Roman abacus
[1] The Roman abacus 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.
[citation needed] Karl Menninger said: 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.
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.
[citation needed] 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.
[4] These latter two slots are for mixed-base math, a development unique to the Roman hand abacus[5] described in following sections.
This is however even more strongly supported by Gottfried Friedlein[3] in the table at the end of the book which summarizes the use of a very extensive set of alternative formats for different values including that of fractions.
The symbol for the sicilicus is that found on the abacus and resembles a large right single quotation mark spanning the entire line height.
However, he stated specifically in the penultimate sentence of section 32 on page 23, the two beads in the bottom slot each have a value of 1/72.
This results in two opposing interpretations of this slot, that of Friedlein and that of many other experts such as Ifrah,[4] and Menninger[2] who propose the one and two thirds usage.
Even more significant, it is logically impossible for there to be a rational progression of arrangements of the beads in step with unit increasing values of twelfths.
It would not be unremarkable if the makers of these instruments produced output with minor differences, since the vast number of variations in modern calculators provide a compelling example.
Furthermore, the biquinary-like nature of the integer portion allowed for direct transcription from and to the written Roman numerals.
No matter what the true usage was, what cannot be denied by the very format of the abacus is that if not yet proven, these instruments provide very strong arguments in favour of far greater facility with practical mathematics known and practised by the Romans in this authors view.
