Origin of the inch

The story actually began in 2500 BC with the Babylonian Gudea's Cubit of 49.5 cm. It was divided in 30 fingers or 6 palms of 5 fingers (a finger being 1.65 cm)..
Ensuite, chez les Hébreux la  coudée de 6 palmes passe à 48 cm, chaque palme étant composée cette fois de seulement 4 doigts de 2 cm.
In parallel, Egyptians used another cubit. It was divided in 6 palms and measured 44.8cm. Each palm was composed of four fingers as for the Hebrews. But fingers were reduced to 1.87 cm. Note that Newton gave to the angled a length of 45 cm and 30 cm for the Egyptian foot.
Much later, Greeks in the time of Solon (594 BC) used the attic cubit. It was 44.4 cm and was divided in 6 palms of 4 fingers (a finger being 1.85 cm).
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.