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Roman abacus


The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of the previous Babylonian abacus. It was the first portable calculating device for engineers, merchants and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals.

As Karl Menninger says on page 315 of his book, "For more extensive and complicated calculations, such as those involved in Roman land surveys, there was, in addition to the hand abacus, a true reckoning board with unattached counters or pebbles. The Etruscan cameo and the Greek predecessors, such as the Salamis Tablet and the Darius Vase, give us a good idea of what it must have been like, although no actual specimens of the true Roman counting board are known to be extant. But language, the most reliable and conservative guardian of a past culture, has come to our rescue once more. Above all, it has preserved the fact of the unattached counters so faithfully that we can discern this more clearly than if we possessed an actual counting board. What the Greeks called psephoi, the Romans called calculi. The Latin word calx means 'pebble' or 'gravel stone'; calculi are thus little stones (used as counters)."

Both the Roman abacus and the Chinese suanpan have been used since ancient times. With one bead above and four below the bar, the systematic configuration of the Roman abacus is coincident to the modern Japanese soroban, although the soroban is historically derived from the suanpan.

The Late Roman hand abacus shown here as a reconstruction contains seven longer and seven shorter grooves used for whole number counting, the former having up to four beads in each, and the latter having just one. The rightmost two grooves were for fractional counting. The abacus was made of a metal plate where the beads ran in slots. The size was such that it could fit in a modern shirt pocket.

The lower groove marked I indicates units, X tens, and so on up to millions. The beads in the upper shorter grooves denote fives—five units, five tens, etc., essentially in a bi-quinary coded decimal place value system.


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