the inch
The cubit length did not stop reducing over time. From 49.5 cm in Babylonian civilization it shrank to 44.4 cm in Ancient Greek civilization. It was then adopted by Romans. In Roman civilization, the cubit was approximately 44.16 cm. It was divided in 6 palms of 4 fingers (a finger being 1.84 cm).
At the beginning of our era, a new division of the foot was established. It was based on the roman monetary divisions: the foot was divided in 12 parts (oncia). Confusion set in because the foot was indifferently divided in 16 digitus or 12 digitus.
The new word inch (which refers to 1/12 of the foot) didn't appear until late Middle Age in Europe. From this moment, it changed. Indeed, the palm (which had been divided in 4 fingers for more than 2000 years) was from then divided in 3 inches.