Reckoning

Anyone receiving pay or buying and selling was wise to learn arithmetic and check weights and measures rather than trust the seller. While in some places coins with a known silver content were used, there were all kinds of tricks to turn 20 drachmas into 21, so it was wise to check the weight for any important transaction. Studying ancient arithmetic can be a good way for people who are not interested in rhetoric or religion to understand how very different familiar aspects of life were in antiquity.

stones for a counting board like the Salamis tablet: acrophonic numeral, finger computation, and finger reckoning can be good keywords. There is a picture of a Persian official using a counting board on the Darius Vase from fourth-century Apulia (Museo Archaeologico Nazionale, Naples, H3253).

?weights and a balance? McCown, Nippur I, p. 102 fn. 105 “Two bronze balance pans (e.g. Pl. 153:3) were found near the hands of the skeleton in TA III burial 1B 209 (see p. 133). Above the knees were a bronze “nail” (Pl. 153:5) and a bronze sleeve (Pl. 153:4) containing traces of wood and a bronze ring (PI. 153:6). All of these items probably constituted elements of a balance. Perhaps the “nail” pierced the center of the balance arm with its hooked end pivoting on the ring. The ring could have been suspended from a horizontal peg set in the upright member of the balance, around which was the sleeve. The sleeve thus would have served no functional purpose. The partially preserved flare at its broken end may be due to malformation. This suggested reconstruction is based in part on a large balance pictured in an Assyrian relief (Bruno Meissner, Babylonien und Assyrien I [Heidelberg, 1920] Fig. 209, right). Our balance, of course, would have been portable.”

• W.F. Richardson, Numbering and Measuring in the Classical World Second Edition (Bristol: Bristol Phoenix Press, 2004)
• Turner, J. Hilton (1951) “Roman Elementary Mathematics: The Operations,” The Classical Journal 47.2 pp. 63‑74, 106‑108 http://penelope.uchicago.edu/Thayer/E/Journals/CJ/47/2/Roman_Elementary_Mathematics*.html

In a world without universal literacy and printed labels, there must have been ways to negotiate prices across a language barrier. In Roman times there was a system of hand signs which could be used for computing: it shows up in Bede, and another one in one of the Arab archery manuals. Just how old it is is hard to say, but see the article on “Roman Elementary Mathematics” by J. Hilton Turner.

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