The Gerbert abacus and the abacus with lines

The pictures hereafter are reproductions of an IREM publication (Institut de Recherche sur l'Enseignement des Mathematiques).

The abacus of Gerbert d'Aurillac

The picture shows the design of the abacus. The figures drawn on the jetons (apices) are reproduced from a manuscript of the 11th century. From right to left, the headings of the first three columns I, X, C are for the units, the tens and the hundreds. In the three following columns the lines above the I, X and C are for the thousands, the ten of thousands and the hundreds of thousands.

The table on the right of the abacus is the translation with the today digits.

Note the missing null digit on the Gerbert abacus.

The middle age abacus

This abacus has been used by merchants from the 13th century until the french revolution (1789 ). The horizontal lines are for the successive decimal powers. These powers are marked with jetons at each intersection between the horizontal lines and the vertical one. From the bottom to the top, the drawings on the jetons means : units tenth, hundreds, thousands and tenth of thousands.

A figure is materialized by as many jetons as necessary on the lines representing the powers of ten. In order to reduce the number of jetons, 5 jetons on a line are replaced by one jeton in between this line and the line immediatly above.

The picture is drawn out of a Jean Trenchant book published in 1558 (republihsed in 1561, 1588, 1602, 1610, 1617, 1618, 1632, 1643 and 1647). The number 763 is written with the jetons on the right side of the vertical line. The number 35098 is on the left side of the vertical line.