To define the word as the art of counting on the fingers is to severely underestimate the skill of those who employed this technique. For it was not just a matter of using the whole finger, as some of us are likely to do when we suffer temporary numerical embarrassment. After all, every finger has a knuckle, two joints and three bones (one joint and two bones for the thumb) and all of them, on both hands, were used to count up to 9,999.
There are descriptions of the method from the Middle East, Asia and other places, and by the Venerable Bede from the north-east of England in the eighth century AD. Paintings exist from more than four thousand years ago showing Egyptians counting in this way, and we know it was common in classical Greece and Rome. Related methods were used in some civilisations to negotiate prices between buyer and seller, with the hands hidden under a cloth, in a serious exchange reminiscent of paper-scissors-stone, or that ancient finger game called morra in Italy.
The word is from Greek daktulos, finger, plus –nomia, related to nomos, law, that we use to mark some specified area of knowledge.