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## abacus

An abacus (ἄβαξ, ἀβάκιον), a counting board, was the usual aid to reckoning in antiquity. The Greeks and Romans alike used a board with vertical columns, on which (working from right to left) units, tens, and hundreds; or (where money was in question) units of currency, for instance the Attic signs for ⅛ obol, ¼ obol, ½ obol, 1 obol, drachma and so on, could be inscribed. The Salamis abacus is an example of a type of flat, large counting board, made of stone, of which more than twenty have survived from antiquity (Figure 1).There are also significantly fewer examples of small, bronze abacus. (Figure 2).The extant flat, large counting boards have been found in the Greek-speaking part of the Mediterranean, whereas the small bronze abaci appear to originate in the Roman world, and are engraved with Roman numerals. There are different possible reconstructions of how calculations were carried out on the ancient Greek or Roman abacus, which would seem to indicate that different procedures were also in use in antiquity In general, with addition, the totals of the columns were carried to the left, as in ordinary 21st-century addition.

## arithmetical tables

Greek arithmetical tables are systematic series of calculations written on papyrus and other light materials such as potsherds, wooden and wax tablets, and paper. About 150 items stemming from Egypt and covering a wide chronological range (4th century bce–13th century ce) have been published. Calculations are normally written in columns and separated by vertical and horizontal lines. They consist of addition, multiplication, squares and division, which are expressed in form of fractions (4: 2 = 2 is expressed as ½ of 4 = 2), and their results are given as the addition of juxtaposed unit fractions, a feature originating in Egyptian mathematics. Every kind of operation presents different patterns and features which can be of help in determining chronology and context. It is particularly challenging to establish the context of the tables, as they can belong to reference books used by professional accountants or be school texts. Material, handwriting, spelling, and the presence of other inscriptions on the same item, such as drawings, personal names, or even school exercises, can shed light on this point.